Cumulative Races Led

by Sean Wrona

As earlier discussed, several years ago I calculated the statistic average percent led to correct the bias in the laps led statistic due to races having a differential number of laps. This is most significant in series like IndyCar and NASCAR where races on short ovals tend to have many more laps than large ovals or road courses, so evaluating dominance based on laps led will be tremendously biased towards drivers who dominate on races that have more laps (short ovals, or generally, shorter tracks in general). However, even in Formula One, there is a fairly large difference between the race with the most number of laps this season (Monaco with 78) and the race with the fewest (Spa-Francorchamps with 43), although for road racing series, a laps led statistic will be somewhat more accurate since the number of laps in each race is more consistent. While I have stated before that I believe dominance is the best predictor for results in the future (since current results include many team-related, luck, and/or strategic factors unrelated to the driver), the laps led statistic is clearly flawed, which led me to invent the average percent led statistic, counting all races as equally important. In NASCAR, leading 45 of 90 laps at Watkins Glen, 94 of 188 laps at Talladega, and 250 of 500 laps at Bristol should be considered equivalent, and using this statistic, they all would be, counting as 50% of a race led. Average percent led properly measures dominance in a way laps led does not. To cite another example, Josef Newgarden led 100+ laps at Milwaukee and Iowa, which led him to lead IndyCar in laps led, but when equating all races using this statistic, he was behind Scott Dixon and Will Power, which makes more sense (one can still argue given the car Newgarden drove that he may have been more impressive regardless), so this distinction can make a big difference. Unfortunately, average percent led, much like other statistics like percent beat, average finish, and so on, has its own problems. Drivers who raced far after their prime or took several years to get into good equipment will invariably be underrated. Darrell Waltrip continued to race eight years after he won his final race, which greatly weakened all his career average statistics, to the point that his average percent led is behind some drivers with lesser reputations such as Speedy Thompson, Dick Rathmann, Dick Linder, and Davey Allison, who had relatively short careers with lower peaks but a smaller percentage of bad seasons (and his percent beat, the field-adjusted average finish, comes out even worse). As a result of the flaws this initial list produced, I decided to expand this to an overall career statistic, which I have termed cumulative races led. This is simply defined as the sum of average percent led for all drivers for all races, but I have divided this statistic by 100 to make it more intuitive. The driver who led half of a race at Watkins Glen, Talladega, or Bristol would simply receive .5 of a cumulative race led. While the established statistic of races led has value in determining how many different races a driver is relevant, unfortunately it is also biased towards drivers who take the lead during pit stop exchanges but are not actually relevant, while this statistic directly reflects distinctions in dominance without being biased toward particular track types.

The cumulative races led statistic can be best interpreted as how many races drivers should have won based on their level of career dominance, which naturally leads to interesting results. Racing fans frequently consider certain drivers 'chokers' if they dominate early in the race before fading late and others 'closers' if they come on strong at the end of the race, but few have attempted to actually quantify this as best I can tell. Now we can. Drivers who have more wins than cumulative races led (more wins than they 'should' have) can be considered 'closers', as they are clearly better at the end of races than their in-race dominance can predict, while drivers who have more cumulative races led than wins (fewer wins than they 'should' have) can be considered 'chokers'. I leave these phrases in quotes because there are many reasons why drivers can win or lose races. This statistic does work in the sense that drivers who have reputations for being aggressive hotheads and driving too hard for their equipment do invariably have more cumulative races led than wins (and a ratio lower than 1 in the below tables), while more conservative drivers who come on strong on the end have more wins (and a ratio above 1) in almost all cases. However, this is just a statistic, so it completely ignores whether the driver is actually responsible for their wins/losses (for that you would need to do an analysis like the 'How the Races Were Won' I did early this year. To understand why a dominant driver lost a race you need to view the individual race results. Some drivers may have lost races due to unreliable equipment (while many fans say drivers such as Mario Andretti, Michael Andretti, Buddy Baker, and Geoff Bodine were too hard on their equipment and it was their fault they lost races as a result, I am not sure you can determine so clearly in what cases unreliability was a given drivers' fault rather than the fault of the engineers or just dumb luck). Some drivers may have lost due to their teams' mistakes, getting caught in a crash caused by another driver, equipment failures, miscalculation on fuel conservation, and so on. It is so easy to blame the driver as the representative of the team for many failures the driver may have control over, but it is not so clear in some cases (particularly mechanical failures and running out of fuel) how much is the driver's fault and how much is the team's fault. In a lot of cases, it can be argued either way, so I would tend to prefer to give the driver the benefit of the doubt. I firmly believe that in most cases drivers with more cumulative races led than wins are underrated while most drivers with more wins than cumulative races led are overrated. There are some exceptions I would disagree with, but in general, the finish is not the best measure of predicting future results, since actual finishing results in a given race include too many team or luck-based factors, while dominance now best reflects dominance and I think even consistency in the future (although I haven't mathematically tested any of these hypotheses yet, which I may do at some point in the future). In other words, I would prefer the cumulative races led ranking as a measure of talent than the pure win ranking.

