Who is the fastest driver? Attempting a 'Speed Index'

Discussion in 'Statistics & Analysis' started by Galahad, Dec 28, 2017.

  1. Galahad

    Galahad Not a Moderator Valued Member

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    So the question in the thread title is necessarily a subjective one (leaving aside the question of whether "fastest" = "best"). However we do have some objective data to try to make an assessment. Although cars' performance varies we do have team mate comparisons to draw on, and qualifying times are a 'cleaner' data set than race results given the number of variables involved in a Grand Prix.

    So, with apologies and thanks to Rutherford, I've analysed the relative performances of team mates in qualifying sessions for the past decade and more, the results of which are shown below. The basis of measurement is a percentage, representing the average gap between the faster and slower driver(s) over the course of a season. To save decimal places and for easier interpretation, I've scaled them up by a factor of 10,000. So in the chart below, +1 means a difference of +0.01%, and +100 means a difference of +1%. Over a typical lap time of 1m40s, +1 = +0.01% = +0.010s compared to the faster team mate. In this case, +10 would be a difference of one tenth, and +100 would be a difference of one second and so on.


    The comparisons all exclude wet sessions and those in which drivers have had mechanical problems - as far as possible from contemporary reports.

    Then I have tried to create a basic model of driver speed from this data. One of the problems with this approach is that occasionally there are situations where A > B > C > A. A classic one is when Damon Hill beat Jacques Villeneuve in 1996 (+43), who beat Heinz-Harald Frentzen in 1997 (+43) and 1998 (+21), who beat Damon Hill in 1999 (+61). I would argue that there are two effects at play here: a rookie effect (disadvantaging Jacques in 1996) and an age effect (Damon was 38 in 1999) that explain the apparent anomaly: Villeneuve got faster over the period while Hill got slower.

    Analysis of the past decade seems to suggest most drivers gain speed from their first into their second season. A minority appear to improve further in the third season. This seems to be independent of the age they make their debuts. Additionally, some drivers show signs of losing pace from the age of around 33 onwards - although this isn't consistent or true for everyone.

    So I've taken a simple model that assumes a driver's speed is constant, except in their rookie season (or two), and assumes they decline gradually from age 33. Then using the historic team mate comparisons, create an estimate of their speed over the course of their career.

    I've chosen Hamilton as my baseline, driver 0, on the basis that he's a qualifying expert and has had some long-term team mate relationships providing a good sample of data. So from Hamilton we can get estimates for Button, Rosberg and Bottas; from Button on to Alonso, from Alonso on to Raikkonen and so on.

    This is what I came out with for the 2017 grid, plus Button and Rosberg included for reference:


    As you'd expect there are a few adjustments where the model didn't quite fit. It made sense to assume Raikkonen wasn't the same driver after his two year break, given the wide margin between him and Alonso and, latterly, Vettel. I assumed Massa took some time to recover from his 2009 accident, while I've chosen to represent Kvyat declining after 2015 - although you could take an average of his deficit to Ricciardo across those seasons, which would move him and Sainz up a bit in 2017.

    Finally the only driver who I couldn't fit to the model at all was Magnussen. He was marginally faster than Button in his rookie year of 2014 (shown on the chart) but has been very underwhelming against Palmer and Grosjean since. I've put him at +88 since it's easier to assume one season was the outlier rather than 2016-17.
    Last edited: Dec 28, 2017
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  3. Galahad

    Galahad Not a Moderator Valued Member

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    A few thoughts:

    Verstappen: I've assumed that Max is one of those who has continued to improve into a third season, on the basis of the 25-point turnaround with Ricciardo from 2016 to 2017. Time obviously will tell whether this is true or not - so I may be overestimating him here. Or underestimating him.

    Vettel: I know many will be surprised to see him so low on this chart. One of the potential weaknesses of the model is it can't deal with 'bad seasons' - since all you can see is the performance. So he is penalised for being outpaced by Ricciardo in 2014. But it's also worth noting that his average margin over Raikkonen hasn't been as great as that Alonso had - and Kimi was 34 then, now 37.

    Sainz: This is a tricky one, since on the basis of his performance against Kvyat, he should have been faster than Hulkenberg. Therefore I'm banking on him having a slight advantage over the German next season, and putting 2017 down to new team settling-in.

