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Mathematical Model to compare F1 drivers


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#51 JvsKVB77

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Posted 17 November 2023 - 05:38

 

 

 

 

Some notes:

George Russell's ranking has been elevated by the fact that Robert Kubica's good years are starting to be included, and so his destruction of Kubica in 2019 actually makes a difference now. This is one comparison that arguably shouldn't be included, but for now I will leave it as I want the model to be totally objective, and hopefully I will be able to limit the effect of this season once I improve the model to include age and experience effects.

 

 

I have something similar to your comparision, but with race pace too.  And i did it  Kubica-1 and Kubica-2, because it was not physically same driver. Even with some corrections on age and years without F1 which i did it was something like 0.8-0.9 between Robert's levels. 


Edited by JvsKVB77, 17 November 2023 - 05:47.


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#52 F1Frog

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Posted 17 November 2023 - 10:23

I have something similar to your comparision, but with race pace too. And i did it Kubica-1 and Kubica-2, because it was not physically same driver. Even with some corrections on age and years without F1 which i did it was something like 0.8-0.9 between Robert's levels.


The problem is just that every driver’s form fluctuates and it seems unfair to eliminate some bad seasons and not all. Kubica is probably the most extreme example in this time period.

But I am very interested in your model. How did you include race pace?

#53 William Hunt

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Posted 17 November 2023 - 11:02

No mechanical model will ever be a reliable measuring stick for a sport like F1. At least they should apply Einstein's relativity law then :D



#54 JvsKVB77

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Posted 17 November 2023 - 13:55

The problem is just that every driver’s form fluctuates and it seems unfair to eliminate some bad seasons and not all. Kubica is probably the most extreme example in this time period

I am agree, but for me it is not case of a bad season , Robert has severe hand injury which was not completely gone, especially in tight F1 cockpit.  And i think same can be for Wendlinger case too. 

 

 

But I am very interested in your model. How did you include race pace?

Calculate by myself, all laps are taken from each driver except the first, last, pit enter/exit, laps that differ from the next or previous one by more than 1.5% from the best time for the weekend (some mistakes,  laps effected by track battle or lapping/being lapped  e.t.c) ) and laps under the VSC/SC, and the average lap time for the race is calculated, the same is done adjusted for the number of stints, each extra stint is worth an addition to the average lap time of the time required to make up the loss of pitlane time calculated for each race. (loss in pitlane/number of laps). If driver complete more than 15% of the race, but not finished, his pace based on what was his pace difference to other drivers with same strategy at moment of DNF or some car problems which effected pace but was not terminal.And this average lap then go to % like in your system.  I know on this forum has race pace tread with correction on fuel and tyre types, and that my version have some problems and not 100% correct of course) 


Edited by JvsKVB77, 17 November 2023 - 13:57.


#55 FTB

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Posted 17 November 2023 - 15:00

These are the new results having added the 2009-2011 seasons:

 

 

Didn't 2009 still have the 'start race with Q3 fuel' rule? Did you correct for fuel? Or use Q1-Q2 times (which I would disagree with)? Great effort by the way.


Edited by FTB, 17 November 2023 - 15:08.


#56 F1Frog

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Posted 17 November 2023 - 16:17

Didn't 2009 still have the 'start race with Q3 fuel' rule? Did you correct for fuel? Or use Q1-Q2 times (which I would disagree with)? Great effort by the way.

Thank you. For every season, I am using the fastest lap of the weekend. So usually that would be Q3 but occasionally it is instead a different session, like if someone has a problem or if it rains in qualifying. So in 2009 the fastest laps are almost always Q1 and Q2. It isn’t ideal and I particularly don’t like situations like Interlagos 2009 when all the fastest laps are in practice 2, but one race doesn’t make a huge difference and this method prevents massively anomalous results skewing the statistics.

