F1 Analysis
Mathematical and Statistical Approach to Formula 1
2021 F1 Mathematical Driver Rankings
formula1stat	Statistics and analysis	 December 14, 2021 January 12, 2022 15 Minutes
Determining who is the best F1 driver in any year is always a tricky business due to the major differences in car performances. Here is a ranking of the best drivers based on a mathematical model (more info on how the model works here). In short, looks at the results of a driver each year versus their teammate, and predicts what ratio of the team's points each driver will score. The predictions are then adjusted for the actual results.
There are some pros and cons to this approach. One big advantage is that there's no chance of favouritism. It also doesn't suffer from recency bias , with each GP being valued the same. On the other hand, only focusing on race results can oversimplify things, with a lack of nuance in how results were obtained. For this reason the results should not be considered to be absolutely definitive, and where appropriate I have provided some context to the ratings. A good way of thinking about the rankings is that they are measuring how impressive a driver's results are, given their machinery. This is subtlety different from ranking how good each driver has been, although obviously there's a high degree of correlation between the two.
Prediction vs Reality
Before the season began, I used the model to make some predictions about the 2021 season. Since those were made, the model went through some significant changes (most notably accounting for age and experience), which have generally improved the predictions (lowering expectations for Alonso, for example). The main adjustments made during the season is that is that the Sainz/Norris pairing has been raised considerably, due to both of them having a strong season and Sainz's poor stint at Renault counting for less of his career overall. In addition, Russell is now considered to be stronger than Latifi, who was previously placed higher than Russell due to having stronger race results in 2020.
Who performed better than expected?
Before we get to the actual rankings themselves, let's have a look at whether a drivers performed better or worse than expected given their career as a whole:
Just a reminder, the only thing that matters here in points (or finishing position), If one driver is considered to overdeliver, their teammate is considered to underdeliver, because the assessment is only made relative to their teammate, assuming 1 teammate throughout the year. Most of these results are probably expected given the 2021 season. If your favourite driver has performed worse than expected, it doesn't necessarily mean that they've done a bad job (3 of the underperforming drivers are in the top 8 of driver rankings), it just means that the model expected their results relative to their teammate to be stronger given their previous F1 careers.
*No predictions were made for AlphaTauri and Haas due to rookie drivers. In the case of AlphaTauri, a ranking has been obtained for Gasly and Tsunoda based on Gasly's previous F1 career. The Haas drivers do not have any link outside of each other, so there's no ranking for 2021. The only conclusion the model makes is that Schumacher's results were stronger than Mazepin's this year.
Driver Rankings
Percentages are relative to an average season of Hamilton's career in a competitive car. The placement into tiers is to provide a bit more context to the results, but the tiers themselves are somewhat arbitrary. They start at C Tier (results probably not strong enough given the car they drove) and progress to S Tier (an fantastic performance). Every driver has a graph showing how their ranking changed and stabilised over the season, placed together with a few other similarly ranked drivers. Please take note of the differing y-axis if comparing different graphs.
C Tier
18) Yuki Tsunoda, 52%
Tsunoda is not only the lowest ranked driver, but he has been so (by a reasonable margin) for almost the entire season. After initially impressing (Ross Brawn called him "the best rookie in years" after his debut) Yuki struggled to keep pace with Gasly, both in qualifying and race trim. Whilst he may be considered lucky to be kept on another year, Red Bull typically give drivers 2 years despite their ruthless reputation. Improvements in qualifying towards the end of the season were encouraging, and his fantastic 4th place in the season finale may serve as a springboard going into 2022. However, the fact remains that Gasly ended up with more than twice as many points finishes and three times as many points. There's no doubt that Tusnoda will need to find further improvements to stay on beyond 2022, particularly as backers Honda are pulling out of the sport.
17) Antonio Giovanazzi, 56%
Giovanazzi's season had some highlights (particularly in qualifying), but the results were not strong enough to save his drive. At points his form seemed erratic, qualifying 7th and 10th in the Dutch and Italian GPs before lining up 18th on the grid in the next 2 races. Of course this was mostly a trait of the season, with Russell suffering a similar fate at times, but it does undoubtedly make it tricky to rate his performances.
Race finishes as a whole were similar to Räikkönen's, which the model doesn't consider particularly impressive considering Kimi's age. Furthermore Kimi landed the bigger results, which is the reason Antonio ended in the disappointing C Tier. Whilst he is clearly good enough for F1, that isn't always enough in this sport given that there are probably at least 25 drivers that fit that category at any given time. The fact that he was not selected, or even seriously considered, for a Ferrari drive last year when one became available speaks volumes about his ultimate potential, and no one can say that he wasn't at least given a fair opportunity.
