75 replies to this topic

[JvsKVB77]

 

 

 

 

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.

[F1Frog]

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?

[William Hunt]

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

[JvsKVB77]

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.

[FTB]

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.

[F1Frog]

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.

[FTB]

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.

[F1Frog]

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.

[F1Frog]

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.

[Zmeej]

 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.

[vista]

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

[eab]

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.

[Gravelngrass]

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?

[F1Frog]

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.

[tyker]

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.

[eab]

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

Designed to win

[F1Frog]

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.

[F1Frog]

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/

[F1Frog]

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.

[F1Frog]

I applied the same model to the Super Touring era of the BTCC (1991-2000), and these were the results. Worth noting that if it weren't for John Cleland and Yvan Muller spending one season as teammates in 1999 at Vauxhall, the whole section of Cleland-Warwick-Tarquini-Thompson-Simoni-Allam-Simoni-Briggs-Kox would all be cut off from the rest, so that is the only connection they have to the rest of the pack, hence why they are all lower than you would expect as Cleland was in his farewell season in 1999 and was not at his best at all. The fact that there were only ten years in this era and many drivers stayed with the same team for a long time means that there isn't the largest data set for most of these drivers, which hurts the accuracy.

 

 

1.  Rickard Rydell

FASTEST

 

2. Steve Soper

+0.180%

 

3. Alain Menu

+0.288%

 

4. Joachim Winkelhock

+0.324%

 

5. Anthony Reid

+0.352%

 

6. Paul Radisich

+0.478%

 

7. Tim Harvey

+0.516%

 

8. Patrick Watts

+0.553%

 

9. Kelvin Burt

+0.579%

 

10. Yvan Muller

+0.592%

 

11. Laurent Aiello

+0.600%

 

12. Jason Plato

+0.604%

 

13. Roberto Ravaglia

+0.610%

 

14. Simon Harrison

+0.617%

 

15. Jan Lammers

+0.627%

 

16. Will Hoy

+0.662%

 

17. Julian Bailey

+0.677%

 

18. Andy Rouse

+0.752%

 

19. David Leslie

+0.760%

 

20. Bobby Verdon-Roe

+0.764%

 

21. Frank Biela

+0.776%

 

22. Vincent Radermecker

+0.776%

 

23. Gianni Morbidelli

+0.815%

 

24. Jonathan Palmer

+0.882%

 

25. Tom Kristensen

+0.940%

 

26. Jean-Christophe Boullion

+0.944%

 

27. Tim Sugden

+0.968%

 

28. James Thompson

+0.997%

 

29. Giampiero Simoni

+1.049%

 

30. Gabriele Tarquini

+1.055%

 

31. John Cleland

+1.074%

 

32. James Kaye

+1.115%

 

33. Derek Warwick

+1.117%

 

34. Robb Gravett

+1.202%

 

35. Eugene O’Brien

+1.248%

 

36. Craig Baird

+1.271%

 

37. Ray Bellm

+1.283%

 

38. John Bintcliffe

+1.311%

 

39. Matt Neal

+1.370%

 

40. Steve Robertson

+1.423%

 

41. Gary Ayles

+1.493%

 

42. Jeff Allam

+1.554%

 

43. Peter Kox

+1.581%

 

44. Laurence Bristow

+1.594%

 

45. Mike Briggs

+1.756%

 

46. Owen McAuley

+1.936%

 

47. Harry Nuttall

+2.092%

 

48. Alex Portman

+2.145%

 

49. Thorkild Thyrring

+3.424%

Edited by F1Frog, 16 May 2024 - 17:30.

[Secretariat]

F1Frog: I did not get an opportunity to follow the BTCC during the era referenced above, but am aware of the usual suspects. Also, I can certainly appreciate seeing various other names that pop up on your list.

[F1Frog]

Results for 2024 so far:

 

1. Max Verstappen (FASTEST)

2. Lando Norris (+0.145%)

3. Charles Leclerc (+0.211%)

4. Oscar Piastri (+0.234%)

5. George Russell (+0.240%)

6. Carlos Sainz (+0.296%)

7. Valtteri Bottas (+0.381%)

8. Lewis Hamilton (+0.467%)

9. Nico Hulkenberg (+0.514%)

10. Pierre Gasly (+0.549%)

11. Yuki Tsunoda (+0.565%)

12. Esteban Ocon (+0.593%)

13. Fernando Alonso (+0.611%)

14. Alexander Albon (+0.664%)

15. Sergio Perez (+0.777%)

16. Daniel Ricciardo (+0.838%)

17. Kevin Magnussen (+0.839%)

18. Lance Stroll (+0.926%)

19. Zhou Guanyu (+1.006%)

20. Logan Sargeant (+1.515%)

 

1. Red Bull (FASTEST)

2. Ferrari (+0.189%)

3. McLaren (+0.206%)

4. Mercedes (+0.352%)

5. Aston Martin (+0.372%)

6. Toro Rosso (+0.521%)

7. Williams (+0.706%)

8. Haas (+0.994%)

9. Alpine (+1.144%)

10. Sauber (+1.491%)

 

Seems pretty reasonable, I think.

[Bleu]

The car performance above changed to time gaps on a 90-second circuit:
Red Bull 1.30,000

Ferrari 1.30,170

McLaren 1.30,185

Mercedes 1.30,317

Aston Martin 1.30,335

RB 1.30,469

Williams 1.30,635

Haas 1.30,895

Alpine 1.31,030

Sauber 1.31,342

Edited by Bleu, 09 June 2024 - 06:25.