This certainly is not infallible and I understand the statistic's drawbacks. I do not correct for the strength of equipment nor do I correct for the strength of the field (as I did in my most recent columns, but I may undertake these adjustments later). Particularly in NASCAR and IndyCar, some races were indeed unquestionably more valuable than others yet they are all regarded equally. For instance, the twin 125 qualifying races for the Daytona 500 used to count for points (before 1972, when new title sponsor Winston refused to sponsor any race shorter than 250 miles) so leading a certain percentage of those races counts the same as leading the same percentage of the Daytona 500, even though the twin 125 races had weaker half fields and much shorter distances. Admittedly, no one would argue the races were more important, nor would they argue that 200 lap/100 mile dirt track races equal 500-mile superspeedway races either, but this honestly doesn't bother me much. For one thing, the actual win list has exactly the same drawbacks. Figuring out the proper mechanisms to correct the biases in the win list where races of unequal value count the same will also correct the cumulative races led list. Furthermore, another drawback is that I only included races where the entire lap leader data were available. For Formula One, this is no problem as every race has complete lap leader data. IndyCar also has complete lap leader data available for every race after 1946 except for two, all Indy 500s before that, and many races from the pre-World War II period also. NASCAR however has missing lap leader data from many '50s/'60s races. These races with incomplete lap leader data are completely ignored to correct for any bias that may result (particularly when comparing drivers' win totals with their cumulative races led totals) so that is why some drivers on the IndyCar and NASCAR lists will have more actual wins than listed wins. There were some odd cases I ended up excluding by this metric as well, such as the early 1974 NASCAR season when the early season races were shortened 10% due to the United States oil shortage, but they chose to advertise the same race distances for several events (so a 500-mile race would only run 450 miles, but they would start it as if the number of laps equivalent to 50 miles had been completed); I ended up not including these, even though the lap data besides the 'missing laps' were available, although that's highly debatable. Regardless of the idiosyncrasies this produces, most of them are exactly the same bias the win list also produces. Properly correcting the cumulative races led statistic for equipment strength, strength of the field, and perhaps some measure of longevity and versatility would in my opinion be almost the best measure possible for career strength.

Formula One

Despite my earlier stated preference for drivers with higher cumulative races led than wins all else equal, the Formula One list below is one thing that may make me change my mind. Invariably drivers who had a history of being weaker than their teammates had more cumulative races led and ratios below 1 (this applied to Rubens Barrichello, Mark Webber, Riccardo Patrese, David Coulthard, Gerhard Berger, Felipe Massa, Nico Rosberg, and most other drivers who were considered good but grossly overpowered by legendary teammates), while most of the drivers with a ratio above 1 truly are legendary. Sure, there are a few uber-legends with more cumulative races led as well (Senna, Vettel, Mansell, Clark, Moss, Ascari) as well and several of those drivers did have a history of inconsistency and arguably overdriving their equipment relative to their peers. Drawing conclusions from this list is much less obvious because there are definite legends with fewer wins than cumulative races led, while there are some drivers considered by many to be lesser legends who do have ratios above 1. I think this kind of analysis ends up being much better for IndyCar or NASCAR than series like Formula One, because F1 has so few cautions relatively that races are ultimately decided on pace, whereas they are much less likely to be decided on pace in US races, hence I would not say that drivers with more wins than cumulative races led are necessarily overrated here, because races are overwhelmingly decided on pace most often (even though pace is largely determined by the strength of the equipment). I think cumulative races led still has value here, but if I were inclined to rate wins higher for any series, it would certainly be this one. Since I believe Formula One results do reflect pace and are a good predictor of what will happen in the future (at least within the same season, ignoring the sometimes sudden year-to-year changes in the strength of a team's equipment) I will be spending more time discussing IndyCar and NASCAR, where this is much less the case, and where this particular statistic is more important. I do think cumulative races led reflects something for Formula One but in this case, when the #1 drivers on teams usually tend to have higher win to cumulative races led ratios than the #2 drivers, it is less clear what it reflects.)

