In aerodynamically intense stock-car races like the Daytona 500, the drivers form into multi-car draft lines to gain extra speed. A driver who does not enter a draft line (slipstream) will lose. Once in a line, a driver must attract a drafting partner in order to break out and try to get further ahead. Thus the effort to win leads to ever-shifting patterns of cooperation and competition among rivals. This provides a curious laboratory for several social science theories: (1) complexity theory, since the racers self-organize into structures that oscillate between order and chaos; (2) social network analysis, since draft lines are line networks whose organization depends on a driver's social capital as well as his human capital; and (3) game theory, since racers face a "prisoner's dilemma" in seeking drafting partners who will not defect and leave them stranded. Perhaps draft lines and related "bump and run" tactics amount to a little-recognized dynamic of everyday life, including in structures evolving on the Internet.
Basic Dynamics of Drafting
Complex Dynamics of Long Draft Lines
Social Science at 190 MPH
Concluding Comment: Drafting in Everyday Life
No motor sport is more American, and to many eyes more simple-minded, than stock-car racing on oval tracks. As a sportscaster wryly remarked last February, before reporting the results of the Daytona 500, the season-opening race of NASCAR's premier Winston Cup series, it's just a matter of "go straight, turn left, go straight, turn left," round and round again. Compared to this, Formula One racing in Europe, on Grand Prix courses several miles long that twist left and right, seems a far more sophisticated motor sport and the sophisticates are sure to tell you so.
Yet, NASCAR (the National Association of Stock Car Auto Racing) is suddenly having its best years. Fan enthusiasm, race-track attendance, television viewership, memorabilia sales, corporate sponsorships and commercial spin-offs (like Jeff Gordon in Pepsi Cola ads) have risen hugely. NASCAR is the fastest growing professional sports league in America.
What gives? A simple explanation is that a stock-car race is a thrilling spectacle, and NASCAR has learned to market it to ever broader audiences. The fan base is no longer dominated by Southern "good ol' boys" as in the 1940s and 1950s. Today, many fans are urbane, well-educated, middle-class professionals. They, like the new tracks, are spread around the country. And they take their families to the races; wives and kids are fans now too. More than that, the races themselves are more competitive and better run than ever before. Television coverage is also superior the announcers for stock-car races are better than for any other motor sport, since the best ones, like Benny Parsons and Ned Jarrett, are former drivers with a keen knack for observation and elucidation, including about crucial details a casual viewer would not spot.
But those truths do not fully explain, Why now? Scott Huler's A Little Bit Sideways: One Week Inside a NASCAR Winston Cup Race Team points to a deeper, cultural reason, as long-time race promoter and track owner H. A. "Humpy" Wheeler, himself struck by NASCAR's awesome growth, speculates that stock-car racing is arousing nation-wide enthusiasm now for the same reason that baseball did likewise decades ago: nostalgia for a passing era. Baseball a slow, serene game played with a wooden bat, a cloth ball, and cowhide mitts on a broad, grassy field surged in popularity just when the industrial revolution was taking hold, leaving masses of urban workers and shopkeepers yearning for the pastoral peace and quiet of the fabled agricultural age. They could relive this for a day by attending a baseball game. By extension, no wonder stock-car racing a fast, furious sport contended on a paved roadway with snarling, smelly machines operated by hand is surging in popularity at the very time the computerized information revolution is transforming our society from top to bottom. Stock-car racing expresses the industrial age more than does any big sport in America. Even NASCAR's efforts to present itself as a sport built around god-fearing, family-oriented drivers who bring their own wives and kids to the track plays into this. Go to a Winston Cup race and get away from all the new revolutions wracking America.
To this insightful cultural speculation, I would add a strategic one that is not so nostalgic and backward-looking, and that so far has not received much notice. Stock-car racing, at its highest levels, reflects an important, desirable American trait: how to compete by doing a good job at cooperating. This is a timeless American trait, but also one that is important to nurture as the information age deepens. Indeed, the Internet itself, from its technical packet-switching bases, through its vast potential as not only America's but also the world's common cyberspace, is such a marvel partly because of the ways in which it advances, and accelerates, people's capacities for both cooperation and competition whether they are acting as agents of global civil society (e.g., as in the International Campaign to Ban Landmines), or as businesses bent on partnering in order to race past marketplace rivals (e.g., as in the AOL-Time-Warner merger). Could it be that much of life is like a Daytona-type race?
Most sports that people follow pit either individuals or teams against each other, all season long. Automobile racing is not a team sport, and stock-car races are indeed mostly about man-to-man competition. The shorter a racetrack, the more this is the case. Thus, races on ovals less than a mile around a "short track" where the drivers scatter and dice at speeds of 120-150 MPH on the straights and half that on low-banked turns often do reduce to rousing spectacles of running in circles, as that sportscaster claimed. But he unknowingly oversimplified the Daytona 500. It occurred on an oval two and a half miles around a "superspeedway" with long straights and high-banked turns, where the racers run full-throttle at 190 MPH around the entire track. What matters on NASCAR's two biggest superspeedways Daytona in Florida, and Talladega in Alabama includes what matters on short tracks: powerful engines, agile handling, grippy tires, expert driving, and fast pit stops. But another factor comes into play that gives Daytona-type racing an unusual quality: high-speed drafting in long, multi-car draft lines.
This makes for a complexity rarely seen in other sports. Drafting can matter in motorcycle and bicycle racing too, but not to the same degree, or in the same way. It matters little in Formula One racing, or in CART and IRL racing in the United States, because their open-wheel, winged cars work best in open air, away from the turbulence created by other cars. Their drivers only use drafting for rapid passing maneuvers, a car at a time. In contrast, NASCAR's Winston Cup races at Daytona and Talladega generate draft lines that range from three to ten cars long. So do races in NASCAR's Busch series, which features smaller, less powerful cars and junior drivers; in the still smaller, invitational IROC series that operates separate from NASCAR; and potentially in NASCAR's Craftsman truck series, which recently received approval to race at Daytona in 2000. These are the very races that attract the keenest, knowingest fans of these series for Winston Cup fans, the season-opening Daytona 500 is the counterpart to the NFL's season-ending Superbowl.
Skill at working a multi-car draft line requires unusual talent. At Daytona and Talladega, every racer is of course plotting to beat every other. But at these tracks the way to out-compete is to out-cooperate, selectively and coincidentally, by entering into drafting partnerships. A driver who does not draft will lose. Stock-car racers organize into draft lines to gain extra speed because of aerodynamics, their closed cars move a bit faster in a draft line than they do running alone and the longer the line, the greater the gain in speed. Then, if a racer in a line wants to break out and get ahead, either by displacing another racer up the line or by creating a new line, he needs at least one partner. If he swings out alone, he is bound to lose momentum, and fall back numerous spots before he can get back in a line. Such cooperation between rivals may last several laps or only a few seconds at 190 MPH, to pass one rival or maybe two, before defection occurs and a racer looks for another rival to partner with. But this episodic, contingent, opportunistic cooperation, which may be arranged through radio communications to drivers' spotters and crew chiefs, becomes a decisive factor in a racer's ability to out-compete other racers and win.
This unusual interplay between competition and cooperation makes draft lines interesting for philosophic as well as sporting reasons. At races on short and medium-size tracks, where drafting cannot develop, the Darwinian struggle for ascendance is continually Hobbesian the survival of the fittest means a war of all against all, and encounters are often nasty, brutish, and short. But at Daytona and Talladega, this struggle also turns Rousseauian by forming drafting partnerships, the competitors cobble together patterns of cooperation that benefit them all, in the absence of a central hierarchy.
There is something alluringly American about this crafty kind of teamwork, and it transcends whether we are in an industrial or an information age. The dynamics of long draft lines even speak to cutting-edge ideas in the social sciences about complexity theory, social network analysis, and game theory. This "dumb" motor sport provides a laboratory for seeing how out-competing can depend on out-cooperating.
Basic Dynamics of Drafting
As a Winston Cup racecar rushes through the air, the design of its body with all wheels enclosed, a cab around the driver, and a "spoiler" across the rear deck creates an air pressure bubble in front and a minor vacuum behind it. And this poses a drag on how many extra miles per hour it can speed at full throttle. Aerodynamic detailing can reduce this drag, but not by much, because NASCAR's rules require that the custom-made bodies match approved templates, notably to replicate the looks of a Chevrolet Monte Carlo, a Pontiac Grand Prix, or a Ford Taurus (and also, next season, a Chrysler Intrepid, as Chrysler returns to stock-car racing).
Drafting, which looks like tailgating or slipstreaming, occurs when a second car tucks closely behind the first, filling part of the vacuum. The car in front loses some of the drag at its rear. The second car still has a vacuum at its rear, but now has less air resistance in front. As a result, both cars quicken a bit the two combined speed a few miles per hour faster than either can alone. This push-pull effect is stronger the closer the second car gets to the first. Indeed, the second may even touch and push the first in a tricky maneuver called "bump drafting." But slipstreaming so closely hinders airflow into the trailing car's radiator and can cause its engine to overheat. Most drafting calls for a half to a full car length between the two cars. (In contrast, open-wheel, motorcycle, and bicycle racers do not gain extra speed by drafting, because a trailing racer does not generate the forward aero push that stock cars do.)
