The season finale of the 2023 Stock Car Pro Series advertised itself by proudly announcing that there were no less than seven title contenders battling for the premier Brazilian motorsport title. That sounds intriguing, right? Only one minor issue with the claim: based on the points standings heading into the Super Final, it would have taken a major misfortune for championship leader Gabriel Casagrande his second title in the two final races of the year. In fact, of the seven title contenders, five were eliminated in the first race and in the second race, the only remaining contender Daniel Serra would have needed a win with Casagrande not finishing higher than 17th to steal the title. While Casagrande surprisingly obliged by finishing 21st and outside the points, Serra fell way short of the needed victory so there was absolutely no doubt about the outcome of the championship.

It should be noted that the author does not begrudge the marketing and social media departments of the series doing their job nor is he complaining about the Interlagos races. The point is that there is a difference between a theoretical and a real championship fight. The 75th season of Formula 1 will begin soon and many fear it is going to be a Max Verstappen walkover – a rather common state of affairs in Formula 1 these days. As the series desperately seeks another last-race showdown like in 2021 and 2016, it does beg the question of what a close title fight actually is. As such a call is inherently subjective, it is very likely for different definitions of a close title battle to emerge. The author himself has, in a different context, once defined a close season as more than one driver having a mathematical chance at the championship with two Grands Prix to spare, but that was a consideration made with marketing departments in mind.

In this Gravel Trap, the author is looking to try a different approach to this question – a mathematical one. Using the magical powers of standard deviation, the idea is to look at the standard deviation of championship winners in the 25-points-for-a-victory era and therefore try to define a range of possibilities for them to lose the championship lead in the final Grand Prix of the season without technical issues getting involved.

There are a couple of issues that need to be addressed first before the number crunching begins. The quintessential problem is the sample we are working with. Because so many seasons since the introduction of the 25-points-for-a-victory system have not gone down to the wire and a number of those have not even been close by anyone’s standard, only going with the five seasons that were decided at the last race of the season is not very helpful. In addition, dominant drivers are the drivers to beat. When trying to conquer Max Verstappen, any driver seeking to claim the title must obviously also match his consistency on Sundays. However, in turn using all seasons leaves the problem of the deviation unduly shrinking – after all, when aforementioned Max Verstappen rolled pretty much unchallenged to ten victories in a row last year, there simply was no deviation. To solve this dilemma, the author decided to include those seasons but will use two standard deviations for seasons that were decided with more than three races to spare. This is by no means a perfect solution but it serves the purpose of this exercise, simulating a hypothetical scenario in which their teammate or a possible rival from a different team was able to go tip for tap with them.

Furthermore, classification despite retirement and poor results caused by technical issues (such as the very first example in the sample: Sebastian Vettel losing a near-guaranteed victory at the 2010 Bahrain Grand Prix because of a spark plug problem) could prove problematic. After a period of consideration, the author decided to remove results where a driver could not finish the race, but take all other results as they are. 

While the point of the exercise is to calculate deviation without technical retirements, it is simply not reasonable to calculate every negative factor within a finish. The line between a technical issue and an expected part of racing is very hard to draw, therefore such a distinction would probably serve to only make the numbers more erratic and subject to bias. To take a simple, fictional example: should a driver be given a better finish when he most likely would have finished higher without picking up damage making contact with another car on lap 1? If so, only if the accident was not his fault? And who decides whether it was their fault? Answering those questions is not productive in a purely statistical approach and thus more suitable for discussions on our forums. 

A minor point of contention the author anticipates is including the pre-turbo years. The very nature of racing in the turbo era has clearly altered F1 as a whole. The author has decided to include 2010-2013 as well: while the impact of power units still is stronger than it was in the V8 days, the sport is also well beyond the period where having a Mercedes-Benz V6t was a guarantee for a competitive car regardless of chassis quality. Therefore, while it is quite unlikely that we will see parity similar to the 2010 and 2012 seasons any time soon, in a genuinely competitive season there is no reason to assume that multiple teams could not at least hypothetically challenge for wins on any given Sunday.

With those issues out of the way, let us take a look at the standard deviations of the 14 seasons we are working with (seasons marked with an asterisk in the table are seasons aforementioned increased deviation was applied to; the average finish in those seasons was multiplied by 1.5 as well to reflect aforementioned hypothetical competitiveness). This table is not sponsored by Microsoft Bing, but the author will still mention that he used its standard deviation calculator in the hopes of getting GP Rejects a sponsorship arrangement.

Taking the average from these 14 seasons we conclude that the average deviation of the championship winner in a competitive season is 2.208 positions with an average finish of 2.477. What does this mean for the purposes of this exercise? Simply put, an average championship contender cannot reasonably be expected to finish any lower than 4.685th – since you cannot finish in a partial position, this needs to be rounded; based on the way these numbers have decreased in recent years, the author feels it is a safe choice to round down. Therefore the worst finishing position that can be expected for a title contender in the current era of Formula 1 in a normal race is fourth place.