The idea is that the fastest lap of the weekend is the absolute limit (often in 2009 it was not), but I found it interesting that some drivers, specifically Daniil Kvyat and Nelson Piquet Jr, very often seemed to have a fastest lap that was in practice rather than qualifying, suggesting they weren’t so good at maximising their potential when it mattered.

Edited by F1Frog, 17 November 2023 - 16:19.


#57 FTB

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Posted 19 November 2023 - 12:30

Thank you. For every season, I am using the fastest lap of the weekend. So usually that would be Q3 but occasionally it is instead a different session, like if someone has a problem or if it rains in qualifying. So in 2009 the fastest laps are almost always Q1 and Q2. It isn’t ideal and I particularly don’t like situations like Interlagos 2009 when all the fastest laps are in practice 2, but one race doesn’t make a huge difference and this method prevents massively anomalous results skewing the statistics.

The idea is that the fastest lap of the weekend is the absolute limit (often in 2009 it was not), but I found it interesting that some drivers, specifically Daniil Kvyat and Nelson Piquet Jr, very often seemed to have a fastest lap that was in practice rather than qualifying, suggesting they weren’t so good at maximising their potential when it mattered.

Thanks for the answer. I think the FIA released the fuel data for 2009 by the way. I don't like Q1 or Q2 times of drivers for teams that go into Q3 because some of the fastest drivers do better laps than their teammate in Q3 compared to Q1-2 when it really matters.  


Edited by FTB, 19 November 2023 - 12:32.


#58 F1Frog

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Posted 20 November 2023 - 16:43

As it stands, removing Robert Kubica's 2019 season from the ranking adjusts his score to be just above Raikkonen and below Schumacher and Albon (who swap places). Meanwhile Russell drops to between Hulkenberg and Gasly. The only changes in score of over 0.01% are:

 

Robert Kubica -0.206%

Nick Heidfeld -0.102%

Vitaly Petrov -0.071%

Senna/Chandhok/Yamamoto -0.041%

Kovalainen/Trulli/Glock/diGrassi/d'Ambrosio/Pic/VanDerGarde -0.038%

Kamui Kobayashi -0.028%

Pedro De La Rosa -0.019%

Ericsson/Nasr -0.012%

Pastor Maldonado -0.010%

 

Nicholas Latifi +0.027%

George Russell + 0.080%


Edited by F1Frog, 20 November 2023 - 16:49.


#59 F1Frog

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Posted 30 November 2023 - 19:23

Here are the updated scores once the 2006-2008 seasons are added. There are a lot of weird results in there so just remember that anything before 2006 is as if it never happened at this stage.

 