This list is updated through the 2015 Grande Prêmio Petrobras do Brasil. All drivers with 0.5 or more cumulative races led plus all winners with fewer than 0.5 cumulative races led are listed.

IndyCar

On the other hand, series that race primarily, or often, on ovals are very different as there are many more cautions which bunch up the field, and in recent years since the pits were closed on road courses, races can be determined more by strategy roulette than actual pace (see this year's ugly, ugly Mid-Ohio race for proof of that). In such an environment when the field is designed to be closer than in a lot of international road racing series, this also means a small difference in team strength (for instance, pit crew strength) is much more likely to lead to large differences in results than the equivalent difference in a race where the field is much more spread out, even more considering IndyCar has been spec over a decade. IndyCar certainly has its own problems, such as the split, where the value of some fields greatly diverged, but the beauty of this is that since these statistics are on the same scale as win totals, the biases are the same. Since I calculated that CART was about 6.25 times stronger from 1996-2001 than the IRL, you can divide the cumulative races led of any of the IRL drivers of that period by that amount if you want. However, this list is unadjusted and has the same biases the win list itself does. If you find certain periods stronger/weaker than others, you can make adjustments as you see fit, but here I strongly prefer the cumulative races led list in general, because much more frequent cautions, restarts, and closer gaps throughout the field make it less likely that pure dominance is going to be reflected, just as any means which tighten the field make it less likely for the best to be rewarded (such as playoffs in almost any sport). I am not much of a believer in clutch. Just like I believe playoffs are merely the final data points of a season and should not completely overshadow the entire much longer season results when evaluating talent, I do not think finishing results (which I view as the final data point of a race) should not completely overshadow what came before too. I realize teams gear themselves to win the prize that is most valued so perhaps some high-profile events like playoffs may deserve more value, but in most cases, there really isn't a significant difference between how hard a team works in the regular season and how hard they work in the playoffs. The playoffs just increase the luck factor, as finishing results do in a race. In Formula One, this is much less apparent because there were for most of Formula One's history fewer competition gimmicks that randomized the field, but they are (let's face it) a way of life in American racing, and I do roll my eyes when many IndyCar fans cite its integrity over NASCAR. It is not as bad, but still has many of the hallmarks of American racing and oval racing in general. This is not to besmirch oval racing at all, which I do enjoy, but it is simply a different culture, and one that reflects pace much less, which is why cumulative races led becomes much more important in evaluating a career.