Now, even in that scenario it logically cannot be guaranteed that the other title contender will be on the top step of the podium. Formula 1 history has seen a few final races of the year won by drivers aiding their teammate by denying points to their championship rival. Bruce McLaren and Maurice Trintignant finishing 1-2 ahead of Tony Brooks to aid in securing Sir Jack Brabham’s first title as the Australian ran out of fuel on the final lap and 1993 F1 Indoor Trophy World Champion Rubens Barrichello taking victory at the 2003 Japanese Grand Prix to deny Kimi Räikkönen’s small chance at the crown are examples that come to mind of the passionate F1 fan.

Therefore the mathematical conclusion is to take aforementioned average position of a championship winner and compare it to the “worst-case scenario” for his title rival. With that we come to the final result that the points differential between a second-placed driver hoping to win the title without needing to depend on retirements and the championship leader ahead of the final race must not be larger than the difference between second and fourth place – 6 points under the current system. This also fits when looking at it from a much more primitive mathematical perspective, as even if the two challengers trade 1-2s all year, six points is the difference between first place and second place with a fastest lap of the race, therefore making this also the difference if teammates hypothetically ceased to be a factor. 

Once it becomes clear just how small those margins are, it is also evident why even the slightest edge over a 20+-race season will spiral into a premature title decision. More than six points – Max Verstappen had that edge over the second-place finisher in the WDC after the fifth Grand Prix in 2023 and after the seventh race in 2022. Sir Lewis Hamilton had it after the fourth in 2020 and after the fifth in 2019. Even in his fights against Vettel in 2017 and 2018 he had those margins before the end of the European season despite Vettel pulling off one of the greatest seasons of a Ferrari driver in the team’s long history in 2017. With the ever-increasing corporatisation and professionalism of the ten franchises, Formula 1, as it currently is, does not really allow for exciting title fights unless things align perfectly.

In an interview with Channel 4, Sir Lewis Hamilton indirectly pointed out the issue with these extremely small margins: 

“If we continue like this, maybe Ferrari will dominate in the next few years, or maybe McLaren will, or maybe Mercedes will get back in front but I think this is not the best thing for the fans. We shouldn’t have the chance to dominate for a large number of years, the battle for the top positions should be closer. Unfortunately, however, Red Bull could seriously dominate even in the next three seasons.”

While it must be emphatically stated that Hamilton only has an issue with this state of affairs because it is no longer him that is the dominant force, it is also true that he is factually correct. This is very much exemplified in the only season of the 2020s (so far) that went down to the wire: the 2021 season cannot really be described in the way old title fights (or even the early phases of 2017 and 2018) were, a give-and-take between two (or more) strong teams with great cars working better or worse at any given venue. Instead, after the feeling-out process of the first few races, it was more Red Bull and Mercedes trading periods of dominance that more or less just – for lack of a better term – happened to mathematically align in a way that left both Max Verstappen and Sir Lewis Hamilton tied on points ahead of the Abu Dhabi Grand Prix, along with other highly unexpected happenstances such as the Azerbaijan Grand Prix, where both title rivals lost clear-cut chances at 25 points, the chaotic Hungarian Grand Prix and the half-points farce at the Belgian Grand Prix.

It is undeniably the most fatalistic position to take, but the thought that 2021 may very well have been the only genuinely close championship battle of this decade is not as improbable as one might think it is. With those considerations in mind, it regrettably feels like the introduction of a NASCAR-esque “playoff system” – despite how much it would hurt the series in the future – seems only a matter of time, as one-sided seasons like 2020 and 2023 will become much more common. There are better solutions available, such as reducing the number of Grands Prix or significantly reducing the margins in the point system to reduce the value of victories, but right now there has been no call for either of those changes by prominent figures inside the sport.

For the time being, all Formula 1 fans are left with are more complaints about whomever currently wields the sceptre of domination in their hand and hoping that the 2026 rule changes will finally complete the parity puzzle Liberty Media is working on. This is not only sad for the fans, but also for the very drivers who achieve these feats of dominance, as their undeniable greatness will be buried under an avalanche of boredom and accusations that they only are as great as they are because of their superior cars.

To put it in the words of American mountaineer Conrad Anker: “The summit is what drives us, but the climb itself is what matters.”

Sources: Channel 4, Palm Beach Post, StatsF1, Stock Car Pro Series

Image Sources: emperornie (licensed under CC BY-SA 2.0, cropped and resized), Lukas Raich (licensed under CC BY-SA 4.0, cropped and resized), Stock Car Pro Series, Wastrick (licensed under CC BY-SA 4.0, cropped and resized)