1. Lando Norris FASTEST

2. Max Verstappen +0.034%

3. Charles Leclerc +0.135%

4. Carlos Sainz +0.252%

5. Fernando Alonso +0.307%

6. Daniel Ricciardo +0.324%

7. George Russell +0.351%

8. Anthony Davidson +0.386%

9. Pierre Gasly +0.396%

10. Nico Rosberg +0.404%

11. Lewis Hamilton +0.416%

12. Nico Hulkenberg +0.420%

13. Valtteri Bottas +0.493%

14. Adrian Sutil +0.524%

15. Sebastian Vettel +0.527%

16. Pascal Wehrlein +0.528%

17. Paul di Resta +0.562%

18. Michael Schumacher +0.565%

19. Antonio Giovinazzi +0.584%

20. Rubens Barrichello +0.593%

21. Sergio Perez +0.610%

22. Jenson Button +0.615%

23. Esteban Ocon +0.629%

24. Kimi Raikkonen +0.633%

25. Giancarlo Fisichella +0.638%

26. Sebastien Buemi +0.651%

27. Alexander Albon +0.652%

28. Romain Grosjean +0.657%

29. Daniil Kvyat +0.660%

30. Felipe Massa +0.671%

31. Mark Webber +0.713%

32. Pastor Maldonado +0.714%

33. Heikki Kovalainen +0.714%

34. Jean-Eric Vergne +0.735%

35. Esteban Gutierrez +0.751%

36. Kevin Magnussen +0.779%

37. Stoffel Vandoorne +0.784%

38. Kamui Kobayashi +0.800%

39. Brendon Hartley +0.806%

40. Takuma Sato +0.812%

41. Vitantonio Liuzzi +0.816%

42. Jarno Trulli +0.818%

43. Juan Pablo Montoya +0.839%

44. Felipe Nasr +0.843%

45. Kazuki Nakajima +0.854%

46. Sergey Sirotkin +0.876%

47. Marcus Ericsson +0.889%

48. Pedro de la Rosa +0.891%

49. Mick Schumacher +0.909%

50. Robert Kubica +0.918%

51. Sebastien Bourdais +0.918%

52. Zhou Guanyu +0.937%

53. Timo Glock +0.941%

54. Ralf Schumacher +0.956%

55. Rio Haryanto +0.960%

56. Nelson Piquet Jr +0.989%

57. Christijan Albers +0.993%

58. Lance Stroll +0.999%

59. Jaime Alguersuari +1.002%

60. Yuki Tsunoda +1.043%

61. David Coulthard +1.073%

62. Alexander Wurz +1.083%

63. Nick Heidfeld +1.110%

64. Vitaly Petrov +1.151%

65. Scott Speed +1.188%

66. Nicholas Latifi +1.196%

67. Bruno Senna +1.196%

68. Charles Pic +1.213%

69. Christian Klien +1.222%

70. Jolyon Palmer +1.226%

71. Jacques Villeneuve +1.247%

72. Tiago Monteiro +1.257%

73. Narain Karthikeyan +1.360%

74. Jerome d'Ambrosio +1.360%

75. Sakon Yamamoto +1.451%

76. Franck Montagny +1.456%

77. Nikita Mazepin +1.471%

78. Lucas di Grassi +1.568%

79. Giedo van der Garde +1.782%

80. Karun Chandhok +1.860%

 

Notes:

 

The most glaring silly result in there is Anthony Davidson's high placing. This is due to his large advantage over Takuma Sato in 2007. However, Sato is probably overrated due to facing Yamamoto as a rookie, and Yamamoto also being teammate to Sutil who is overrated on here. And many of Davidson's fastest laps in 2007 came in practice so he wasn't delivering at the important time. This score will hopefully go down once Button vs Sato is included, but not by enough.

 

Rosberg, and by extension Hamilton, saw their scores take a minor hit due to Webber beating Rosberg in 2006, and currently being very underrated by the model. The effect of Schumacher's destruction of Massa helped them a bit, but not enough yet that it will make a significant difference, once more of peak Schumacher is included. It will skew the model in favour of Rosberg a bit. Alonso also wasn't as far ahead of Fisichella as one might expect in 2006 so that brought his score down a touch.



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#60 Zmeej

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Posted 08 December 2023 - 05:17

 I miss DOHC. :(

 

FYI: he’s a mathematician who has done lotsa work with the Fields Institute. He stopped posting several years back.

 

FWIW, I miss his posts, we’re still in touch. :)


Edited by Zmeej, 08 December 2023 - 05:17.


#61 vista

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Posted 08 December 2023 - 08:49

This thread reminds of https://f1metrics.wordpress.com/ - some fantastic analysis on that website too.



#62 eab

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Posted 08 December 2023 - 14:29

This thread reminds of https://f1metrics.wordpress.com/ - some fantastic analysis on that website too.

Analysis let loose on assumptions that are worse than sketchy.



#63 Gravelngrass

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Posted 08 December 2023 - 14:51

Isn’t this just a fancy version of the >< system?

Seriously, congrats for your dedication, a few very interesting results there. Isn’t there a way to exclude teammate comparison in the model?