16) Kimi Räikkönen , 64%
Kimi's final year can be considered a success given that he easily outscored his teammate despite missing 2 races. He was much closer to teammate Giovanazzi than the 10-3 score in his favour suggests, with a pair of 8th places elevating his standings considerably. The model partially corrects for his by giving credit for non-points finishes, as well as accounting for the ease in which a driver can rack up a high percentage of a. teams points in an uncompetitive car. Whilst Kimi failed to go out on a high in Abu Dhabi, his performances over the year were perfectly respectable.
15) Valtteri Bottas, 67%
This year was a good demonstration of Bottas' strengths and weaknesses. His qualifying performances have remained impeccable, which is probably what kept him in the team for so long. He actually holds the record for most poles without a championship win. (The contrast to Red Bull regularly switching drivers due to qualifying underperformance is not a coincidence.) However, he has been much less impressive at recovery drivers and general race pace. Overall his results have been consistently adequate, with more 3rd places than any other driver. The low ranking at the start of the season was mostly due to DNFs (at Monaco and Imola), but subsequently recovered to about the level expected of him.
14) Sergio Pérez, 70%
Pérez was hired by Red Bull after a long deliberation during 2020, and the results were mixed. The model thinks that Pérez is a slightly stronger driver than either Albon or Gasly, but also concludes that either would have been able to rank up as many points as him in 2021 due to a disappointing year.
There's a perception that Pérez improved as the year progressed, but that certainly isn't shown in the points: He scored 36% of Red Bull's points before the summer break and just 29% afterwards. Pérez's ranking ahead of Bottas may raise a few eyebrows given that Bottas easily outscored him. It comes from the fact that the Red Bull driver has had a slightly stronger career thus far compared to his Mercedes equivalent. The model also concludes that the Mercedes was the better car/team over the course of the year, which makes Pérez lack of consistently strong results more forgivable.
13) Lance Stroll, 74%
This is considered to be Stroll's strongest year yet. I don't think many people would predict that he would be within 10 points of Vettel at the end of the year. A review at the summer break (written before Vettel's unfortunate penalty) suggested that Stroll was perhaps more consistent than Vettel but with a lower peak, and this is still a reasonable summary of their results across the season. Stroll still ended the year with more points finishes (9 vs 7), but a significantly worse best result (6th vs 2nd). Despite (somewhat justified) accusations of only keeping his seat due to his personal relationship with the team, Stroll continues to demonstrate that he is indeed F1 worthy.
12) Nicholas Latifi, 75%
The 2020 season the model considered Latifi to be a stronger driver than Russell due to his surprisingly better race results that year. Given the lack of data and lack of a competitive package, it was a tentative conclusion, which has corrected itself in 5e 2nd half of this year. Two points finishes for Latifi can be considered a successful season given where Williams were before the year started. However, Latifi actually had the same number of top 11 finishes as last year, despite several more races and a better car. Qualifying continued to be a major issue, only narrowly avoiding a clean sweep of defeats against Russell. A hangover from 2020 probably means that Latifi is still rated a little high, and the challenge of Albon next year will be fascinating to see.
A Tier
11) Sebastian Vettel, 79%
Vettel has fallen from his 7th place last year, despite the general perception that his performances have improved. After being hired by Aston Martin to lead them into a new era, any disappointment at their slide from the front to the back of the midfield has been well hidden. The model thinks that Vettel significantly underperformed in 2021 (as in 2020), with several points scoring opportunities coming to naught. The most notable was of course Hungary, a race which showed, if any proof was needed, that Vettel can still perform at a high level when the car allows.
10) Pierre Gasly, 82%
Whilst Gasly's performances are effectively locked in for the year given his rookie teammate, his rating has been steadily rising throughout the year. This is because his poor 2019 performance (and therefore overall career performance) seems considerably more forgivable given Pérez's struggles versus Verstappen. Gasly's performances have been hard to read at times, but he ended the year with his highest ever points total.
9) Esteban Ocon, 84%
It may be hard to recall so far back, but Ocon's performances at the start of the season were impressive. In the first 5 races he scored 4 times, and had over double the points of his teammate Alonso. Alpine renewed his contract around this time, only for his form to slump for a few races. He returned to the points, then earnt a fantastic first victory in Hungary, holding back Sebastian Vettel for much of the race. Overall, he was outpaced and outscored by Alonso in the last two-thirds of the season, and amazingly his fortunate (but well earnt) victory his only top 6 finish of the year. Despite this, the model considers 2021 to be his strongest year to date.