    So, what do you think? Bearing in mind this is only measuring qualifying speed, nothing else?
    Last edited: Dec 28, 2017
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  4. Titch

    Titch Smile Premium Contributor

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    I think that’s hugely complex Galahad, well done you
  5. gethinceri

    gethinceri Daniil Kvyat Fan. Contributor

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    I think it's brilliant.
    I don't understand it, but it's brilliant.
  6. jez101

    jez101 Bookies drive nice cars because of people like me Contributor

    I did something very like this about 10 years ago. I will have to dig it up because the data went right back to Jim Clark.

    I posted a tiny fraction of it on the Vettel thread because Webber was an awesome qualifier before Seb came along and beat him.

    Current - Sebastian Vettel

    That chain of events (Webber beats everyone, then gets beaten by Seb, who then gets beaten by Danny who gets beaten by Max) is hard to factor in! You also have eras like the blown diffuser which suited some more than others in addition to the form factors that are evident.
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  7. RasputinLives

    RasputinLives Happy to be me again Contributor

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    One thing I've noted on this is that Gasly comes off very well from just a handful of races clocking in above Ocon!

    Of course there is the Prost Factor for drivers (winning races in the slowest possible time) with those types of drivers always notoriously being down in quali. I wonder if it's possible to incorporate the comparison of race fastest laps between team mates and thus add a race pace element to it.

    Brilliant stats by the way. Why aren't you employed he FOM and presenting these on your own social F1 feature?
  8. Galahad

    Galahad Not a Moderator Valued Member

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    Indeed. If I get time I'll take the data back a few years and see where I think Webber should best fit in. He was into his mid-thirties for most of the time he and Seb were team mates. Still by common consent that season of Vettel and Ricciardo together at Red Bull was dominated by struggles with the non-blown diffuser car. It may make more sense to put that as a 'dip' season for SV. Or maybe 2009-13 was the blip?

    If you go back to 2006, Michael Schumacher (based on relative pace to Massa) is faster than any current driver, by the way (-19).
    Last edited: Jan 1, 2018
  9. Galahad

    Galahad Not a Moderator Valued Member

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    As ever, we should take care drawing conclusions from a small sample! It'll be difficult to know what progress Pierre is making since Hartley isn't a known benchmark at this point. Of course, maybe the Toro Rosso revolving door will spin again.
  10. teabagyokel

    teabagyokel #dejavu Valued Member

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    Webber’s team-mates over this period were Coulthard and Vettel, so there’s not really a lot of comparison there either.

    Red Bull have rather existed in their own bubble for the majority of their time in F1 - they will be more comparable to the rest of the field when Sainz has a full season against Hulkenberg, and when Vettel gets a new team-mate at Ferrari.

    Pre-Hamilton, Rosberg was always an odd case as he’d had a series of unknown quantities (old Wurz, Nakajima, old Schumacher) as team-mates.
  11. dinsdale

    dinsdale Spectator

    This is really good! I've just spent 15 minutes looking at it. Have a few questions:

    - By using Hamilton as the baseline we can't see how he himself changed over those years, right?

    - I sort of feel if the polarity were reversed it would all be more clear. In other words if -5 for Verstappen were +5 and of 12 for Ricciardo were -12 it would be more clear. Or is my perspective wrong?

    - Verstappen, Ricciardo and Bottas do really well here, right?

    - If Hamilton is the baseline how can he be anything but 0 in 2007?
  12. Galahad

    Galahad Not a Moderator Valued Member

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    The model I've used assumes that a driver's overall performance level is constant from when they stop being a rookie (after 1 or 2 full seasons) until they reach the age of 32, at which point there's a gradual decline. I think assuming a flat performance level is the only sensible approach, because 20 data points per season isn't enough to draw reliable conclusions: the results will vary due to individual circumstances in each qualifying session, regardless of whether the driver is driving better, worse or the same.

    So the model assumes that fluctuations in performance from year to year aren't due to changes in the driver's underlying speed or ability, but in external factors, or plain old random variation (a "lucky" or "unlucky" run). It's a simplification, for sure.

    No, you're right, it would work either way. Because the analysis started out with laptimes, (-) = fewer seconds = faster, so I'm used to a negative being, er, positive. But useful feedback.

    Indeed. The result forecasted by the model is that, if all drivers were in identical cars in 2017, on average Verstappen would have qualified fastest, Ricciardo 3rd and Bottas 5th. Conversely Vettel is 8th (although within 0.3s of pole - it would be much closer!).