This has two marvelous effects for Daytona-type racing. First, there is an unusual incentive to cooperate. So long as two racers stay together in a partnership, they can catch up to or pull away from equivalent cars that are not drafting, and keep pace with rivals who are already in line. But there is also an incentive to defect at some point eventually the time comes for this opportunistic partnership to dissolve, as the second car aims to get around the first. And when this occurs the advantage usually goes to the second, because of the "slingshot" effect. If he can drop back a little, by a car length or two, and then gain speed back into the draft zone, perhaps as the cars descend off a high-banked turn onto a straight, he may use his tiny extra momentum of a few miles per hour to swing out and pass the car in front, which loses momentum as soon as the vacuum reappears behind it.
Famous races have been won this way. By now, it is a simple calculation. But it was "discovered" in 1960, at the second-ever Daytona 500. Junior Johnson reluctantly agreed to drive a Chevrolet, knowing it lacked speed and power compared to Plymouth entries. But he found that as long as he left the pits behind a Plymouth and drafted Plymouths on the track, he could stay with the front-runners. He won the race after the lead Plymouth spun out temporarily when it lost its rear window to the suction of the backdraft. In another famous case, near the end of the Firecracker 400 at Daytona in 1974, David Pearson knew for sure he had the more powerful engine as he led a two-car draft, ahead of Richard ("The King") Petty. But Pearson worried he would still fall prey to a slingshot. So entering the last lap he suddenly slowed and let Petty shoot past him by nearly two hundred yards, then used his car's extra power to regain speed back into the draft and slingshot by on the final turn, leaving Petty and everyone else awestruck and dumbfounded.
However, a slingshot is not always a simple calculation to bring off. A skillful leader who sees that his drafter is starting to "pedal back" to gain room may defend his position by slowing proportionally so as to maintain a small gap between the two. To fans in the stands or on television, the two racecars appear to be in a flat-out, pell-mell charge to the finish line. The unmuffled engines sound at full roar. But both drivers, by barely moving their gas pedals and delicately pressing their brake pedals, are engaged in an almost invisible dance of slowing and accelerating. At the same time, the leader may block the drafter by "mirror-driving" steering to the inside or outside of the race track to keep his car in front of the path he thinks the drafter may use to slip around. If the lead driver does all this just right, and if the second driver sees that this dance risks letting third- and fourth-place cars catch up and pass, then the leader may well go on to victory. This occurred on the hair-raising last lap of the 1999 Daytona 500; Jeff Gordon, the sport's young Golden Boy, won by anticipating and fending off a nose-to-tail challenge from Dale Earnhardt, an aging master at high-speed drafting maneuvers.
If a classic slingshot cannot be executed, a skillful driver still has two aggressive techniques to exploit the draft. Both work by unsettling the traction of the rear wheels of the lead car. One technique, which Earnhardt tried unsuccessfully against Gordon, is to "fan the tail." The second driver moves to within inches, or less, of the lead car and fans the nose of his car back and forth along a tail corner of the lead car in order to "take air off the spoiler." Disrupting the air flow causes the car to lose "downforce," the downward grip generated by the spoiler and other aerodynamic aspects of the car's body at high speeds. Its rear wheels start to spin; the car starts to slide sideways; the driver has to fight for control, including by easing up on the accelerator and the rear car slips around. But the rear driver must be careful; as he gets close enough to fan, the air flow lessens across the hood of his car, and he risks losing downforce on his steering wheels. However, at Daytona and Talladega, with their long straights and high-banked turns, this latter risk is minimal. It arises mainly on "speedways" that are one to two miles around and have low-banked turns there, a trailing racer can quickly lose front downforce, and traction, if he plays this game as his car changes speed when entering or leaving a turn.
In the second technique "bump and run" the drafter physically nudges the rear of the lead car, causing it to lose traction. (This is a common tactic on short tracks too, without drafting.) But it should be done gently, because a sharp blow will spin the lead car into a crash that could destroy it, multiple pursuing cars, and even the drafter's car. Beyond that, Winston Cup drivers function like a clan. They know they are the best at what they do, and may be racing against each other for many seasons (at 30 plus races a year). Mutual respect and familial solidarity are important to their sporting culture. Acts that invite retribution and develop into personal feuds are generally avoided. The drivers also know that image is crucial to their corporate sponsors, team owners, loyal fans, and NASCAR overseers. Thus, blunt ramming "driving into" a rival is unwelcome among today's Winston Cup elite (and sometimes prompts NASCAR officials to penalize a driver for recklessness), though it occurs often in lower levels of stock-car racing and was not unusual in early eras of Winston Cup racing. Nonetheless, a "loving tap," sufficient to unsettle a car's grip but not cause it to crash, is an acceptable tactic, even an honored mark of skill, if done judiciously.
But "bump and run" is a gray area, where tactical tit for tat, perhaps motivated by momentary anger and revenge, may come into play despite the overall ethic of mutual respect. In a combination of the Old Testament rule of "an eye for an eye" and the New Testament's Golden Rule of "Do unto others ...," many veteran Winston Cup drivers aver that, "I treat another driver like he treats me. If he races me hard and clean, I do the same to him. If he doesn't, then payback is okay." Since the tracks are banked, the advantage usually goes to the driver on the inside the outside car is more vulnerable. Thus, in some oft-noted examples (not all involved drafting), Jeff Burton refrained from bumping Jeff Gordon as Gordon passed him on the outside, fender-to-fender, to win on the final lap of a race at Darlington in 1997; and Gordon responded by racing equally clean when Burton seized the lead to win in a similar side-by-side situation a year later at Richmond. In contrast, Gordon did execute a flagrant bump to pass race leader Rusty Wallace at Bristol in 1997, which reportedly explains why Wallace nudged Gordon into a crash (that Wallace may not have intended) a year later at another Richmond race, as Gordon passed on the outside and started to swing in front.
In a 1999 interview on ESPN's excellent RPM2Night program, Gordon noted that deciding whether to bump depends on the heat of a race and the rival at hand. He might have bumped and beaten Burton at Richmond if that had been Gordon's first year in the Winston Cup series and his first opportunity to win. He also noted, "Every driver out there, you race him a different way." The implication: a driver not only keeps a mental log of a rival's style, strengths and weaknesses, but also of where he stands in deserving tit-for-tat treatment, based on encounters during the current race and over time.
Blocking by mirror-driving, especially if done by a less established or a "rookie" driver, or even by a veteran in a slow car, can rile a trailing driver to the point where he feels he has a justification to bump and run. Post-race interviews about crashes may reveal that a trailing driver refrained from backing off and just went ahead and banged a rival in the tail or side, simply because he felt the rival had cut him off too many times earlier in the race, or stubbornly refused to get out of the way of a faster car at the time.The last lap is the grayest area of all. Many drivers espouse an "anything goes" attitude a cavalier bump-and-run to gain position is more permissible then than at any other time. Thus Gordon applied a sharp nudge to "loosen up" Dale Jarrett, enabling Gordon to seize third and make Jarrett finish a fourth in the Jiffy Lube 300 at the New Hampshire International Speedway in July. And Earnhardt, just after losing the lead to Terry Labonte, bluntly bumped his car into a crash that meant Earnhardt finished first and Labonte eighth in the Goodys Headache Powder 500 at Bristol Motor Speedway in August. These instances, the best from the 1999 season, left Jarrett and Labonte very angry, Gordon and especially Earnhardt booed by fans, the racing media with storied controversy for a week or two, and much wonderment and questioning of NASCAR officials about ethics and egos on the race track.
Of the Winston Cup elite who prefer to race "hard and clean," the cleanest may be Mark Martin, who gets criticized by die-hard fans for not exploiting opportunities. The hardest may be Earnhardt, nicknamed "The Intimidator." He has made his bump-and-run technique such an art form that no veteran takes serious umbrage for long if it falls into the "loving tap" category. But even he sometimes refrains from nudging a leader in order to win. He used soft taps on the last lap to win the first two races of this year's IROC season, first to get around Martin at Daytona, then Wallace at Talladega. Yet, while fanning Gordon's tail, he refrained from bumping him aside in the final yards of the Daytona 500 in marked contrast to what he did to Labonte at Bristol.
These dynamics come together in this description from A Little Bit Sideways of the situation late in a race at the Charlotte Motor Speedway a mile-and-a-half speedway with low-banked turns where downforce matters much more than drafting in October 1997, as Earnhardt and Martin battle for the lead:"When Earnhardt leads, Martin hunches behind his tail like he's the back end of a horse costume, following Earnhardt's line perfectly and waiting to spring, waiting for Earnhardt to drift high in one of the turns or loosen up when Martin takes the air off his spoiler, reducing the down force on his rear tires. Then Martin slingshots down underneath him and takes the lead, in racing's most common move, and its least preventable. Earnhardt mirror-drives him, putting him off, but Martin can find his spot. When Earnhardt is behind Martin, on the other hand, he drives like the Intimidator his name makes him out to be, poking his nose underneath Martin whenever he's got the smallest chance, looking high if Martin's hooked too cleanly on the lower line. He's pushy, poking at Martin constantly, trying to force the chance rather than waiting for it."