8) Fernando Alonso, 87%
After a quiet start to the year, Alonso became a beacon of consistency, with more points finishes than teammate Ocon. The podium in Qatar was well earnt, despite some good fortune with his starting position, and he has also shown some feisty defensive driving without ever clearly going over the limit.
Before the start of the season the model didn't factor in Alonso's age or the fact he was returning after a gap, and thought that this match up would be very one-sided, but factorising these into the equation leaves the model thinking Alonso only slightly underperformed compared to where he should be. The effect of these additional factors should not be underestimated- Schumacher's return for Mercedes struggled for exactly those reasons. Next year Alonso doesn't have the excuse of returning to the sport, but is a further year older, meaning any breakthrough into the top 5 drivers of the year is probably unlikely.
7) George Russell, 87%
Four points finishes, including a second place in Belgium, suggest a big step up for Russell and Williams in general. Of course his efforts in Spa were aided by a 2 lap "race" with no overtaking, but George still deserves immense credit for putting the car on the 2nd row. The Williams car seemed especially effective in the wet, with Hungary, Belgium and Russia all proving fruitful. At Mercedes he will be expected to be more consistent in results, although in return Russell will expect the car to deliver those results. The smart money is still on Lewis Hamilton winning that particular intrateam battle, but it will be great to nail down Russell's level with such an established benchmark.
6)Daniel Ricciardo, 92%
Ricciardo very much had a season of two halves, and he was down in 15th place at the Summer Break. The improvement was partly due to the model realising just how good his teammate is (both due to Norris' own performances and Sainz's at Ferrari), but also due to Daniel improving over time. At the summer break, he'd scored just 44% of Norris' points, but he returned to outscore Norris from then on. Ricciardo managed fairly consistent points finishes throughout the season and a historic win at Monza (McLaren's first triumph in almost a decade) was well deserved. Norris vs Ricciardo will be another teammate battle to keep an eye on in 2022.
S Tier
The model thinks that there were 5 drivers delivering very strong performances this year. Whilst this is partially a consequence of the grid getting stronger over time, it really is unprecedented to have so many drivers being ranked so highly. The rankings 5th through to 2nd are also incredibly close.
5) Charles Leclerc, 106%
Given that the model expected Leclerc to easily outscore Sainz, his slim deficit at the season's end could be interpreted as a poor season for the Monacan driver. However, the closeness of the battle was predicted before the start of the year, and can be explained by both Leclerc being slightly overrated due to the strength of his 2020 campaign (which was discussed in the 2021 predictions here) and the fact that the Sainz/Norris pairing at McLaren was underrated by the model. Leclerc did at least enjoy a step up in car performance from 2020, with 2 pole positions and a near victory at Silverstone. However, his single podium (fewer than in 2020) suggests that he didn't always take advantage of opportunities throughout the season, with the non-start in Monaco being an obvious example. It serves as a demonstration of his talent that the model considers the season to be slightly underwhelming in terms of results, but he is still considered to be the 5th best driver, and just a whisker away from a top 2 spot.
4) Lewis Hamilton, 107%
Hamilton's season didn't quite have the consistency of some of his Mercedes years, but did feature some of his strongest drives against stiff opposition. Mistakes included sliding into the gravel at Imola, hitting the Magic button at Azerbaijan (although Lewis blames this one more on a design feature) and playing his part in Verstappen's Silverstone crash. He also failed to get his tyres working properly at Monaco, his only weekend when he was truly off the pace. However, he had more than his fair share of victories, with Bahrain, Spain and an epic couple of drives in Brazil from the back of the field being among the highlights. There's much discussion on the numerous collisions and near collisions of Hamilton and Verstappen throughout the year, but out of the two drivers Hamilton's approach seemed the more nuanced, particularly as the season went on. Overall the model thinks that this season wasn't his absolute peak, but he wasn't far off either, and Hamilton would have been a worthy champion.
3) Carlos Sainz, 107%
The hierarchy of F1 drivers is ever evolving, but Sainz demonstrated this season that he is good enough to fight with the best. The season long battle with Leclerc was fascinating to watch, and a timely reminder that rivalries do not have to spill over into regular collisions and bitter words. Although he's still waiting for his first victory, his reputation as a points accumulator is as secure as ever, and he recently earnt the dubious honour of being the highest scoring driver ever without a win. Should he continue with this form for Ferrari he'll surely break his duck sooner or later. The general suspicion among many F1 pundits (and seemingly Ferrari themselves) is that Leclerc will still be the number one driver if and when the car comes together, and the model agrees with this assessment, even as Sainz's rating rose throughout the year. The message from 2021 is clear though: Carlos Sainz should not be underestimated.