Using cumulative races led as a measure instead of wins suddenly puts Mario Andretti in the lead instead of A.J. Foyt. Do I agree with this? Most of the other raw stats seem to favor Foyt, as he had 15 more wins (67-52), three more titles (7-4, although to be fair Foyt's 1979 USAC title had no competition, as the other elite drivers were in CART), and three more Indy 500 wins (4-1). However, Andretti had more poles and laps led in his overall career, which seems to imply more pace (admittedly, Foyt spent a great deal of his career as an owner-driver, even many of his winning years in the '70s, while Andretti did not). Foyt had 10 more wins than cumulative races led while Andretti had 9 fewer, which was enough to swing the difference in favor of Andretti. Andretti does have other advantages, such as longevity, as there were 28 years (1965-1993) between his first and last wins, while only 21 for Foyt (1960-1981), but Foyt probably would have won some for Newman-Haas in the '80s also. However, we aren't talking about equipment here since this is unadjusted for equipment strength. Who should be higher according to this? I think Andretti should. You can always debate whether the Andrettis were unlucky and brought their poor luck on themselves (and Mario and Michael had nearly identical ratios in terms of cumulative races led and wins, implying very similar driving styles, while Marco's was substantially worse). I tend to side with a dominant, potentially unlucky driver because it is very, very hard to distinguish a driver's role versus a team's in terms of mechanical failures. Mario Andretti only failed to lose the 1987 Indy 500 because he intentionally slowed his pace down to be more conservative after he had dominated the earlier portions of the race, and this decision to take it easy (as any team owner or manager would recommend) led to an ignition failure as the change in pace was a mechanical shock. Is Mario responsible for this? That's easily open to debate. If drivers like the Andrettis and Paul Tracy had not overdriven their equipment, would a more conservative style have led to more wins (because they didn't have failures) or fewer (because their aggressive style is what put them in position to win in the first place)? None of this is remotely clear, but what I do think is clear is that IndyCar (and NASCAR) drivers with more cumulative races led than wins are undervalued by history for the most part (although there are still a few drivers this applies to who I consider overrated), while those with more wins are generally overvalued (again, there are a few exceptions). Regardless, I like this list better, especially when it comes to drivers with relatively few wins. Raul Boesel and Vitor Meira may have never won races, but they factored in a lot more than many drivers actually did win, which this properly reflects. Just because a driver won a race does not automatically make him or her better than a driver who did not, anymore than Foyt's win advantage over Andretti necessarily makes him better and I suspect that Andretti would have all records except maybe Indy 500 wins if he had completely focused on IndyCar racing in the 1970s and not spent most of the decade focusing on Formula One. Also undervalued will be drivers from earlier periods, which had fewer races per season than the current drivers do, were less likely to have lap leader data recorded in their races, and often raced at Indy and skipped the minor races (some of the most dominant Indy 500 drivers like Mauri Rose, Wilbut Shaw, and Bill Vukovich skipped the races outside Indy not infrequently. This doesn't make Raul Boesel better than Louis Meyer, or on the NASCAR list, this doesn't make Michael Waltrip better than Dan Gurney. The number of starts still matters too.

This list is updated through the 2015 IndyCar season. All drivers with 0.5 or more cumulative races led plus all winners with fewer than 0.5 cumulative races led are listed.

NASCAR Cup

While IndyCar is certainly more of a crapshoot nature than NASCAR, NASCAR has steadily built up the greatest crapshoot mentality in motorsports, stealthily inducing competition gimmicks to make the competition closer over the past decade or two at least (although fans can debate when this started). This is best reflected by the Chase for the Championship, which steadily over time has added more drivers and shorter rounds over the time, making it less and less likely that the champion will actually be deserving. I think Joey Logano has been the best driver this season but unless he wins today at Phoenix (which I don't expect) he will be mathematically eliminated from championship contention, while Jeff Gordon, who has no business inside the Final Four on merit, is automatically locked in (even though he deserved to last year and missed out). NASCAR consistently sacrifices integrity for the sake of the show (and one can argue they were even doing this decades ago when considering the advent of restrictor plates and the balance of performance adjustments to reduce any perceived advantage a manufacturer has), which has led some fans of other forms of racing to compare NASCAR to the WWE. While I think that is going too far (I certainly don't believe they manipulate outcomes to benefit specific drivers...would Jimmie Johnson have won five straight titles while Dale Earnhardt, Jr. has no championships and Danica Patrick no wins if this were the case?) I do think they manipulate the show to make many or most races closer than they arguably should be through the use of debris cautions that would not be cautions in most other series (and would not have been cautions in NASCAR in the '90s or earlier). As a result, dominance is really not rewarded especially now while random luck is rewarded too much, within individual races and the championship as well. In a series run in this fashion, cumulative races led are arguably more important than wins, especially in terms of the most recent drivers. Almost without exception, I consider drivers with more cumulative races led than wins from the last thirty years underrated and drivers with more wins than cumulative races led overrated (although I admit there are still a couple exceptions). In a sanctioning body that has such a crapshoot mentality as NASCAR does, dominance is far more likely to predict future results than consistency will, and that is why their points system is so terrible. Joey Logano and Matt Kenseth get to eliminate each other from subsequent rounds of the chase because their in-race dominance didn't matter anywhere near as much as their poor finishes, because NASCAR does not reward top positions nearly enough and rewards the mid-pack far more than the bottom positions, against the principles of almost any other racing series. Hence, their dominance won't be reflected in their championship ranking most likely (unless Logano wins today), while Harvick is only going to make the Final Four most likely because he probably intentionally caused a wreck on the last lap at Talladega. While this isn't how an organization should be run, we can correct from the biases this induces by using cumulative races led.

