Saturday, November 04, 2006

Doing The Maths - A Reprise

Earlier in the year, I posted an analysis of F1 drivers' average fastest laps over the course of the season. My point was that, unlike final qualifying, where drivers' pace is to some extent dictated by fuel loads, fastest race laps can give a more honest impression of who is fastest.

Of course, its not perfect. In modern F1, where overtaking is seriously difficult on many tracks, a driver may never be able to run as fast as his car or his talents might allow - for the sake of traffic. And fuel loads can affect fastest lap pace too. A driver on a one-stop strategy should not be able to run at the same kind of pace as a driver on a three-stop strategy. The driver on the three stop strategy, though, loses their advantage by having to spend longer in the pits. The figures can be skewed, too, by what statisticians call 'out-liers' . In this context, the out-liers, were the Super Aguris. Their times were so far from the pace, particularly at the beginning of the year, that they artificially dragged the average lap-speed down such that the vast majority of the field posted better-than-average lap times.

A couple more points to bear in mind. I've included some drivers who only completed part-seasons, but I'd take their numbers with a pinch of salt. By comparison to their team mates, they might simply have driven for the team at a point when their team was stronger, or weaker. A case in point being Yamamoto, who was slower than Sato almost everywhere, but who came out ahead because his average times were not dragged down by driving the awful early-season Super Aguri SA05. But anyway, with the relevant caveats now in place, here are the numbers:

1. Michael Schumacher +1.42s
2. Fernando Alonso +1.38s
3. Kimi Raikkonen +1.17s
4. Felipe Massa +1.01s
5. Giancarlo Fisichella + 0.88s
6. Juan-Pablo Montoya + 0.87s
7. Jenson Button + 0.57s
8. Robert Kubica +0.51s
9. Pedro De La Rosa + 0.45s
10. Rubens Barrichello + 0.28s
11. Ralf Schumacher + 0.25s
12. Mark Webber + 0.22s
13. Nick Heidfeld +0.18s
14. Jarno Trulli + 0.13s
15. Nico Rosberg + 0.09s
16. Jacques Villeneuve +0.08s
17. Vitantonio Liuzzi -0.22s
18. Scott Speed -0.25s
19. Christian Klien -0.35s
20. David Coulthard -0.41s
21. Christijan Albers -0.96s
22. Tiago Monteiro -1.27s
23. Takuma Sato -2.43s
24. Franck Montagny -2.87s

Data excludes wet races, Indianapolis, owing to low number of drivers who set a representative time, and, in the case of individual drivers, any race where they retired before being able to set a worthwhile time (this last one being a bit subjective).

It is said that you can prove anything with statistics, and perhaps you can. This week, in Autosport, Mark Hughes made the point that , while most would instinctively think that Massa did a better job than Fisichella, the raw numbers from qualifying show that while Massa was, on average, 0.4s off his team mate, Fisichella was within 0.1s of Alonso. Counter-intuitive? Certainly. But then, until he went to Renault and found himself up against Alonso, Fisichella had a reputation as a demon-qualifier. It was his race pace that was considered suspect. And here, the numbers show that on race pace, Massa was closer to Schumacher than Fisichella was to Alonso. Does this show that Hughes was wrong about Massa? Maybe, but you could make a case for using either set of data really.

Perhaps most strikingly, it is the real superstars, Michael Schumacher, Fernando Alonso, and Kimi Raikkonen who have the largest margins of superiority over their team mates. The data perhaps makes a case for Jenson Button's inclusion in this group - as his margin of superiority over Rubens Barrichello was almost as great. Even in these cases though, the average difference is never more than 0.5s. These guys, after all, are all professional racing drivers. None of them are slow.

There's an embarrassing statistic in there for Red Bull too. The raw numbers suggest that they were in fact slower than their junior team, Toro Rosso, in race trim. Now to some extent, that might be because Coulthard, in particular, tended to run very fuel-heavy strategies but that can't be all there is in it. There can be little doubting that, while they may have beaten Williams in the constructors championship, this year's Red Bull was a bit of a lemon.

The numbers also tend to bear out the claim I made last week that ditching Montoya for De La Rosa was probably not a smart thing for McLaren to have done. While Montoya was few tenths slower than Raikkonen, De La Rosa was almost a second slower. Now, undoubtedly, this is a dangerous comparison to draw, as De La Rosa didn't compete in all that many races, especially once one eliminates Hungary (wet), China (wet), and Germany (car failed in opening laps). All the same, it accords with a general impression that De La Rosa was really rather anonymous in the second Mclaren this year.

Anything else? I thought it interesting that Ralf Schumacher turned out to be faster over the season than Trulli, for one thing. The sheer similarity of pace of the two Toro Rosso drivers also came as something of a surprise. I'd had the impression that Liuzzi was comfortably quicker than Speed, but the more I look at the numbers (and not just these ones) the less certain I am that this was really the case.

Lies, damned lies and statistics, eh?


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