The main motivation for two cars to form a draft line is to win a race. But other motivations figure as well. Not only first place but also finishing positions from second through last yield prize moneys from that race, and points (175 for 1st, 34 for 43rd) that accumulate toward the annual championship. (This year's Winston Cup championship was won by Jarrett, and most other drivers mentioned in this article fell within the top ten.) There may be other moneys for achievements during a race e.g., leading at half-way. In addition, for leading any single lap, a driver acquires an extra five points, and another five if he leads the most laps. Indeed, if the drivers in first and second are well ahead of everyone else and accommodating toward each other, the leader may even let the second pass so he can get five points for himself, with an understanding that they will trade back a lap or two later. This is arranged through radio calls to each driver's "spotter" the spotters, who serve mainly to warn of wrecks and report on nearby cars but can also act as diplomatic envoys, are situated together atop the grandstands. And it may be easy to arrange if the two drive for the same team several owners have multi-car teams on the Winston Cup circuit. But if not, it may involve a threat that the driver in second will nudge the leader aside if he does not accept the deal. Yet another motive also figures: The closer a racer gets to the front, the less likely his car will be "collected" by a wreck. A multi-car wreck is a serious worry when the cars are drafting in packs, as occurs at Daytona and Talladega.
Finally, the drivers and owners know that their racecars are "200 mile an hour billboards." The more positions a car gains, the more it will be eyeballed by fans in the stands and by viewers of the television station broadcasting the race, to the delight of a car's corporate sponsors. It costs millions of dollars to establish a Winston Cup team, and more millions a year to field it. A major sponsor pays millions to get hold of a car's paint scheme and cover the hood and sides with its name and logo. Associate sponsors pay hundreds of thousands for prominent spots on the sides and tail. In other words, NASCAR teams are in the entertainment and advertising as well as the racing business. "Humpy" Wheeler, owner of Charlotte (now Lowe's) Motor Speedway, claims, "The NASCAR stock car is the only race car that's ever been designed with entertainment in mind: the spectator, the TV audience."
(On a speedway one to two miles around, a racer may have one more incentive to gain first place. Speeds on these tracks rarely get high enough for drafting to matter. But the air gets so turbulent from the cars' rushing about that a driver may worry about the disruption of downforce on the nose of his car. The best way to run in "clean air," and thus maximize downforce, is to gain first place. Then, he may be able to run a few MPH faster and open a gaping lead. This does not occur on short tracks, where speeds are low and there is no room to run in the open for long, or on superspeedways, where cars' performances are so evened out that nobody can break away by himself for long.)
These are the basic dynamics of two-car draft lines. Physics and strategy rule, but culture and psychology make a difference. And this is the case with long draft lines too.
Complex Dynamics of Long Draft Lines
Long draft lines often five to ten cars long take shape at Daytona and Talladega mainly because they are high-speed, high-banked, full-throttle raceways. But that is not the only reason. NASCAR's rules make drafting more likely than ever.
One is the innovation known as "restrictor plate" racing. Winston Cup racecars are not truly stock cars. They are custom built in detail. But to maintain the perception that they are the traditional stock cars of yore, and to keep the playing field fairly level for all contenders, NASCAR mandates that the cars must have V-8 engine blocks made of iron (no aluminum). The engines cannot have overhead camshafts or more than two valves per cylinder. They must have four-barrel carburetors, with no superchargers. Today, the engine displacement is limited to 358 cubic inches; the compression ratio, to 12:1; and fuel octane, to 110. Rear-wheel drive and solid rear axles are required. Power steering is permitted, but not an automatic transmission. On-board computer systems, such as for traction control, cannot be used during a race. Other rules govern weight, size, shape, and materials. The rule book is very thick.
Thus. according to the Stock Car Race Fan's Reference Guide, Winston Cup racecars lie "on the cutting edge of yesterday's technology." Still, they are very powerful their engines generate around 750 horsepower at high RPMs. This could rush them around Daytona and Talladega well in excess of 200 MPH. But when that began to occur in the late 1980s, so did horrendous wrecks; in one accident, parts of a crashing car hurtled into a grandstand, injuring fans. So NASCAR figured the cars should be slowed by requiring a "restrictor plate," a metal plate with small holes that is mounted below the carburetor in order to restrict the flow of air and fuel. This plate, which NASCAR provides, drops a Cup car's horsepower to about 450, thereby reducing top speeds by at least 30 MPH.
As a side effect, the restrictor plates turned out to make it difficult for any team to tune its motors better (or much better) than any other team. The plates leveled as well as weakened the horsepower of all the cars. So now, a single car or set of cars can rarely break away from the pack in a restrictor-plate race for a lap or so maybe, but not for long before a draft line catches up. The cars run in packs more than ever, and the only way to get ahead of a pack is to enter a draft line. (Ironically, the restrictor plates may help keep cars from hurtling into the stands, but the increased tendency to run in packs makes multi-car wrecks more likely. To the ugly delight of some fans but the dismay of drivers who dislike restrictor-plate racing and many do dislike it "the big wreck" is a frequent feature at Daytona and Talladega.)
Other changes in the rules that govern stock-car racing NASCAR alters the rules constantly have compounded the importance of drafting. Prior to 1999, the rules stipulated that the front nose (really the valence, or air dam, beneath the nose) clear the roadway by five inches, and that the rear spoiler be five inches high. This "five and five" rule was changed to a "two and seven" rule late in the 1998 season; the minimum front clearance was lowered to two inches, and the spoiler height was raised to seven. NASCAR gave several reasons. One was to improve downforce, to assure that the faster a car went the more its aerodynamics, from nose to tail, created pressures that weighed the car down on the track, making its tires grip better. Another reason, which led to some tinkering with the exact specifications of the spoiler height for each make of car, was to even out some aerodynamic differences among the Ford, Chevrolet and Pontiac body shapes approved by NASCAR. But a major effect of raising the spoiler height, intended or not, was to deepen the rearward drag at speed, and thus to heighten the importance of drafting.
Winston Cup races allow 43 cars to participate. They start by lining up in rows, two-cars wide, according to qualifying speeds at time trials a day or two earlier, with the fastest in front. The picturesque starting grid then looks like two parallel lines, each 21 cars long, with a lone 43rd car at the back. In restarts, say after a yellow-flag caution slows the cars and halts passing because of an accident or debris, they usually realign in two parallel lines, according to their positions at that point (and according to NASCAR rules that put lapped cars on the inside line). At Daytona and Talladega, both starts and restarts occur with the cars rolling at 80 MPH. After that, it may take two or three laps to attain top speeds of around 190 MPH. The cars are nearly there within a lap, but the tiny final increments arise as their tires heat and expand from racing.
Immediately after the start or a restart of a race at Daytona or Talladega, then, two long, parallel draft lines automatically emerge, one following the inside "groove" of the oval, the other an outside groove. In the early laps, cars on the inside usually move a little faster, because that is where the racers prefer to run and thus it tends to be stickier from tire wear in racing parlance, it is a groove. Later, as more tire rubber spreads on the track, the outside groove may work as well, even better for some cars. A track rarely develops a third groove, though cars contesting for position often run three and four "wide" at the same time.
Once the racers sort themselves out after ten to twenty laps it is common to see a single draft line of four to seven cars running in front, pursued a hundred or so yards back by a second line of cars, all another hundred or so yards ahead of a large pack of cars that may still be running in parallel lines but are doing more dicing than drafting with each other. But sometimes two parallel lines endure up front for many laps. Whatever the configuration, multi-car lines are a more common sight than two-car lines all around the raceway. Cars that run alone, often stuck dangerously between two draft lines, will appear to drift irrevocably backward.
Even though restrictor plates even out the horsepower of the cars, some still have slightly more powerful engines. They also handle better, and are driven better. These cars get worked toward the front. Presumably, they started up front, because they did best in the qualifying time trials. But this is never entirely the case, partly because the engines and the "set-ups" that a team uses at qualifying time are not the same as at race time. The qualifying trials require that a car go fast for only a lap or two, alone on the track. So light engine oils, soft springs, and low tire pressures are used; cooling ducts to the radiator are taped almost shut to reduce air currents; and the engine is allowed to run at very high RPMs none of which can be sustained in a long race, and all of which is changed by race day. Many teams install different motors for qualifying and racing.