In general, the drivers who have a reputation of overdriving their equipment (Rusty Wallace, Geoff Bodine, Ernie Irvan, Buddy Baker) who usually got worse points finishes as a result do all have higher cumulative races led than wins (Wallace's is neck-and-neck with Jimmie Johnson's, despite Johnson's much greater win and championship total, but note that Johnson is ahead of him when reflecting all races equally, as opposed to laps led where Wallace still holds a sizable margin due to his dominance in short track races which have more laps). Because I believe as I stated several times that it's difficult to tell who precisely is responsible for an equipment failure, I believe drivers who dominate early and don't get the results commensurate with how they ran earlier in the race are undervalued while others are overvalued. It can be a measure of equipment or just of sheer luck. For instance, Bobby Labonte was the luckiest driver from 1990-present according to my 'How the Races Were Won' series (indeed, he won two races due to unnatural last lap passes, when Jerry Nadeau ran out of gas at Atlanta in 2001, and when Bill Elliott cut a tire at Homestead in 2003, not even mentioning his off-track win in the 2000 Southern 500 when he took the lead in the pits a few laps before rain ended the race under the same caution). This statistic puts his career more properly in place, where he's behind several drivers considered less than legendary (Sterling Marlin, Ryan Newman, Kasey Kahne, Donnie Allison, etc...) I was already tempted to take Marlin over Bobby Labonte historically because as little as I care about restrictor plate racing, I do think being the best at a particular discipline is better than being a 6th-10th place driver everywhere as Labonte was for most of his prime, and I think Marlin would have been more likely to replicate what Labonte did in the #18 than Labonte would have in the #4 or the #40. While I alone seemingly rate Ernie Irvan over Davey Allison and I don't think it's close (primarily because he was more dominant and more consistent after taking the #28 than Allison ever was, and because he won a far greater percentage of his races naturally), this statistic makes a far better case for it than the win statistic (Allison was generally lucky in his wins, while Irvan was frequently unlucky in the races he lost). While I'm rather indifferent between the cumulative races led list and the win list for Formula One, for IndyCar I prefer the cumulative races led list, and here, I far prefer it. This is one of the best ways to remove team and luck-related factors in a series that seemingly wants to induce them to help the 'show'.

If you asked most fans who the best 'closer' was, they would probably say Kevin Harvick thanks to media hype from Darrell Waltrip and the FOX booth, while if you asked most afns who the worst 'choker' was, they would probably say Kyle Busch because he has a reputation of throwing race wins away and fading. While Harvick is on the 'closer' side and Busch is on the 'choker' side, neither of them are the most extreme examples of that today. Carl Edwards, who has 47% more race wins than he 'should', Jimmie Johnson, who has 32% more race wins, and Brad Keselowski, who has 24% more would be the best closers, while Kyle Busch (.9128) is admittedly the second worst among active drivers with a large number of wins, behind only Dale Earnhardt, Jr. (.8723) but barely ahead of his brother (.9158) would be the worst 'chokers', but bear in mind that you really have to review each individual race to determine whether it was a choke or not. Regardless, the usual perceptions of Harvick as the best closer (and he was definitely a lot closer to that before he arrived at Stewart-Haas, but not since) or Kyle as the worst choker are misguided, and when you compare Kyle to other drivers with a similar driving style in an era with less reliable equipment, Buddy Baker (.5481), Geoff Bodine (.6637), and Ernie Irvan (.7885) are examples of far worse 'choking' than Busch. I think the whole choker/closer thing can be a false dichotomy especially when there are so many factors in determining a race win however. Mike Skinner, the most dominant non-winner ever, should have 3.69 wins by this metric, slightly behind Brian Vickers, Joe Nemechek, Jimmy Spencer, and Elliott Sadler, and slightly ahead of Steve Park, Robby Gordon, and Ricky Craven which definitely sounds about right with regard to how often these drivers factored in a given race in their career. Should he necessarily be considered the worst just because he didn't win? I don't think so. His 3.69 expected wins reflect his ability more than the fact that he got unlucky and never won a points race does. Other drivers who 'should have' won at least one race but did not were Banjo Matthews (2.86), Joe Ruttman (2.57; he is the only other driver besides Skinner to lead the NASCAR points without ever having won a race), Tommy Irwin (1.75), Rick Mast (1.37), Hut Stricklin (1.37), Ted Musgrave (1.09), and Dave Blaney (1.04). Are all those drivers worse than Trevor Bayne (0.14), Daytona 500 win or not? I would say all are better. Winning is not the only thing matters. To be fair to Bayne, he is still a rookie, he has multiple sclerosis, and Roush Fenway Racing is not what it once was, but on a statistical basis, he is definitely lucky to have a win at all.