    The observation from the data is that drivers get quicker from their first into their second season (a few show yet further improvement from second into third - e.g. Verstappen, Ricciardo). So even with Hamilton as the baseline I have assumed that was also the case for him. And the evidence supports that: he was almost identical to Alonso in 2007, but on average had a bigger advantage over Button as his team-mate than Alonso did subsequently in their careers.
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  13. dinsdale

    dinsdale Spectator

    Thanks. The minus/plus thing makes sense the way you have it, on second thoughts.

    Hamilton's 33 now and I'm having trouble getting my head round how that would affect using him as the baseline if you do another one of these. Your model assumes he'll start dropping off but what if he doesn't? Either way will his curve go down or stay flat?
  14. Greenlantern101

    Greenlantern101 Super Hero And All Round Good Guy Contributor

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    The answer is Wing Commander Andy Green. You're welcome.
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  15. Galahad

    Galahad Not a Moderator Valued Member

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    I don't know yet. I expect Bottas will be a bit closer than in 2017, in which case Hamilton's curve can start to decline. If that's not what happens, it might need a review of Bottas' level as well as Hamilton's.

    But he's only the baseline in the sense of a starting point. Once that's established, all the other drivers are placed in relation to each other. I could have started with Vettel, Rosberg, Button or anyone. And I plan to work back to the pre-Hamilton period shortly.
  16. dinsdale

    dinsdale Spectator

    OK. There are some thing I still don't understand about your graph, but it's very interesting - I really had good look at it. Sorry about all the questions. I have a splinter in my finger now from scratching my head.
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  17. Toni2305

    Toni2305 Learner

    As a statistics fan, i made speed index for seasons 2010-2013 (i currently working on 2018, and will make for seasons that i didnt make).
    My English is not good by i will try to explain how i did it. For whole weekend i took fastest lap (usually it is from qualyfication, but sumetimes is from free practices if there was rain on qualy). Than i divided times with fastest lap time and multiplied it with 100 to get speed index.
    If anyone is interested i can post my speed indexes here (and if autor of this topic allows, because i dont want to spoil his topic)
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  18. gethinceri

    gethinceri Daniil Kvyat Fan. Contributor

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    Go for it Toni2305
    There are many things that make such an index non-representative but I am hungry to see what you've come up with.
  19. Toni2305

    Toni2305 Learner

    OK, here it is for season 2010:

    1. Mark Webber (Red Bull-Renault) 0,260
    2. Sebastian Vettel (Red Bull-Renault) 0,290
    3. Fernando Alonso (Ferrari) 0,968
    4. Robert Kubica (Renault) 1,111
    5. Nico Rosberg (Mercedes) 1,182
    6. Jenson Button (McLaren-Mercedes) 1,228
    7. Felipe Massa (Ferrari) 1,337
    8. Michael Schumacher (Mercedes) 1,560
    9. Rubens Barrichello (Williams-Cosworth) 1,602
    10. Nico Hulkenberg (Williams-Cosworth) 1,767
    11. Adrian Sutil (Force India-Mercedes) 1,851
    12. Nick Heidfeld (Sauber-Ferrari) 2,028
    13. Vitaly Petrov (Renault) 2,059
    14. Kamui Kobayashi (Sauber-Ferrari) 2,363
    15. Jaime Alguersuari (STR-Ferrar 2,489
    16. Sebastien Buemi (STR-Ferrari) 2,491
    17. Pedro de la Rosa (Sauber-Ferrari) 2,788
    18. Vitantonio Liuzzi (Force India-Mercedes) 2,859
    19. Jarno Trulli (Lotus-Cosworth) 5,093
    20. Heikki Kovalainen (Lotus-Cosworth) 5,124
    21. Timo Glock (Virgin-Cosworth) 5,372
    22. Christian Klien ( Hispania-Cosworth) 6,098
    23. Karun Chandhok (Hispania-Cosworth) 7,507
    24. Sakon Yamamoto (Hispania-Cosworth) 7,632
    25. Bruno Senna (Hispania-Cosworth) 7,766
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  20. RasputinLives

    RasputinLives Happy to be me again Contributor

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    Toni2305 good stuff - but where is Lewis Hamilton?
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  21. Toni2305

    Toni2305 Learner

    Sorry, my mistake
    4. Hamilton 0,989
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