Thus, the early laps produce a shuffling as differences between qualifying and racing abilities take hold. Crucial is whether a car can be driven "wide open" around the entire track the driver should not have to ease up on the gas pedal in the turns at Daytona or Talladega. This is mainly a function of a car's "set up" the choices a team makes about how to set the engine, drive train, suspension, brakes, tire pressures and aerodynamics for the weather and track conditions that day. At speed, this reduces to concerns about whether the car drives too "tight" or too "loose" tight meaning it is hard to turn, it understeers, and loose meaning it turns too much, it oversteers. Either condition may compel the driver to slow in the turns, and eventually to make a pit stop for adjustments (a fast pit crew can change four tires or alter pressures in existing tires, adjust the springs and suspension, and add fuel in 16 to 18 seconds). Adjustments are often made throughout a race. But once a car is performing at peak the ideal is a "dominant" car that is "dialed in" and "hooked up" the decisive factor is no longer the car itself, but the driver's drafting opportunities and skills.
As noted earlier, a two-car draft line speeds a bit faster than a single car. Long lines gain yet a bit more speed the more cars in a line, the faster it moves though the total difference is tiny, no more than a few miles per hour. Moreover, as the cars sort into lines, the rearward "draw" of a line can be so strong that a trailing line, or a lone car, though more than a hundred yards back, will be "sucked up." This may take many laps, boring or testing the patience of unknowing viewers, but it will happen. Thus a driver who looks hopelessly behind may get patiently back in contention if he keeps his car aligned with a distant draft. The ease of getting sucked up grows if a line breaks asunder and the cars start racing two, three and even four wide. Side-by-side racing slows the cars, as they generate a large "wall of air" in front; it also enlarges the rear suction. This enables trailing cars to catch up. Drivers who are new to NASCAR (and IROC) racing, especially ones who come from open-wheel CART and IRL series, often remark on how much they can feel the unusual effects, both when they are being sucked forward, and when they lose a partner or start racing side by side.
Long draft lines are far more complex than two-car lines, and require a higher level of strategic comprehension on a driver's part. In a two-car line, the second can almost always find a moment to slingshot around. In long lines, this is normally not the case a maxim is that "it takes two to pass one." The change in dynamics starts with a three-car line. If the second car tries to slingshot alone in this situation, he often cannot get around the first as soon as the second swings out to race side by side, the third can catch up, tuck behind the first, and reestablish the draft line. This leaves the second car "hung out to dry," unable to get ahead or retake his former place in line. He drifts back. The best way to get around the first racer is for the third to follow the second second and third should form a drafting partnership and slingshot jointly in order to be sure of displacing the first.
Suppose the line is seven cars long, and the fourth wants to slip out and slingshot ahead. Again, he (so far, it's all male in Winston Cup racing) will not get far by himself. He can be sure to get ahead either by displacing a car farther up front in a line, or by creating a separate new line only if the car just ahead (in third) or behind (in fifth) goes with him, or better yet, if all three go together. He needs at least one partner and a prospective partner must not abandon him at the last moment. Again, if a racer ends up out of long line alone, it is likely to seal up; and if "the door slams shut," he will lose momentum and fall back sharply, sometimes losing more than ten places before he can squeeze back into a line without causing a multi-car wreck.
Thus, long lines generate a constant interplay between cooperation and defection. In a two-car line, the second driver can pick his moment for defection, and if he fails to achieve a slingshot, usually the worst outcome is that he sidles back into second. But in long lines, a racer should not act before calculating what his nearby rivals are about to do. Suppose he is in the middle of a long line: Is it better if the driver ahead goes with him? Or the driver behind? What are the signs that either will go with him? Or is there a driver off to the side that he can swing out to partner with? What if he is betrayed after he pops out? Should he be the one to deceive and defect?
Instability in the formation of multi-car lines tends to occur soon after the start or a restart, when the racers initially fight for position and test the set-up of their cars. Once established, long lines tend to cycle through many laps of orderly stability, where the cars stay in line, followed by sudden moments of chaotic mayhem that last less than a lap. Draft lines rarely disintegrate into anarchy for long; realignments occur quickly, as the racers balance their tactical interests in disrupting a line, with their strategic incentives to cooperate in reestablishing it. The greatest stability in the lead lines may occur during mid race if there is a long "green" a period under a green flag as the racers settle into position and wait for a break (such as a "yellow" caution when most cars make pit stops and reassemble for a restart). The greatest instability usually ensues during the final ten laps the last lap may be the wildest as each driver weighs taking chances to improve his position, and anticipates that all other drivers are about to do so too. All drafting "deals" are presumed null now. In the lead line, the first-place racer worries about a last-lap slingshot from the driver in second. But both drivers know that the outcome may depend on what the driver in third does. If the latter cannot or will not help the driver in second, his own attempt will probably fail. Similar calculations are being made back through the line.
When the cars stay in a line, it may look steady and straight, circuiting the oval in the same groove as the drivers play follow the leader. But at times it may waver like a "conga line." The leader may move back and forth sideways to block an anticipated run from the car in second. Or a car farther back may be probing to one side, testing to see who might be ready to run with him. Or perhaps a driver is steering a bit higher or lower to affect the spacing between his and adjacent cars, or to keep the driver behind him from trying to take the air off his car's spoiler. Slight disturbances like these ripple throughout the line, inducing the waver. The waver itself, plus slight changes in the spacing between cars, may then create an opportunity for a set of cars to break out.
Finally, someone makes a run. The falling out of order is usually the result of a single or a two-car effort to slingshot ahead. A single car might gain a spot if it has just received a bit of an aero push from the car behind, if it takes the air off the spoiler of the car in front, and/or if it makes its move by swinging inward and downhill as the line descends off a banked turn to enter a straight. Of course, the likelihood of success is vastly amplified if a partner goes with it. However, if three cars break out together, especially to the inside, all cars behind them are likely to follow, as a band-wagon effect takes hold. Then the draft line segments, and a new one forms alongside it. The longer a line, and the more urgently competitive the racers in it, the more likely it will segment and yield two parallel lines. Once this occurs, some racers may jump from one line to the other when openings appear, depending on their sense as to which line is moving faster or may offer better opportunities in the near future.
During a race, a driver is constantly concerned about exactly who is just in front and who is on his tail. Can the adjacent driver be trusted as a drafting partner? How experienced is he at working a line? Where does he stand in the season's total points race? How well is his car performing? Is it better at pushing or pulling other cars in a draft? Looking beyond the immediate concerns about adjacent cars, a genius at drafting strategy, like Earnhardt, will also try to envision where multiple cars may be located a few laps later, especially the cars he may want to partner with.
Veterans rarely want a newcomer or "rookie" nearby, much less as a partner, in a Winston Cup race. This year's star newcomer, Tony Stewart, found that he had to earn "confidence" so the veterans would accept him as a drafting partner. In IROC races, the NASCAR invitees prefer to form with each other and to avoid CART and IRL invitees, whose open-wheel experiences rarely involve drafting. Earnhardt, who won three of the four 1999 IROC races, commented after the one at Talladega that he did not want an IRL or CART driver on his tail as he worked his way from last to first place.
A driver benefits greatly if he has a trustworthy drafting partner, but prolonged cooperation between two racers lap after lap is rare. The propensity most exists only when the two come from the same team. For example, Rusty Wallace and Jeremy Mayfield, both with teams owned in part by Roger Penske, dominated first and second places respectively in the lead draft line for numerous laps of the Daytona 500. Their cars were running so well, and their collaboration was so evident, that nobody else in the lead line could challenge them. Their demise came late in the race after a yellow-flag caution, when they opted to stay in position while other racers made pitstops for new tires. Not long after the restart, as the lead line reemerged, Mayfield's worn tires began to lose grip, obliging him to drift out of the line. This left Wallace exposed to runs by the next racers in the lead line Gordon and Earnhardt in particular a few laps later.
But being on the same team is no guarantee of cooperation. Along with Earnhardt in that lead line was Mike Skinner and both drove for the team owned by Richard Childress. Cooperation to challenge the Wallace-Mayfield duo was hindered by the fact that another car always ran between Earnhardt and Skinner they couldn't "hook up." But they are so independent and competitive toward each other that collaboration may have been unlikely. Instead, with four laps left, in a moment of mad disarray, when Gordon dashed to the inside of Wallace and Skinner drove to the outside, Earnhardt first swung to the outside behind Skinner but then dropped down behind Gordon and helped draft him into first place and himself into second.
In short, cooperation among rivals is not natural in Winston Cup racing. Yet, it emerges spontaneously in the initial formation of long draft lines, then calculatingly as drivers compete to get ahead within a line or to create a new one. As Wallace remarked on the eve of the season's second race at Daytona, the Pepsi 400 in July, "Teamwork is everything here. If you can get a good drafting partner, ... you can cover a lot of ground." How is this arranged? Quite simply, the answer is communications.
Some deals may be cut before a race starts. Drivers know that drafting partners, however temporary and coincidental, are essential for doing well at Daytona and Talladega. So friendly drivers may discuss beforehand that they should hook up to help each other at times, perhaps especially if they are near each other on the starting grid or at a restart.
Most partnering emerges on the fly. How do drivers communicate an intent to partner while racing? For line-of-sight communication, there are customary hand gestures for indicating whether a driver wants someone to follow him, and in which direction he aims to swing his car. But hand gestures are not always easy to see, and a driver does not want to take his hands off the steering wheel for long. So, the key medium is radio.
