Mathematical Model to compare the fastest F1 drivers (1987-2023)

[BTCC frog]

There are plenty of other mathematical models comparing the greatest Formula 1 drivers of all time, but I have made one of my own which I hope you will find interesting.

https://f1frogblog.wordpress.com/202...ver-1987-2023/

My model is comparing only the outright qualifying speed of the drivers, as it is based on supertimes, the fastest laps of the weekend, compared to teammates. Essentially it takes an average supertime for each driver in each season and says that if, for example, Max Verstappen was 0.5% faster than Sergio Perez, and Perez was 0.5% faster than Lance Stroll, then Verstappen is 1% faster than Stroll, and sort of takes the average of all the different combinations. There is a more comprehensive explanation in the article.

The main advantage of the model compared to others, I think, is that it is quite simple so it is very easy to spot where a weird result comes from, and I have provided all the data in the article to make that clear. I have also provided an explanation about every driver's position so as to try and understand why they are there and if they should be higher or lower based on subjective factors.

However, there are many obvious flaws, which is why I am not at all claiming that the results shown are an accurate representation of the drivers' ability. For example, due to everything about modern day F1 like simulators, training and telemetry, the gaps between the drivers are very close together, compared to in the past. Nigel Mansell was 0.7% faster than Riccardo Patrese in 1988, and Fernando Alonso was 0.7% faster than Lance Stroll in 2023. Therefore, Patrese and Stroll rank similarly in the overall list, and this is the reason why. So the model is biased in favour of more recent drivers, and so it isn't a good way of comparing two drivers of wildly different eras. I have provided season rankings at the bottom of the article as it seems fairer to compare drivers of similar eras in this way, and those tables show this more clearly.

Also, there are the same disadvantages that apply to all models that drivers' level changes throughout their career so you get strange circles like the fact that Damon Hill beat Jacques Villeneuve, who beat Heinz-Harald Frentzen, who beat Damon Hill. But again, I have tried to address the potential reasons this could happen in the explanations about every driver in the article. And this model is only comparing qualifying speed, rather than overall results and points are won in the race.

So the results could be taken as a base, objective measure but shouldn't be taken too seriously as they should then adjusted significantly by subjective factors to get a more accurate ranking of the drivers, because there are plenty of factors that cannot be explained by maths.

I hope you enjoy reading it.

[Aysedasi]

Interesting. I haven't read all that much of it (yet) nor have I fully grasped the methodology (yet) but it seems strange to see the likes of Wehrlein and Sutil just outside the top 20...... And as for at the top? Only 0.6%......??? But then I am biased....

[BTCC frog]

Originally Posted by Aysedasi

Interesting. I haven't read all that much of it (yet) nor have I fully grasped the methodology (yet) but it seems strange to see the likes of Wehrlein and Sutil just outside the top 20...... And as for at the top? Only 0.6%......??? But then I am biased....

Thank you for reading. If there is anything specific that you think I need to explain better about the methodology then please let me know. As I said, I think the greatest strength of this model compared to others is that I think it is understandable, and I have provided the data that got the results, so you can make your own subjective adjustments based on which teammate connections seem unrepresentative of their actual positions, and when something strange happens you can see why.

In the table under each driver's name, there is a list of all their teammates and what the gap was to that driver in an individual season, and the effect is how different it was to what the model expects based on the overall results. So with Adrian Sutil, he was 0.793% faster than Vitantonio Liuzzi in 2010, but only places 0.279% faster in the overall table, and so the 'effect' number is -0.514. And these 'effect' numbers add up to zero for every driver (occasionally up to 0.002 but just because of rounding to 3dp).

For why Adrian Sutil and Pascal Wehrlein are so high up, part of this is due to the fact that gaps are smaller in modern F1 compared to the past so the current drivers will all be closer together on a model like this. But I also agree that they seem too high compared to other drivers of that era. For Sutil, this is largely due to that huge gap to Liuzzi in 2010, as you can see on the effect column that has by far the greatest effect at lowering his gap to first place, (while being beaten by Fisichella has the greatest effect in the opposite direction). Liuzzi is probably too high in the list because he faced Vettel and Ricciardo when they were joining mid-season, and so Sutil benefits as a result from beating Liuzzi. Sutil beat Liuzzi by an average of 0.626% across 2009-2010, while Liuzzi beat Vettel by 0.117% in 2007, so this suggests Sutil could be 0.743% faster than Vettel. But taking another route, Sutil was 0.062% slower than Fisichella in 2008-2009, who was 0.631% slower than Raikkonen in 2009, who was 0.223% slower than Vettel in 2015-2018. So here, Sutil could be 0.916% slower than Vettel. This is an example of just how much driver ability changes across their careers. There are many other ways of connecting them and overall Sutil ends up 0.051% slower than Vettel, which I think is too close, but only because I believe the results against Fisichella and Raikkonen seem more representative of their actual levels than the ones against Liuzzi, and that is just a subjective opinion and the opposite could be true.

For Pascal Wehrlein, it is because of 2016 where he was faster than Esteban Ocon by 0.449%. This is a large gap and again is because Ocon came in mid-season so didn't have anywhere near the preparation that Wehrlein had. Force India picked Ocon for 2017 over Wehrlein despite this gap because they believed that it could all be covered by that extra experience, and the fact that Wehrlein was only 0.013% faster than Marcus Ericsson in the Sauber that year suggests that they were right, but this model has no way of knowing whether Wehrlein's results against Ocon or Ericsson were more representative of his actual level and just averages them, which leaves him much too high in 21st place.

For Ayrton Senna, it seems unlikely that he could have beaten Michael Schumacher by 0.6%, but then again he did beat Alain Prost by 0.7% across their two seasons as teammates. The result that most helps Senna's score is the enormous 4% advantage over Satoru Nakajima in 1987, when Nakajima was only about 1.25% behind Piquet in the following years and similarly far off Alesi and Modena. But he would still be top without that result, and there is no reason particularly to discount it as it did happen.