[F1Frog]

These are the end of season results for 2024 (as it is only on qualifying pace):

 

Drivers

1. Max Verstappen (FASTEST)

2. Lando Norris (+0.145%)

3. George Russell (+0.280%)

4. Oscar Piastri (+0.319%)

5. Carlos Sainz (+0.323%)

6. Charles Leclerc (+0.327%)

7. Pierre Gasly (+0.454%)

8. Valtteri Bottas (+0.495%)

9. Lewis Hamilton (+0.541%)

10. Nico Hulkenberg (+0.581%)

11. Yuki Tsunoda (+0.640%)

12. Fernando Alonso (+0.662%)

13. Alex Albon (+0.765%)

14. Daniel Ricciardo (+0.815%)

15. Esteban Ocon (+0.832%)

16. Liam Lawson (+0.862%)

17. Sergio Perez (+0.915%)

18. Kevin Magnussen (+0.923%)

19. Franco Colapinto (+0.924%)

20. Lance Stroll (+1.035%)

21. Zhou Guanyu (+1.090%)

22. Logan Sargeant (+1.510%)

 

Cars

1. McLaren (FASTEST)

2. Red Bull (+0.047%)

3. Ferrari (+0.084%)

4. Mercedes (+0.166%)

5. Aston Martin (+0.427%)

6. Haas (+0.635%)

7. Williams (+0.648%)

8. Toro Rosso (+0.664%)

9. Alpine (+0.981%)

10. Sauber (+1.307%)

[F1Frog]

For the overall rankings, I have now calculated back to 1971. Top of the list currently is Pedro Rodriguez courtesy of his excellent few races in the BRM that season, but he probably won't stay there once I have his whole career, so of drivers with their whole careers calculated, it is still Senna top from Schumacher, with Verstappen now ahead of Norris in third.

[F1Frog]

I extended the explanation from earlier of how this works, for the overall results, does this make sense to people?

Take Carlos Sainz, his results against teammates (average supertime for the season compared to his teammate - calculate this by finding their fastest lap of each weekend as a percentage of the overall fastest and averaging them across the season) are:

+0.100% against Verstappen (2015)

-0.420% against Kvyat (2016)

-0.108% against Kvyat (2017)

+0.038% against Hulkenberg (2018)

+0.028% against Norris (2019)

+0.032% against Norris (2020)

+0.132% against Leclerc (2021)

+0.166% against Leclerc (2022)

+0.164% against Leclerc (2023)



In the first column of my excel table is a list of every driver from 1987-2023 (actually it is now 1971-2024 as I have done more seasons since writing this) in the final ranking.

In the second column, every driver has a value of 100.

In the third column, is the formula. Sainz's number = Verstappen's number of the previous column (100) +0.100 + Kvyat's 100 - 0.420 + Kvyat's 100 - 0.108 etc. then divided by 8 as there are eight teammate connections here. The result given for Sainz in this third column is now 99.996. As all his teammates had a score of 100 before, this means that -0.004 is actually the average of the eight percentages listed above.



However, the same formula has been done for all the other drivers and all their teammates. Verstappen's score is now 99.577. Kvyat's is 100.218. Hulkenberg 99.735. Norris 99.712. Leclerc 99.646. This shows that actually Sainz was up against a strong set of teammates. If you drag the formula across to the fourth row, now Sainz's score is being compared to all these lower numbers instead so his score drops to 99.804. Then to 99.813. Then 99.744. It seems to move around randomly for a while but eventually tends towards a score of 99.258. At this time, every other driver has also tended to a single point. Lando Norris' tends to 99.022. So that is why Sainz has a score overall of +0.256% compared to Norris (the exact number 99.258 is irrelevant because 100 is an arbitrary starting point, but you could start anywhere and he would end up 0.256% behind Norris). These exact numbers might not match the article because my spreadsheet now includes the seasons back to 1971 and 2024, but they will be super close, and the section below will only be according to the 1987-2023 era.

When there are this many teammate connections, every driver tends to exact point by the end, so here is how it works now:

Leclerc overall is 0.772% to Senna.

Norris overall is 0.660% to Senna.

Hulkenberg overall is 1.079% to Senna.

Kvyat overall is 1.305% to Senna.

Verstappen overall is 0.669% to Senna.

Next step is to combine each of these overall scores to Sainz.

2015: (Verstappen's score 0.669%) + (Sainz's gap to Verstappen 0.100%) = 0.769%.

2016: (Kvyat's score 1.305%) + (Sainz's gap to Kvyat -0.420%) = 0.885%.

2017: (Kvyat's score 1.305%) + (Sainz's gap to Kvyat -0.108%) = 1.197%.

2018: (Hulkenberg's score 1.079%) + (Sainz's gap to Hulkenberg 0.038%) = 1.117%.

2019: (Norris' score 0.660%) + (Sainz's gap to Norris 0.028%) = 0.688%.

2020: (Norris' score 0.660%) + (Sainz's gap to Norris 0.032%) = 0.692%.

2021: (Leclerc's score 0.772%) + (Sainz's gap to Leclerc 0.132%) = 0.904%.

2022: (Leclerc's score 0.772%) + (Sainz's gap to Leclerc 0.166%) = 0.938%.

2023: (Leclerc's score 0.772%) + (Sainz's gap to Leclerc 0.164%) = 0.936%.

Now take the mean of all those numbers. (0.769+0.885+1.197+1.117+0.688+0.692+0.904+0.938+0.936)=8.126

8.126/9 = 0.903.

Now check the article, and Sainz is 0.903% slower than Senna overall.

Someone pointed out to me on Reddit that it is sort of an invariant row vector and matrix system, although I hadn’t made that connection before because I had just trusted the Excel spreadsheet dragging the columns across because it gets the answer I need, but I will try to work this out exactly as I did learn this in my degree.