NASCAR racecars have radios (IROC cars do not) that enable drivers to talk with their spotters in the stands and crew chiefs in the pits (but not to other drivers). The talk largely concerns how a car is performing, what needs to be adjusted, when to make pit stops, and what is happening on the track that the driver should know about. But in addition, the radios are used to arrange deals about who is ready to partner with whom, maybe for a few laps, but more likely for no more than 10 seconds at 190 MPH to draft around one rival before trust turns to defection, and the erstwhile partners look for new ones. Most efforts to cut deals go through the drivers' spotters, who then act like diplomatic envoys, clustered together high atop the stands. But the crew chiefs and car owners may also get involved. Who knows what quid pro quos may be added to the stakes then. Usually, these communications seek assurances about partnering with an adjacent car. But sometimes they inform a driver who cannot find an adjacent partner to wait for a driver who is working his way up the line, and then to go with him.
These communications travel on open frequencies (lists of which are available on the Internet, and for sale at the track). Spectators with radio scanners (for rent at the track) can eavesdrop during a race. So can radio and television broadcasters, and rival race teams. Thus, most drivers, spotters, and crew chiefs are circumspect about what they say. Some also use multiple frequencies, and guard them from disclosure. Yet, chatter often develops on a few frequencies, and may be picked up by the broadcasters. Thus, for example, they reported during part of the DieHard 500 at Talladega in April that Earnhardt's crew was craftily trying to convince crews for other drivers in the lead draft line that the line moved fastest when his car was in front, and therefore to let him stay in front but they evidently did not care for this argument, for they kept displacing him anyway.
Revealing comments about who would or would not draft with whom surface in post-race interviews. First-rate drivers with strong cars, after not doing well at a race at Daytona or Talladega, typically complain that "nobody would draft with me," or "my spotter couldn't find anybody to draft with me." Gordon had even mused, late in his winning streak for the Winston Cup championship in 1998 (his third), that other drivers were avoiding him as drafting partners. That may have been one of his problems this year as well.
While bump-and-run remains the classic act of tactical treachery, the dynamics of long draft lines make "getting dumped" an equally classic tactic. One is almost the antithesis of the other. Instead of nudged from behind, a driver is indeed dumped he swings out of line believing he has a partner to his front or rear, but is betrayed, as the latter defects and opts to close the line or swing in another direction. This can happen wherever a driver is located in a multi-car line.
Another ingenious tactic, one that so far only Earnhardt and maybe a couple other drivers appear to grasp, works best if a racer is second in a long line. He moves his car so close to the leader's as to give it an aero push, maybe even a bump-draft, that propels it ahead by several car lengths. Then he waits for the lead car to lose momentum and drift back to the line. As it does so, the driver in second swings around, gaining first place and taking the rest of the line with him, while the former leader falls back to the end of the line. This is not a bump and run; it is more a push and run.
In sum, working a long line is not just a matter of grasping the physical dynamics of drafting and applying skillful driving techniques. It is also depends on interpersonal communication, dealing and diplomacy. A driver's reputation as a trustworthy person may affect the outcome as much as his reputation as a driver.
These are the basic dynamics of long draft lines, and many of them come together in this Associated Press story about Earnhardt's win at the Diehard 500 at Talladega in April, when he crossed the finish line about two car lengths ahead of Jarrett, the second driver in what had been the lead draft line:Dale Earnhardt says racing at Alabama's Talladega Superspeedway is like a big game of chess ... . "It's knowing when to move and where to move to," ... . Earnhardt had to make his way back to the lead after a four-tire pit stop dropped him to 16th place. Then, he had to hold off a determined bid by Dale Jarrett over the final four laps on the 2.66-mile, high-banked oval. "Man, it was like who was going to work with who and what was what ... . I was going to settle for second place until the last few laps, but when they got to jumping around, I got out front and stayed with it." ... Jarrett managed to get up to his bumper several times, but never was able to pull alongside. "I was just glad to have the chance just to contend there at the end," Jarrett said. "It seems like every time I finish second here, the guys behind me start racing side-by-side and I don't get any help. That's what happened today."
The tables turned at the season's second race at Daytona, the Pepsi 400 in July. Jarrett won, while Earnhardt came in second, two car lengths behind. With three laps left in the race, Earnhardt was preparing to slingshot, with a boost from the racer in third, Jeff Burton, who was running another car length back. Burton and his crew chief had already decided he should follow wherever Earnhardt went, rather than try to pass him. Jarrett knew the attack was inevitable; and while it looked as though he was running flat out, he was already alternately slowing and accelerating his racecar in tiny increments so that Earnhardt could not open enough space for an unpreventable run. Jarrett's win was assured when a yellow-flag caution, the result of a minor wreck in mid pack, consumed the race's final three laps.
This was a classic situation, and much of the post-race commentary reflected on whether Earnhardt could have pulled it off (again). Still, events a few laps earlier were more illuminating about the dynamics of long draft lines. Jarrett ran first. Wallace, who led an early part of the race, ran second. Meanwhile, Bobby Labonte and Tony Stewart, both with a team owned by Joe Gibbs, had worked their way forward and were right behind Wallace. The two swung out together to "express train" around the outside. Labonte got by Wallace to gain second. But before Stewart could pass, Wallace swung to slip between them, and his car made contact with Stewart's front bumper, causing him to "check up" and slow. Earnhardt and Burton, who were behind them all, scooted past Stewart, whose loss of momentum caused him to slide way back in the lead lines.
Soon afterwards, Wallace, now in third, aimed to regain his spot from Labonte, and maybe pass Jarrett too. And he believed Earnhardt, now in fourth, would go with him Wallace said so after the race. So he swung to the inside, but then hung there alone, dumped, as Earnhardt stayed in line and closed it up behind Labonte. Wallace then fell way back to finish eleventh, wondering what had gone wrong. Post-race commentary suspected that Earnhardt defected because, early in the race, when Wallace was running first, he maneuvered wildly to block Earnhardt, in second, from passing him. Perhaps Earnhardt also disapproved of Wallace's crash-risking maneuver to block Stewart right in front of him.
Those who block inadvisedly are not cherished as drafting partners, and end up arousing distrust and tit-for-tat treatment. Curiously, this race was never marred by the usual "big wreck" and Wallace was the one credited for having spoken in the drivers' meeting before the race to caution all not to take risks by fighting desperately for every position.
Social Science at 190 MPH
Understanding these dynamics can help a viewer appreciate races where drafting matters they no longer look simply like lines of cars going in circles at steady speeds. But this analysis leads to more than a primer for spectators. As noted earlier, most sports pose non-stop, head-to-head, I-win/you-lose competition between individuals or teams. But because of drafting, Daytona-type races depend not only on competition but also on ever-shifting, opportunistic cooperation between rivals as they maneuver to outdo other rivals. That makes this subject theoretically interesting, for the dynamics of long draft lines can be seen to exemplify cutting-edge ideas in the social sciences about complexity theory, social network analysis and game theory.
In discussing this, I draw on the last Winston Cup race of the 1999 season that revolved around long draft lines: the Winston 500 at Talladega in October.
Complexity Theory on the Racetrack
Complexity theory is a recent field of scientific inquiry intent on looking into an array of "complex, adaptive systems": physical, biological, social and computational systems that are well structured and orderly most of the time, but slip into chaotic flux some of the time like an anatomy, the weather, an economy or possibly the Internet as it grows. As Mitchell Waldrop's Complexity a fine introduction to the field puts it,all these complex systems have somehow acquired the ability to bring order and chaos into a special kind of balance. This balance point often called the edge of chaos is where the components of a system never quite lock into place, and never quite dissolve into turbulence.
In this view, complex systems are composed of myriad "agents" molecules, species, corporations, computer automata, whatever that are "constantly organizing and reorganizing themselves into larger structures through the clash of mutual accommodation and mutual rivalry." Complexity theory is thus about "the magical fact that competition can produce a very strong incentive for cooperation, as certain players spontaneously forge alliances and symbiotic relationships with each other for mutual support." Indeed, complex, adaptive systems, from biology to politics, are so dynamic that they are never quite "in equilibrium." Yet, they are rarely chaotic for long either, as they have a capacity to absorb shocks, recover and even reorganize into a stronger system. Indeed, the chaos itself as discussed so well in James Gleick's Chaos turns out to have structure; it is not utterly random disorder, for a chaotic system tends to oscillate in some kind of scientific pattern around limits defined by an "attractor."