This list is updated through the 2015 AAA Texas 500. All drivers with 0.5 or more cumulative races led plus all winners with fewer than 0.5 cumulative races led are listed.

Finally, below I provide the ten best 'closers', ten worst 'chokers', the ten most dominant drivers to win a race and least dominant drivers to win a race, for all three series:

Ten Best Closers in Formula One History (with 5+ wins)

Ten Worst Chokers in Formula One History (with 5+ wins)

Ten Best Closers in IndyCar History (with 5+ wins)

Ten Worst Chokers in IndyCar History (with 5+ wins)

Ten Best Closers in NASCAR Cup History (with 10+ wins)

Ten Worst Chokers in NASCAR Cup History (with 10+ wins)

Ten Most Dominant Non-Winners and Least Dominant Winners in Formula One History

If you exclude Ruttman and Sweikert on the basis of the 1950-1960 Indy 500s not actually being Formula One races even though they counted for the World Championship, the next two are Alessandro Nannini (0.53) and Bruce McLaren (0.54; yes, despite winning 4 races).

Ten Most Dominant Non-Winners and Least Dominant Winners in IndyCar History

Note that some drivers prior to WWII may have certain lap leader data not counted.

Ten Most Dominant Non-Winners and Least Dominant Winners in NASCAR Sprint Cup History

Note that some drivers from prior to the modern era may have certain lap leader data not counted.

While I think the top ten closer list is stronger overall than the top ten choker list for Formula One, I definitely think the IndyCar choker list is stronger than the closer list, as the closer list overrepresents early IRL drivers (probably because it is easier to close when you are an experienced driver and your opposition are not). While there are admittedly a staggering six champions plus Tim Richmond on the closer list in NASCAR, I find myself more impressed by the non-champions on the choker list and I'd take most of them over Bobby Labonte too. I do think the interpretation may not be as obvious as it seems because especially for drivers with relatively few wins, it can be easy to get really lucky and thereby have more wins than you deserve. I don't really think Bobby Labonte is the best closer in NASCAR history, but merely the luckiest driver. Was Buddy Baker the worst closer or merely the unluckiest? Where does luck begin and properly assessing risk end? All that can be said for these lists is they definitely do reflect something, and particularly on the winner/non-winner lists, I would invariably prefer the driver who had more cumulative races led. If you believe that drivers are responsible for their overdriving inducing their own poor late-race results, you will invariably prefer the drivers with more wins than cumulative races led ('closers') all else equal, but if you think racing is moving in a crapshoot direction in general (as I do, and I think even Formula One is moving in that direction but it is masked because of the Mercedes dominance) you might prefer the cumulative races led list. However, what matters most is that there is not only one way to assess careers. There is more to consider than merely championships and wins, and hopefully this statistic will be a step in understanding that.

Sean Wrona is the Managing Editor of racermetrics.com, the Webmaster of race-database.com, the winner of the 2010 Ultimate Typing Championship at the SXSW Interactive Conference in Austin, and the ratings compiler and statistician for the Mensa Scrabble-by-Mail SIG. He earned a master's in applied statistics from Cornell University in 2008 and previously digitized several seasons of NBA box scores on basketball-reference.com. You may contact him at sean@racermetrics.com.

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