Competitive Depth

by Sean Wrona

After compiling weighted season scores for Formula One, IndyCar, and NASCAR, my next goal was to use these data to measure field depth, but my earliest attempts at doing so which simply involved summing drivers' scores were not turning out right. Over the past few years, I have been sharing ideas with Adam Steele of Football Perspective, who is also interested in advanced auto racing statistics. He suggested I measure the competitive depth of auto racing fields by taking the average season score for each driver in the field, dividing it by the standard deviation of season scores in the field, and then multiplying by the number of starters. The ratio of mean to standard deviation is known as the signal-to-noise ratio and is the reciprocal of the coefficient of variation. Consider two fields of three cars, one of which contains season scores of 15, 8, and 1, and another where all three drivers have season scores of 8. While both sets of data average out to 8, most fans would argue the second field is more competitive because any of those three drivers could theoretically win as could any superstar driver (which I have previously defined as a driver with a sustained weighted season score average of 5). It stands to reason that a win is more impressive when there are more potential contenders who could win, so fields with smaller standard deviations (those seasons where the slower cars are better able to compete with the faster cars) should be rated higher than those fields where the faster cars are pretty much uncontested. Needless to say, this year's Formula One season will not do well.

Formula One

The deepest period in Formula One was quite a long time ago but it shouldn't be a surprise if you think about it. Excluding the early Indianapolis 500s, which claimed the top ten positions in competitive depth largely because it's easier to score a sizable average percent led or percent beat in a single race than to sustain it over several races, and the Indy 500 drivers almost never crossed over to race in Formula One-sanctioned races in the 1950s, while the F1 drivers almost never crossed over to race in the Indy 500, which was a World Championship race, but not a Formula One race. One might as well throw those races out. Having done so, the four deepest races in Formula One races all came from the same season: 1978. Although this may seem counterintuitive since there were only six winners that year (which isn't that abnormal historically in F1), it's easier to understand this when you realize that there were seven consecutive different champions from 1976-82 (James Hunt, Niki Lauda, Mario Andretti, Jody Scheckter, Alan Jones, Nelson Piquet, and Keke Rosberg). The deepest race ever, the 1978 French Grand Prix, not merely contained seven World Champions (although not those seven, since Emerson Fittipaldi was in the field and Piquet was not) but also fourteen other race winners (Ronnie Peterson, John Watson, Jacques Laffite, Riccardo Patrese, Patrick Tambay, Didier Pironi, Gilles Villeneuve, Jochen Mass, René Arnoux, Vittorio Brambilla, Carlos Reutemann, Patrick Depailler, Clay Regazzoni, and Jean-Pierre Jabouille). I realize several of these drivers did not win many races, but still, that makes 21 winning drivers in a 26-car field. That is amazing, and when many people cite Peterson, Villeneuve, Arnoux, Reutemann, and Regazzoni as being some of the best drivers to never win a championship, that makes this even clearer. How often has Formula One ever had twelve legitimate championship contenders at once (and that's even leaving out Laffite, Patrese, and Pironi)? That field had more winning drivers in it than the current field has drivers in it. Clearly an average win is more valuable in that period than in more recent decades when usually only two or three teams have been competitive, although one could make a counterargument that drivers winning in weaker cars had more value in seasons with less competitive depth. The entire period from 1974-1984 rates astonishingly highly, as those eleven seasons are all ranked within the top twelve. Schumacher's era does rate towards the bottom as most would expect although there are other seasons from other eras that appeared rather weak as well (certain seasons in the 1950s). However, the nadir for competitive depth in Formula One is actually now. It may not end up being so because my season scores are generally based on a five-year weighted average and in the first or last year of a period, they are only based on three years of data (the first year and the two years after or the last year and the two years earlier). This will likely increase the standard deviation of the field and therefore result in a shallower field overall, which partially explains why 1950 and 2015 are the bottom two seasons in history. Upon ignoring the standard deviation, this season is below average in competitive depth and appears to be worse than most seasons, but it isn't necessarily the worst. However, anyone watching Formula One in 2015 will note that there are only three drivers winning or for the most part even contending for wins, which is historically low even when compared to the Prost/Senna, Schumacher, or Vettel periods, so it wouldn't surprise me at all if this season does actually end up as the weakest in history in terms of competitive depth, even when considering the as of now unknown late 2015, 2016, and 2017 results. These data are based on all Formula One races excluding today's just-completed race at Monza.