In figuring all this out, complexity theorists are fascinated that agents interacting according to even simple rules can accomplish "spontaneous self-organization" into a system that exhibits "emergence" structures, processes or behaviors that are not inherent in the agents but arise from their interaction. In studying self-organization, emergence and the oscillation between order and chaos, complexity theorists look for communications networks and self-reinforcing feedback behaviors among the agents. They emphasize "nonlinear dynamics" whereby small perturbations may have large effects later (also known as "sensitive dependence on initial conditions"). They examine "micro-macro interactions" the interdependence of the parts and the whole in order to learn how a system and its parts adapt to challenges. They focus on conditions of "criticality" that lead to chaos, and on the nature of "phase transitions" as a system goes from one state to another (e.g., solid to liquid), or oscillates between chaos and order. Some theorists also wonder about "normal accidents" Charles Perrow's concept about the fact that accidents are sure to occur occasionally in high-tech high-risk systems (e.g., some electrical grids) whose parts are tightly rather than loosely coupled, and whose interactions are complex (nonlinear) rather than linear. Ultimately, complexity theorists may aspire to assess a system's "fitness" and to explain how evolution happens and "entropy" is averted through learning and adaptation.
Why, they could almost be talking about NASCAR (and IROC) races at Daytona and Talladega! For these races exhibit this set of phenomena. The racers are agents set to combine and compete according to a set of rules. And they are all so similar in their capabilities in that context that they must seek mutual cooperation in order to advance their competitive agendas vis-á-vis each other. They self-organize into cooperative draft lines, and then into competitive (but still cooperative) break-out lines. They use radio communications to generate information, overcome uncertainty, and seek allies. And this creates a fast-moving, dynamic structure, or system, that exhibits a kind of order oscillating lines in front of a milling pack, tightly coupled and fraught with nonlinear processes that is often on the verge of criticality, chaos and catastrophe. Yet, chaos that arises in this structure minimally as a result of a break-out effort, or because an accident collects numerous cars and requires a restart soon yields to a regeneration of order.
As for the Winston 500, it was won by Dale Earnhardt, after he weaved skillfully from 27th to 5th place in the first five laps, to everyone's amazement, then kept his car in the lead lines (mostly the top ten) during the constant shuffling and regrouping that characterized the rest of the race. He led four times, including the final few laps, in a race that saw thirty-two lead changes among sixteen drivers. Twenty-one cars finished on the lead lap, all bunched only a few seconds apart because of the suction of the draft. Earnhardt's own margin of victory over the second-place finisher, Dale Jarrett, was a fraction of a second, about two car lengths. Nearing the end, Jarrett held the lead for ten laps, but he was passed by Earnhardt, who had drafting assistance from Mike Skinner and Bobby Labonte, with four laps to go. As at the Diehard 500 at Talladega in April, Earnhardt held onto first mainly because most racers behind him left formation and jumped around for their own last-second sakes. Again Earnhardt commented, this time to the journal NASCAR Winston Cup Scene, that, "You just had to be careful on what moves you made and when you made 'em and who was around when you made 'em."
Perhaps because the drivers were more careful to give each other room than is usually the case, this race had more structure than most races. A few times a lone first-place car ran barely ahead of two parallel draft lines. But usually the lead line varied in length from three to nine cars (perhaps in keeping with a complexity theory "rule" that it is best for a system's components or levels to number seven, plus or minus two). A long line soon segmented, and two or even three lines would then take shape parallel to each other. Only one multi-car accident occurred, when a group of rivals tried to race four-wide around a turn and banged into each other (perhaps in keeping with another theme in complexity theory: the avalanching and shape-reorganizing behavior of sand piles after too much extra sand has been poured on top).
At present, complexity theory is more a set of concepts, notions and observations than a full-fledged theory. Analysts can say they are going to analyze the complexity of something, but cannot truly claim they are going to do a complexity-theory analysis of that something. There are not enough established conventions and methodologies for that. In contrast, analysts can say they are going to do a social-network or game-theory analysis there are advanced practices for that.
Draft Lines as Networks of Human and Social Capital
Social network analysis is an academic specialty pursued by a relatively small set of anthropologists, sociologists and organizational theorists, though it has grown in influence for several decades. Their approach see, for example, a book like Networks and Organizations, or Social Structures: A Network Approach or Social Network Analysis holds that all social relationships, indeed all social organizations, can and should be, analyzed as networks, that is, as sets of actors (nodes) and ties linkages) that have a patterned structure. This mouthful is easier to digest if it is pointed out that networks come in basically three shapes (or topologies): as line or chain networks, where the members are linked in a row and communications flow through an adjacent actor before getting to the next; as star, hub or wheel networks, where members are tied to a central node or actor and go through that node to communicate with each other; and as all-channel networks, where everyone is connected to and can communicate directly with everyone else. There may be hybrids of these; and any particular network may itself be embedded within surrounding networks. For social network analysts, the network is the mother of all forms, and the world amounts to a network of networks. And for these and other theorists, the Internet is where complexity theory and social network analysis come together in wonderful ways (e.g., as discussed in Kevin Kelly's Out of Control).
In the view of social network analysts, one's power and influence depend less on one's personal attributes (e.g., resources, behaviors) than on one's relationships the location and character of one's ties, or linkages, in the network. The "unit of analysis" is not the individual but the network in which the individual is embedded. Not unlike complexity theorists, social network analysts view a network as a systemic whole that is greater than and different from its parts. And a key aim is to show how the properties of the parts are defined by their interactions, and how the network itself functions to create opportunities for or to constrain the individuals in it.
In particular, many network analysts stress the importance of location: whether an actor's power and prestige stem from his "centrality" in a network, or whether he has greater autonomy and potential power if he is located at a "structural hole" (which I take to mean a peripheral location, but one that provides more access to actors in nearby networks). Other theorists stress the importance of the ties: whether the ties are strong (tightly coupled) or weak (loosely coupled), and what difference this makes for getting and acting on information about what is happening inside and outside the network. Important questions may also be asked about the overall "connectedness" of a network, and about the degrees of "reciprocity" and "mutuality" that characterize flows and exchanges within it.
For social network analysts, then, what is keenly interesting about individuals is not their "human capital" (personal properties) but their "social capital" (interpersonal or relational properties). Social networks are built out of social capital. They thrive when mutual respect and trust are high.
Social network analysts have never applied this thinking to a stock-car race. Their classic studies are about topics like social circles and cliques, interlocking memberships in corporate boards, job search and occupational mobility, business firm alliances and even the structure of the world economic and political system. Yet, they might as well be talking about racers at Daytona and Talladega. A multi-car draft line is essentially a line network; and a race consists of shifting sets of line networks interacting with each other. A driver's car is his physical capital, and his skills his human capital, which he takes to every race. But at Daytona-type races, line networks emerge also because of a driver's social capital, and the choices he makes about the social (as well as the physical and human) capital of the other drivers around him, who represent options for him to link with. A driver's (and a team's) social capital, more than his human capital, may determine how well he does in forming drafting partnerships. A skillful driver can fight his way into a draft line if he has a strong car. But to be welcome there, he should have a reputation not only as a skillful driver, but also as a reliable, trustworthy partner for moving to the front, even though the expectation of partnership may be momentary and contingent.
At the end of the Winston 500, Earnhardt enjoyed significant drafting assistance from his car owner's teammate, Skinner. But there was competition for his allegiance. The television broadcast of the race included live coverage of communications between Jarrett's crew chief and spotter, and of that spotter consulting with other spotters. As the race entered the last 30 laps, with Jarrett running near the front, his spotter sought out Skinner's spotter, seeking Skinner's agreement to draft behind Jarrett so the two could seize first and second (and, by unspoken implication, get around Earnhardt). The deal would last until there were ten laps to go, after which all deals were presumed off. Jarrett and Skinner had helped each other in previous races, and now Skinner did stay in line behind Jarrett briefly. But, after some shuffling that separated him from Jarrett, he switched to push Earnhardt back into first with three laps to go. Then, the disarray of the final lap reshuffled him back to finish thirteenth. Once again Earnhardt's human and social "capital" soared, while Skinner's was tarnished.
Various other drivers fretted after the race that they lacked "friends" to push them ahead, or were "hung out to dry" by rivals. Ward Burton, who took fourth, was pleased his car performed well, but added that"the biggest thing is you had to have (somebody) push you ... . A couple of the top dogs left me out to dry one time, and I never got to repay the favor ... . Some of the guys that have been racing for years in this series, they kind of help each other a little bit more than some of the other racers. (But) everybody got hung out. There ain't a car out there that didn't get hung out."
This constant gauging of other drivers' intentions, this constant interplay between getting helped and getting hung, and their effects on the dynamics of long draft lines provide good material for doing a social network analysis. It also takes us to the next mode of understanding, which is geared to understanding the driver's-eye calculus.
Game Theory The "Drafter's Dilemma"
The most famous book about game theory Robert Axelrod's The Evolution of Cooperation opens with these questions: "Under what conditions will cooperation emerge in a world of egoists without central authority? ... [I]n situations where each individual has an incentive to be selfish, how can cooperation ever develop?" Game theory is a science of strategy, and these questions capture its essence. The games at stake range from simple ones, like how to cut a cake knowing someone else gets to pick the first piece, to dangerous ones, like whether to deploy more missiles knowing the enemy might choose to do so too. New games may emerge as well, ones that are more attuned to the information age, such as whether to share secret intelligence about drug traffickers with a semi-trusted ally, perhaps by way of a secure version of the Internet. Yet, as William Poundstone's book Prisoner's Dilemma observes, all these games consist of conflict situations "where one must make a choice knowing that others are making choices too, and the outcome of the conflict will be determined in some prescribed way by all the choices made." Some games are "zero-sum" if one player wins, the other loses. Yet many games, the most storied ones for theory and real life, are "non-zero-sum," in that the players' interests are not entirely opposed, and some risky moves may allow both to gain, increasing their common good.