#64 F1Frog

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Posted 01 January 2024 - 11:53

I have updated all the way back to the 1995 season now, and will post another update once I get back to 1987, as that is as far as my Autocourse collection goes (the source for all this data). However, while Lando Norris is yet to be displaced from first position, Michael Schumacher is getting closer and closer with every additional year and I hope he makes it to the front soon, although I am sure Ayrton Senna will then jump straight to the top as soon as I get to his years. At the other end of the scale, Taki Inoue has immediately jumped into last place by a considerable margin (with Max Papis second-bottom albeit 0.73% ahead having failed to destroy Inoue in the way that Gianni Morbidelli did). The model predicts that had Lando Norris and Taki Inoue been teammates, Norris would lap around 4.5% faster every lap (putting Inoue 4.5 seconds behind in one lap of Spa). After Inoue and Papis, next from bottom is Karl Wendlinger who was awful in 1995 but will go up with the addition of his prior seasons. Then it is Ricardo Rosset, who is still around 1.7% faster than Taki Inoue. But if 1997 proves to be an abnormally poor season for Morbidelli, Inoue's score will recover to closer to the rest of the pack.



#65 tyker

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Posted 01 January 2024 - 12:12

I've seen several models over the years and they are fun. This one's fun to analyze as well. Well done!

 

However, I don't think models are (and maybe can't be) sophisticated enough to aptly show what's going on. There's endless variables that aren't considered here, and a lot of them cannot be operationalized.

 

I don't want to sound rude, but I think the stuff we used to do in the media section is more reliable. Let subjective experts give a grade for each driver's performance and find the average grade for each driver. Do this year for year, and you can pretty much tell who was/is the fastest driver.

Yes the problem with these mathematical models iis that they tend to be without any kind of context so you end up with Rubens Barrichello being quicker than Michael Schumacher and Nico Rosberg being quicker than Lewis Hamilton despite the opposite being the case when they were teammates, the models done in this way always fail a quick sniff test.



#66 eab

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Posted 01 January 2024 - 12:51

I am sure Ayrton Senna will then jump straight to the top as soon as I get to his years.

Designed to win



#67 F1Frog

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Posted 02 January 2024 - 14:59

Meanwhile, here are the results of the Hill-Villeneuve-Frentzen triangle.

 

In 1996, Hill beat Villeneuve by 0.374%

In 1997, Villeneuve beat Frentzen by 0.363%

In 1998, Villeneuve beat Frentzen by 0.102%

In 1999, Frentzen beat Hill by 0.518%

 

The reason for this is that Villeneuve was a rookie in 1996. Frentzen had extreme difficulty understanding the complicated Williams in 1997 (but recovered somewhat in 1998). Hill didn't give a crap in 1999. But averaging these four results gives the overall result of:

 

1. Jacques Villeneuve

2. Heinz-Harald Frentzen +0.008%

3. Damon Hill +0.076%

 

And when you add all their other teammates (back to 1994 only), it changes to

 

1. Damon Hill

2. Heinz-Harald Frentzen +0.091%

3. Jacques Villeneuve +0.138%

 

So the entire result inverts entirely. This is because they are connected through other teammate connections as well.

e.g. Hill-Coulthard-Hakkinen-Brundle-Panis-Villeneuve

e.g. Hill-Schumacher-Fisichella-Button-Villeneuve

e.g. Hill-Diniz-Salo-Katayama-Blundell-Hakkinen-Coulthard-Raikkonen-Heidfeld-Alesi-Trulli-Frentzen-Villeneuve

 

Effectively, all three are extremely evenly-matched.


Edited by F1Frog, 02 January 2024 - 15:06.


#68 F1Frog

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Posted 02 March 2024 - 13:06

The full model from 1987-2023 with all the data and explanations is done. I hope you enjoy it and don’t read it all.
https://f1frogblog.w...iver-1987-2023/

#69 F1Frog

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Posted 19 March 2024 - 19:56

Now with the 1986-1982 seasons added, Gilles Villeneuve has found himself top of the list. This is based on a tiny sample size (1% faster than Pironi in the first five races of 1982, and Pironi was then 1% faster than Tambay in their four races together). But it would be cool if he stayed there.