Formula One seasons by depth

Now it gets more interesting. What happens if I adjust drivers' win totals to account for the varying strength of the field? Rather simply, pretty much every driver from the '70s and early '80s rises in terms of adjusted win totals while almost everyone else falls. While the above reflects the average field strength for every race in each season, I divided each individual race's field strength by the average field strength for all races in order to determine how valuable each win was. Normalizing the field strength variable allows me to create an adjusted win list wherein the sum of the number of adjusted wins perfectly matches the sum of the total number of races, so we can observe how much on a percentage basis each driver goes up or down relative to their actual win total after considering their level of competition. Considering how much stronger the fields from the mid-'70s to the late '80s were than any other, all the drivers who peaked in this period increased considerably. Among drivers who had five or more Grand Prix race victories, this group was led by Jacques Laffite who gained 27.12% over his actual win total, who was followed by Mario Andretti, Alan Jones, Gilles Villeneuve, Carlos Reutemann, Jody Scheckter, James Hunt, René Arnoux, Ronnie Peterson, Clay Regazzoni, and Niki Lauda, who each had a 20% increase in their adjusted win total from their actual win total. The ten drivers who lost the most were led by Nino Farina (-21.08%), Rubens Barrichello, and Ralf Schumacher, and followed by Mika Häkkinen, Nico Rosberg, Tony Brooks, Juan Manuel Fangio, David Coulthard, Michael Schumacher, and Alberto Ascari. Most of these drivers indeed had such dominant equipment relative to their peers that they were often uncontested at their peak. This indeed gives some idea of which drivers benefited the most from superior equipment. However, in the grand scheme of things, the actual ranking of race winners does not change a great deal after these adjustments are made. Schumacher, Vettel, and Hamilton may have all lost wins due to this adjustment, but they maintain the same positions. However, Lauda's large increase as well as Jones and Andretti's are worth noting. In my previous column, I suggested that Alan Jones was likely one of the most underrated Formula One drivers in history since he managed to lead in weighted season score for three straight years from 1979-1981. Considering how deep the field was at the time, this result only further supports this idea. Andretti winning both against the deepest field in Formula One history (in the 1978 French Grand Prix) and winning the championship in what was also the deepest field in history by a fairly sizable margin is a major feather in his cap and although he is sometimes cited as one of the weaker Formula One champions based on his career after 1978, that would seem to be a mistake, especially considering how strong the field was in that period as well. Interestingly, Stirling Moss no longer appears as the winningest non-champion after this adjustment is made and drops below Carlos Reutemann. However, to Moss's credit, he was a major factor in 1961, the outlier season that also appears among the deepest seasons in history (and no wonder, since Dan Gurney, Jim Clark, Bruce McLaren, Jack Brabham, John Surtees, and Graham Hill all went winless despite driving full-time).

Formula One win list (adjusted for field strength)