Game theory presumes "rationality" for the players, and gets very mathematical, with concepts about "utilities" and "minimax solutions" and "dominant strategies" and "equilibrium points" and "free rider problems" and escalatory "echo effects" and so forth. A game gets represented usually as a payoff matrix that specifies numerical (or ranked) punishments and rewards, reflecting whether a player opts to "cooperate" or "defect" on a turn. But game theory is psychological too; dilemmas involve psychology. Since in these games the players must move simultaneously and without consultation, each player's move may be determined not only by his own preference, but also by his anticipation of the other player's likely preference for that move. Respect and trust come into play. So may greed and fear, niceness and forgiveness, and even irrationality, despite the presumption of rationality.
One might say, then, that game theory is a mathematics of cunning. And it can be used to characterize the dilemmas facing stock-car drivers as they maneuver to form draft lines and then to find partners for breaking out, moving ahead, and creating new lines. Four basic two-person games, each reflecting a situation that poses a significantly different payoff matrix, are known by these names: deadlock, prisoner's dilemma, chicken and stag hunt. Two of these are particularly appropriate for understanding the dynamics of long draft lines and the strategies and tactics that drivers often resort to.
Forming a draft line in the first place reflects incentives that resemble a "trust dilemma" game known as the "stag hunt" (so named after a parable in a writing by the French philosopher, Jean Jacques Rousseau, about why people bother to build societies). The basic situation is this: Two hungry players can hunt a stag and divvy up its meat if they work together. But there are few stags, and it takes effort to get one. However, there are many small rabbits, and thus there is a temptation for either player to defect from the stag hunt and settle for a rabbit for himself. This leaves the other player with nothing, neither a stag nor a rabbit, unless he defects to get a rabbit too. The game thus offers a major incentive to cooperate, with enticements to defect. The payoff matrix usually looks like Table 1. Plays of the game normally lead to a constant choice of the mutual cooperation cell [3, 3] by both players, since cooperation promises a higher payoff than does any other outcome for either player.
Table 1: Stag Hunt (Trust Dilemma) Payoff Matrix Player B Player B Cooperates Defects Player A Cooperates 3, 3 0, 2 Player A Defects 2, 0 1, 1
This looks like a pretty good representation of the situation facing drivers as they initially work to organize draft lines. Actually, a Daytona-type race starts with the cars already rolling in two parallel lines, and this formation is usually sustained for several laps as the cars get up to full speed. But line-jumping and line-reshaping begins soon. For many drivers, the stag-hunt incentive is to pair for the moment with whomever is adjacent. But in fact many drivers will jump around as they try to fight their way up the lines, and look (or wait) for a drafting partner who seems preferable for one reason or another. If the racecars up front are mostly staying up front, and your own is there as well, then the incentives are stacked for you to get in line, as quickly as possible, with those nearby racecars. The options for pairing are more numerous and complex farther back in the pack. Decisions and moves occur in a matter of seconds, if not fractions of seconds. If a driver jumps around inadvisedly (in effect, looking for rabbits), he may well fail to get in line, be hung out to dry, and lose many spots as he slides back in the pack.
Once a lead line takes shape, the drivers may well want to remain securely in it for a while. This too is in keeping with the stag-hunt game. But this is unlikely to last for long. One or more drivers are bound to want to work their way up the line or to create a new one perhaps partly to try to get in first place for at least a lap, so as to earn five points toward the annual championship. And this, among other things, leads to the displacement of the stag hunt by a different, riskier game.
The Rousseauian stag hunt contrasts with the Hobbesian "prisoner's dilemma" game the most famous of all game-theoretic games, for it best captures a dilemma faced in many crucial real-life concerns, including nuclear strategy, trade strategy and coalition formation. The basic situation is something like this: Two prisoners held by police in separate rooms are asked to rat on each other. If both stay mum (cooperate, cooperate), then they may both go free, for lack of evidence. If they both rat on each other (defect, defect), they both end up with light sentences. But if one rats while the other stays mum, the police see to it that the ratter (the defector from his partner) goes free and gets a reward, while the other prisoner (the one who is cooperating in being silent about his partner) gets a long sentence. A standard payoff matrix for a prisoner's dilemma game looks like Figure 2. The marvelous dilemma is that both players benefit significantly if both choose to cooperate [3, 3], but one may be strongly tempted to gain even more if he defects while the other is suckered into cooperating [5, 0]. Yet, in considering this, he must anticipate that the other player may do the same to him [0, 5]. If both defect, they are punished with a jointly minimal score [1, 1].
Table 2: Prisoner's Dilemma Payoff Matrix Player B Player B Cooperates Defects Player A Cooperates 3, 3 0, 5 Player A Defects 5, 0 1, 1
Multi-player versions of the game, ones involving more than two players, reflect a broad social problem that arises in many settings from whether to jump on a subway without paying a fare, to whether to pay ransom to terrorist kidnappers. And that problem, in the words of Poundstone, is "a temptation to better one's own interests in a way that would be ruinous if everyone did it." Self-interest, too widely pursued, runs at odds with long-term group-interest.
If a two-player prisoner's dilemma game is played just one turn, the most logical choice is for both to defect. That way neither risks the disparity where one gains a lot, the other nothing. Yet, when the game is played over and over, for numerous turns a "reiterated prisoner's dilemma game" both players increase their points if they both choose to cooperate some of the time. But how to assure that? How to signal that, in the absence of direct communication? The key experiments related in Axelrod's The Evolution of Cooperation and his sequel, The Complexity of Cooperation show that the most advisable strategy for either or both players to follow is "tit for tat": specifically, to cooperate on the first move, and then on each subsequent move to do what the other player did on the prior move. Thus if he defects on a turn, you defect on the next, and so forth. The "shadow of the future" should entice a player to cooperate now in order to enhance the likelihood of reciprocal cooperation in the future.
So long as the other player is observant, favors reciprocity, and is not following a rigid strategy, like being a "meanie" who regularly defects, then tit for tat leads, better than any other strategy, to a process of mutual learning and anticipation that results in both players cooperating a good part of the time. According to Axelrod,What accounts for tit for tat's robust success is its combination of being nice, retaliatory, forgiving, and clear. Its niceness prevents it from getting into unnecessary trouble. Its retaliation discourages the other side from persisting whenever defection is tried. Its forgiveness helps restore mutual cooperation. And its clarity makes it intelligible to the other player, thereby eliciting long-term cooperation.
The likelihood of cooperation based on tit for tat increases when players are sure of facing repeated, long-term interactions with each other. This motivates reciprocity. The likelihood decreases when a player senses that he is unlikely to encounter another player again soon, maybe because the latter is unlikely to be around much longer as a player. In these respects, the game's conduct is affected by how well "the shadow of the future" looms. Trust proves less important than constancy of interaction as a motivator of reciprocity.
All this sounds wonderfully like the dynamics of a Daytona-type race as drivers maneuver to elicit drafting partners who will enable them to break out and get ahead in one existing line or another. This aspect of a race resembles a reiterated multi-player prisoner's dilemma game, ruled by constant two-player exchanges. The dilemma arises in a driver's concern whether a maneuver will indeed be accompanied by cooperation, in which case he and his partner may gain one or two places right away, or whether he will be subjected to defection, in which case he could easily lose five to ten spots in a hurry or whether he should be the one to defect, causing the other driver to lose spots. The dilemma is affected by caring about the fact that a race will probably lead to many interactions with the same driver. Over the course of a race, the strategy that veteran drivers turn to the most, as earlier discussion in this article attests, is precisely tit for tat: "I drive him the way he drives me." This is the strategy that all drivers best understand and respect. But each driver may practice it a bit differently, depending not only on his particular psychology, but also on his appeal as a driver and drafter, and on his location and situation in the race at that time.
The prisoner's dilemma payoff matrix provides a good approximation of what faces a Winston Cup racer good enough to sustain the notion that game theory applies to Daytona-type racing. But the "drafter's dilemma" may actually be a little different; further analysis may show it means a somewhat different payoff matrix. In particular, the numbers for where one party cooperates and the other defects, [5, 0] and [0, 5], do not look quite right for a drafter's dilemma. In drafting situations, the defector stands to gain a little by defecting, maybe a better partner on the next turn. But he causes the other racer to lose an awful lot, maybe five places. So perhaps payoff entries like [2, -5] and [-5, 2] would be truer to a racer's reality. But that's not all. In most classic games, the payoffs are symmetrical; the payoffs facing one player mirror those facing the other. However, there are variants and hybrid games where the payoffs are asymmetrical one player faces a different set of payoffs from the other. And that may be the case with the drafter's dilemma. It is really the second car, the one behind, that has the advantage when it comes to defecting. Indeed, he gains a place if he defects and leaves the car in front out of line; the same cannot be said for the car ahead. So, the car behind may deserve a somewhat higher payoff for defecting here, say [-5, 3]. Table 3 proposes what a drafter's dilemma payoff matrix would look like then.