2) Lando Norris, 108%
Norris showed potential in his first two seasons of F1, but emerged as an absolute sensation this year. In the opening half of the year he thoroughly drubbed Daniel Ricciardo, and was also ahead of both Pérez and Bottas in the standings despite a clearly inferior car. There seems to be a perception that his form dipped towards the end of the year, but the drop in results is probably more aptly explained by a combination of McLaren's declining form, Ricciardo improving over time and a combination of bad luck and team issues. He ended the season with 10 consecutive points finishes, something matched by only Carlos Sainz, and his 3rd place in qualifying for the final race confirmed that the pace was still there. His 2 big missed opportunities of the year came at Belgium (crashing in qualifying) and Russia (infamously trying to stick it out on slick tyres on a wet track). His Belgium crash was unfortunate, but he surely would have recovered to score points, if not more, had a race actually taken place. In Russia his first victory was cruelly snatched away by late rain, but most of the blame must be placed on his team for not calling him in. Overall it he scored more points, podiums and poles than in his previous 2 seasons combined, despite McLaren falling from 3rd to 4th place in the constructors championship. All that was missing was a first victory.
1) Max Verstappen, 132%
A champions season; Verstappen only once finished a race out of the top 2 (in Hungary after sustaining significant damage at the start). He also thrashed new teammate Pérez (see graph and analysis below). Going into the season, the model thought Max would score 64% of the team's points, but ended up with 67.5%. Whilst this difference seems small, it actually makes the difference between him winning the title and being 2 full race wins behind Lewis.
The only potential negative came from his non-compromising driving style at several flashpoints with title rival Hamilton during the season. Overall, Verstappen was probably a net loser in terms of championship points (due to losing at least a podium at Silverstone), and it will be interesting to see if he adapts his style as he further matures. Nevertheless, the model considers his season as a whole to be beyond exceptional, and possibly one of the greatest seasons ever.
Was Verstappen's season really that good?
Verstappen's 2021 season is currently rated stronger than any season by Hamilton, Alonso, Schumacher or Senna. At this point it's important to reflect on what exactly is being assessed: it's comparing results versus his teammate (taking into account how strong the 2 drivers have been over their careers), and by any metric Max has done incredibly well vs Pérez.
Verstappen had twice as many wins this year as Pérez has podiums. He also has 18 top 2 finishes compared to just 1. It is reasonable to consider whether the comparison is particularly fair, given that Red Bull have a reputation for focusing on their main driver. Pérez's retirement at the final race (caused by a fear that any issues could delay the race restart and scupper Verstappen's chances versus Hamilton) is a good example. However, it's also true that a lot of great drivers, particularly Alonso and Schumacher, have benefitted from a clear #1 status over the years, and this year is still considered exceptional compared to the performances of other great drivers.
Perhaps a useful comparison is how Pérez has faced versus other teammates. He's has only faced a teammate anywhere near to Verstappen's talent once previously: Button at McLaren in 2013. Whilst the circumstances were different, there are similarities. Both times Pérez joined a top team with a strong recent reputation, only for it to take a dent afterwards.
Verstappen's slice of the points is significantly higher than Button's. The model thinks this is partly due to Verstappen being a fundamentally superior driver, but also due to an above average performance during the year (and a relatively weak performance from Pérez). It should also be noted that such a high percentage of points in 2021 is unusual (although not unprecedented) given the competitiveness of the car.
The graph above shows how many points the constructor scored (as a %, x-axis) against what percentage of those were scored by the lead driver (y-axis) since 2010. The higher up the y-axis, the more dominant the teammate battle, but we can also see that a large discrepancy is more likely if the team scores fewer points as a whole. There are 14 occasions where teams have scored more (as a % of points available) than Red Bull in 2021, but of those only Vettel's 2013 performance comes close to Verstappen's level of domination. The most dominant teammate performances (in at least semi-competitive cars) are highlighted, with VER 2021 being comparable to anything anyone else achieved. The difference is that Pérez is considered to be a significantly stronger teammate overall than Massa or Webber. Räikkönen is considered to be a similar level to Pérez, which leads to the conclusion that Verstappen's 2021 performance is comparable to Alonso's in 2014.
I hope the data above goes some way to explaining why Max's season was rated so highly.
I've mentioned before how good it is to see the 2 title rivals take the top 2 spots in the rankings, and whilst that didn't quite keep until the end of the year, it is clear that both Hamilton and Verstappen were operating on a high level. The new regulations for 2021 make guesses at a team's form a bit of a fools game, but it wouldn't be a major surprise to see one of the 2 take the title again. However, the strength in depth currently in the F1 grid is unprecedented. Here's to another classic year in 2022 (hopefully with some more robust stewarding too!)
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Published December 14, 2021 January 12, 2022
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