NASCAR Cup

While I was initially unsure when the peak for competitive depth would be for Formula One, since I knew it would likely be long before I became a racing fan, I was pretty certain the peak of competitive depth in NASCAR would be somewhere between 2000-2003 where there were more legitimate contenders to win races than there were ever before or after. As much as NASCAR has always hyped that fifteen or twenty drivers could win any race, the early 2000s was the only time period when something like that actually came close to existing, as the rookies of that period (such as Tony Stewart, Dale Earnhardt, Jr., Matt Kenseth, Kevin Harvick, Kurt Busch, Jimmie Johnson, Ryan Newman, Jamie McMurray, and Greg Biffle) all fought for wins from the very beginning of their careers while the previous generation's stars like Dale Earnhardt, Rusty Wallace, Bill Elliott, Dale Jarrett, Ricky Rudd, and Sterling Marlin were all still competitive as well. I would have guessed either 2001 or 2002 was the peak in competitive depth, but I was slightly surprised that it ended up being 2002 with 2001 only in fifth. However, just as in the case of Formula One, where the vast majority of the deepest seasons were all in one timespan from 1974-1984, NASCAR's top fifteen seasons in terms of competition all came from the time period of 2000-2014. I must admit I am considerably more impressed by 2000-2003 than anything since, since starting in late 2003, NASCAR moved in a gimmicky direction with a sharply increased number of cautions, many of which were controversial debris cautions, lucky dogs, wave arounds (neither of which I actually mind as long as NASCAR throws cautions as infrequently as they did in the '90s, which they may never do again), the chase, double-file restarts, green-white-checkered finishes, and most recently a win-and-in version of the chase, all of which artificially induce closer competition than actually existed. 2011 in particular was not nearly as competitive as it looks here, as there were a number of unnatural wins from drivers who are rarely competitive for wins (Trevor Bayne, Paul Menard, Regan Smith) or wins that were by definition natural but one could argue weren't (David Ragan, due to the nature of restrictor plate racing and/or tandem drafting) or wins by drivers who were only competitive at a handful of tracks, which raised their season scores for all tracks even if they weren't competitive elsewhere (Marcos Ambrose, who never showed much on the ovals). Clearly, 2011 should be closer to the other seasons between 2009-2013, which still isn't bad, mind you. Interestingly, I notice that NASCAR's peak in competitive depth is exactly in sync with its major league TV deals that lasted from 2001-2014. Now that the NASCAR bubble has clearly popped and it is reverting to a level of popularity more like what it had in the 1990s (only this time in decline, not in ascent, and ESPN, TNN, and TBS, the cable networks that had most of the races in the '90s, were all more popular than Fox Sports 1 and NBC Sports today). As a result, this year appears as the year with the least competitive depth of any since 1999, and was even behind 1991-93, which was a historic level of competitive depth at the time considering how many drivers were competitive for wins in that period, even in questionable equipment (Harry Gant with Leo Jackson, Geoff Bodine with Bud Moore, and Ernie Irvan with Morgan-McClure in particular). Although it is counterintuitive that 1993 (where Dale Earnhardt, Rusty Wallace, and Mark Martin combined for 21 wins) appears deeper than 1991 and 1992 (where no driver won more than 5 races), it is probably helped by Allison and Kulwicki still being alive in several races plus the addition of Gordon and Bobby Labonte (since these are 5-year weighted averages, Gordon and Labonte being the first significant breakouts since 1988 rookie Ernie Irvan's breakout in 1990 gave the field a boost since Gordon and Labonte's 1995 success is included in their 1993 season scores). Seasons which had particularly shallow competitive depth do appear weaker than their surroundings. With Roush and Childress rapidly becoming non-factors after Matt Kenseth and Carl Edwards left Roush and Kevin Harvick left Childress, not to mention teams adapting to NASCAR's attempts to manipulate the race by adopting IndyCar-style split strategies wherein top drivers will be on every strategy, thereby preventing mid-pack and backmarker drivers from stealing wins like they did in 2011, 2014 and 2015 look increasingly dire, but part of that could simply be that the standard deviations for those seasons are higher because they are based on fewer data (when ignoring the standard deviation differences, this season doesn't look all that much worse than the previous few, except for the period when Kyle Busch was injured). It should come as no surprise to NASCAR fans that the 1960s were the worst period, as there were numerous short races on paved or dirt short tracks, most frequently 200 lap events at .5 mile short tracks. Most of these races had 20 cars or fewer and quite often five or fewer stars in them. It seems clear that these races shouldn't count as much as fields that were deeper. I'll add that prior to the modern era of NASCAR, superspeedway races and the races at the Daytona Beach/Road Course generally had way more starters than the now-standard 43. Nowadays, when the field largely contains the same drivers every week, field depth remains constant (except due to injuries or in some rare cases when one-offs like road course ringers are actually competitive), but back then, the superspeedway races and the marquee races in general were indeed the most important to win as many more drivers were entered. Nowadays, not so much, so the superspeedway races prior to the modern era were generally the deepest races in NASCAR history, but the short track and dirt track races were so shallow that the average field in the pre-modern era seasons was considerably worse than anything since, with the notable exceptions of 1950, 1951, 1956, and 1960, which did have more depth than some modern-era seasons. I expected 1965 to be the weakest season in history due to the Chrysler boycott where Richard Petty and David Pearson sat out most of the season, and was surprised that it slightly beat 1964 when everyone was competing, but admittedly Petty, Pearson, and Ned Jarrett were the only stars running the entire schedule and Joe Weatherly and Fireball Roberts's deaths did cause NASCAR to take a considerable hit in field quality.