Table 3: Drafter's Dilemma Payoff Matrix (Preliminary) Driver B (Behind) Driver B (Behind) Cooperates Defects Driver A (Ahead) Cooperates 3, 3 -5, 3 Driver A (Ahead) Defects 2, -5 1, 1
This is just a preliminary suggestion and not the only possibility. Perhaps a good point to add is that a driver's notion of his payoff matrix may change constantly during a race, depending partly on what he thinks of whoever is near him at the time. If so, consideration should be given to extending the joint cooperation payoff a notch, say to [4, 4], and having it oscillate between [3, 3] and [4, 4] depending on a driver's situation.
Axelrod's classic ends with insightful recommendations about how to improve the likelihood of cooperation in a world suffused with prisoner's dilemma situations. But for racers, the ultimate objective is how to improve competitiveness, not cooperation. Axelrod imparts hints about this, however, including when he observes the following:Having a firm reputation for using tit for tat is advantageous to a player, but it is not actually the best reputation to have. The best reputation to have is the reputation for being a bully. The best kind of bully to be is one who has a reputation for squeezing the most out of the other player while not tolerating any defections at all from the other ... . To become known as a bully you have to defect a lot, which means that you are likely to provoke the other player into retaliation.
For many NASCAR fans, this point will call to mind one driver more than any other: Earnhardt. He is not really a bully, but his firm reputation as "The Intimidator," and as the wiliest draft-line maneuverer in racing, speak to Axelrod's point. Yet, it should also be noted that if all drivers act like "bullies" and "meanies," Daytona-type racing would surely deteriorate into an awful mess, with nonstop feuding on the track. Indeed, drivers may want to step aside from pure tit for tat at times be forgiving and refuse to be provoked so as not to spiral into what Axelrod calls "an unending echo of alternating defections." In fact, this is what usually occurs over the course of a season; tempers cool by the next race, and drivers turn to make conciliatory statements through the media, even though memories do not fade.
In sum, the overall structure of a Daytona-type race, from start to finish, reduces to an alternation between stag hunt and prisoner's dilemma games. Frequent restarts intensify the alternation. Specific drivers may also go through alternations of their own. Encounters with the few racers with whom they are already disposed to cooperate (and to expect cooperation in return) may fit the stag hunt model. But most encounters, for most of a race, are likely to fit the prisoner's (or the drafter's) dilemma model. For some adjacent drivers, the final lap may also bring into play two other models that are not discussed in this paper: chicken, and deadlock.
Concluding Comment: Drafting in Everyday Life
Little has been written about the long draft line in automobile racing. I have tried to show that it is a very interesting phenomenon, one that enacts some innovative social science theories. Incorporating its dynamics into computer models for studying complexity, network and game theories, as well as for developing NASCAR-type entertainment games and simulations, may be a worthy future challenge, possibly a profitable one too.
But I shall conclude on a different note: Drafting may be a more common feature of everyday life than has been noticed. Drafting occurs not only on race tracks, but also in quite a few areas of social, economic, and political endeavor. Consider the following:
These few examples and others that wait to be identified suggest that a new range of social science theory might be developed around the concept or metaphor of the long draft line. They also suggest something else that, in short, much of life is like a Daytona-type race. (And by the way, the next Daytona 500, the first race of the 2000 season, occurs on Sunday, February 20 and will be broadcast live.)
- Career advancement in corporate circles, where an executive climbs up a corporate ladder and takes selected staff and lower-ranking executives with him, has some characteristics of a draft line. Its dynamics may be all the more relevant when that executive's climb leads to the displacement, perhaps even the crumbling, of rival draft lines in the corporation; or when a close associate of the executive later defects to go elsewhere, possibly taking others from the original line with him. Examples of this do not come readily to my mind, but my latent memory of past media stories hints that they should not be hard to find (e.g., perhaps in the history of Michael Eisner's rise and the departures of Jeffrey Katzenberg and Michael Ovitz at Disney). In a mundane sense, line drafting, augmented by bump and run tactics, offers a way to try to get ahead in the "rat race" aspects of life.
- International diplomatic and military alliances are commonly depicted as a front, with the allies standing arm in arm, shoulder to shoulder. But in some cases, they may as accurately be depicted as a draft line. For example, the NATO alliance operating in Kosovo featured out-front leadership by the United States and secondly Great Britain, with probing criticism occasionally coming from France. The alliance was acting like a draft line in which the United States could easily retain its lead so long as Britain stayed close in line, keeping rivals from drafting around them both, and so long as possible rivals could not find partners to create a new line. This way of viewing an alliance may work best when there is a strong leader up front, and make less sense if the alliance is a balance-of-power assembly.
- The Internet, in both its technical and social structures, is a complex mix of line, hub and all-channel networks and of variants and hybrids of all these. At the same time, the Internet is increasingly heralded as a metaphor, if not reality, about where life is, or should be, headed on this planet. Most of the attention goes to the all-channel networking possibilities. But line networks figure prominently too. At the technical level, packet switching and routing patterns lead to swarms of message-bearing line networks (though I hesitate to say the packets are drafting each other). At the social level, the Internet and other communications technologies (fax machines, cellular telephones) enable activist NGOs (nongovernmental organizations) to network and act conjointly as never before. There are myriad, mounting example of this, including most recently, and dramatically, in the anti-WTO protests in Seattle. The most effective activist networks seem to be the ones that are all-channel in design, especially when it comes to waging what John Arquilla and I call netwar. But in some instances, what takes shape are competing line networks, often with a well-known group out front and lesser groups lined up with it, ostensibly side by side but in reality more as drafting partners.
About the Author
David Ronfeldt is a senior social scientist in the International Studies Group at RAND in Santa Monica, Calif. He works on ideas about new information-age modes of conflict (cyberwar, netwar) and cooperation (noopolitik). He is also building a theoretical framework about the four forms of organization (tribes, institutions, markets, and networks) that underlie the evolution of all societies. He is co-editor with John Arquilla of In Athena's Camp: Preparing for Conflict in the Information Age(RAND, 1997), and co-author of The Zapatista Social Netwar in Mexico(RAND, 1998).
John Arquilla and David Ronfeldt, 1999. The Emergence of Noopolitik: Toward an American Information Strategy. Santa Monica, Calif.: RAND, and at http://www.rand.org/publications/MR/MR1033/
Robert Axelrod, 1984. The Evolution of Cooperation. New York: Basic Books.
Robert Axelrod, 1999. The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration. Princeton, N.J.: Princeton University Press.
William Burt, 1999. Stock Car Race Fan's Reference Guide: Understanding NASCAR. MBI Publishing.
James Gleick, 1987. Chaos: Making a New Science. New York: Penguin.
Tom Higgins and Steve Waid, 1999. Junior Johnson: Brave in Life. David Bull Publishing.
Scott Huler, 1999. A Little Bit Sideways: One Week Inside a NASCAR Winston Cup Race Team. MBI Publishing.
Kevin Kelly, 1994. Out of Control: The Rise of Neo-Biological Civilization. Reading, Mass.: Addison-Wesley.
Nitin Nohria and Robert G. Eccles (editors), 1992. Networks and Organizations: Structure, Form, and Action. Boston: Harvard Business School Press.
Charles Perrow, 1984. Normal Accidents: Living with High-Risk Technologies. New York: Basic Books.
William Poundstone, 1992. Prisoner's Dilemma. New York: Anchor Books.
M. Mitchell Waldrop, 1992. Complexity: The Emerging Science at the Edge of Order and Chaos. New York: Simon & Schuster.
Stanley Wasserman and Katherine Faust, 1994. Social Network Analysis: Methods and Applications. Cambridge: Cambridge University Press.
Barry Wellman and S. D. Berkowitz, 1997. Social Structures: A Network Approach. updated edition. JAI Press.
Appendix: Selected World Wide Web Sites
Stock-Car Racing Sites
ESPN's NASCAR Web Site
Jayski's NASCAR® Winston Cup Silly Season Site
Cameras in Action Stock Photography
(Pictures of draft lines at Daytona 500, DieHard 500, Winston 500)
The Stock Car Gallery
Complexity Theory Sites
The Santa Fe Institute
The Swarm Development Group
New England Complex Systems Institute
Social Network Analysis Site
The International Network for Social Network Analysis
Game Theory Sites
Axelrod's Evolution of Cooperation Web Site
Axelrod's Complexity of Cooperation Web Site
Paper received 12 January 2000; accepted 19 January 2000; revised 20 January 2000; revised 23 January 2000; revised 26 January 2000.
Copyright ©2000, First Monday
Copyright ©2000, David Ronfeldt
Social Science at 190 MPH on NASCAR's Biggest Superspeedways by David Ronfeldt
First Monday, volume 5, number 2 (February 2000),