NASCAR Cup seasons by depth

Below are the 59 drivers who have won ten or more NASCAR Cup races in their career sorted by adjusted win total (plus Paul Goldsmith, Clint Bowyer, and Jamie McMurray, none of whom managed ten wins but were still ranked higher in adjusted wins than the lowest driver who actually has ten wins). Richard Petty has such a large advantage in actual wins that he still has the advantage when adjusting for field strength, but his win total no longer seems so otherworldly, and David Pearson is no longer second as Jeff Gordon and Jimmie Johnson who competed against the strongest average fields in history surpass him. Does that mean I necessarily think they're better? No, because Gordon and Johnson had the strongest cars almost their entire relevant career (which Petty and Waltrip also did, but one can argue Pearson, Earnhardt, Yarborough, and Allison did not), not to mention that Gordon and Johnson were the only drivers of the lot to stay with one team for their entire career, which helped their career stability (imagine what Bobby Allison could have done with that kind of career stability). However, this still means Gordon and Johnson should not be brushed aside historically as many are willing to do, and I'd definitely unquestionably take both of them over Waltrip, who I would almost certainly put last of the eight megastars. The contingent who argues that Hendrick has benefited from cheating too much to argue in favor of Gordon and Johnson must note that Darrell Waltrip's team owners in Junior Johnson and DiGard were much worse cheaters because teams didn't get away with nearly as much after Gary Nelson became NASCAR's inspector (to be fair, Nelson, NASCAR's top cheater before becoming its top inspector, also spent time at Hendrick but it was before Gordon and Johnson got there). Modern drivers one might not expect to be so high such as Matt Kenseth and Kyle Busch make very strong cases for legend status. However, it's worth noting all the pre-modern era drivers are underrated on this list because lap leader data is missing for many races in the '50s and '60s, particularly those on short tracks, making the pre-modern era races look weaker than they really did, not to mention that the season scores were already likely lowered for many drivers due to those data being missing, so in effect the lack of perfect lap leader data in the '50s and '60s does tend to underrate the earlier drivers, but not by as much as I think most fans underrate the modern drivers. It certainly puts careers in a very different perspective. Obviously, a more accurate list would adjust for whether wins were natural or unnatural (Bobby Labonte and Ryan Newman in particular look way too high, and they aren't the only ones) and would adjust for equipment strength, but this does have value. Ned Jarrett struggled on the superspeedways (where the races were much deeper), dominated on the short tracks (where the races were much shallower), and flat out dominated the 1965 season because the Chrysler boycott eliminated most of his competition. He won over half his races in 1964-65, which were the two weakest seasons in terms of competitive depth in NASCAR history, and when this was considered, Ned Jarrett dropped a whopping 44.97% when adjusting for field strength, the most of all drivers with ten or more wins. He was followed by Bobby Isaac (41.93%), Dick Hutcherson, Jim Paschal, Junior Johnson, Rex White, Richard Petty (who much like Schumacher dominated against weaker fields but still led the list either way), Dick Rathman, Lee Petty, and Joe Weatherly. All drivers who dominated on short tracks prior to the modern era fell, so this does check out. I think all these drivers will likely be underrated since they likely all dominated many races with incomplete lap leader data. Among the primarily modern era drivers, Benny Parsons dropped the most (12.43%) because he had most of his success in the late '70s, which was also a rather weak period with only five or six competitors most races. Drivers from prior to the modern era who primarily raced on superspeedways and frequently ignored the short track races like Fred Lorenzen, Fireball Roberts, Buddy Baker, hardly changed at all even if they raced in weak periods, which indicates that drivers like that may be a bit underrated relative to the full-schedule drivers. It should not be surprising that drivers who peaked between 2000-2005 gained the most from this win adjustment. These drivers were led by Ryan Newman (40.35%), Kurt Busch, Jamie McMurray (whose one win in 2002 likely makes up a good portion of the difference), Dale Earnhardt, Jr., Greg Biffle, Tony Stewart, Matt Kenseth, Clint Bowyer, Kevin Harvick, and Denny Hamlin. Apparently, the last fifteen years were as good as it gets with regard to competitive depth, although I think that era is coming to a close. It's too bad the races were run with less integrity, and it's difficult to tell how much NASCAR's tendency toward gimmickry has artificially increased its competitive depth.

NASCAR Cup win list (adjusted for field strength)

You may notice although I usually cover IndyCar right along Formula One and NASCAR, I have not done so in this article. The reason is that I have not yet decided what to do with the split. Since the early IRL season scores are not adjusted to reflect the fact that the IRL field was weaker than the CART field from 1996-2001 without question, and since I'm not really sure which series was deeper in 2003-2007 (I can see fans arguing either way depending on their preference...all that most people might agree on is that both series were shallow in the later seasons of the split), it's going to take a lot more work to sort out the split and make proper adjustments to reflect field differences between the two series during the split years. Formula One and NASCAR have had nothing quite comparable to that so I only covered those series in this article, but I will be addressing the IndyCar split shortly. Finally I provide below the strongest and weakest fields in both F1 and NASCAR history.

The ten deepest Formula One fields ever (excluding Indy 500s)

The ten shallowest Formula One fields ever

The ten deepest NASCAR Cup fields ever

The ten deepest modern-era NASCAR Cup fields ever

The ten shallowest NASCAR fields ever

The ten shallowest modern-era NASCAR fields ever

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.

---