Titles and Potential Titles

[Schummy]

Hamilton has a WDC and Massa has not it. It is the "reality" of title stats. But a sort of counterfactual analisys could intuitively tell us that Massa is, practically, so much champion in 2008 as Hamilton is. Or reversely, Hamilton easily could have not been champion. It was a kind of cosmic lottery in that Hamilton got the prize and Massa got the tears. Counting titles across he years, in my view, Hamilton and Massa "share" 2008's title on merit. Said in practical terms: Hamilton and Massa have like 1/2 of that title each one.

It is just an introductory example, there are more cases of titles that easily could have changed hands due to minimal circunstances, mostly out of the reach of the drivers themselves. For example, Lewis was in the wrong end of the "lottery" in 2007; he ended with empty hands, but he could have been the champion, just changing minor details in the season or even in the last race.

This is a long (and potentially boring) intro to present the idea after the following numbers. I have tried to calculate in a, hopefully, reasonable way the "percentage" of merit in every title in the last seasons. Merit means here the posibility (let's say probability) of getting that title. For example, Hamilton's title is about 50% on merit (he was about 50% of getting the title and 50% of not getting it); Vettel's title in 2011 is about 100% merit because he was not challeged at all by anybody. "Merit" here DOESN'T mean the driver's virtuosity or skill.

I have done the calculations using "my dear" bootstraping technique. Bootstraping is automatically a sort of counterfactual technique. It says us what sort of things could have happened if we could repeat the past with the same relevant variables. So, I have "repeated" past seasons to see who could have won them; in the end we have "probabilities" of have won the title.

In the following table I put the calculations from 2003 to 2012 (I have chosen 2003 to consider the career of all current relevant drivers).

 
     12  11  10  09  08  07  06  05  04  03    VT  RT   Dif  Rank
VET  52 100  34  19   0   0   0   0   0   0 = 2.05  3  +0.95  1
ALO  47   0  27   0   0  28  75  83   0   0 = 2.60  2  -0.60  2
RAI   1   0   0   0   5  37   0  17   0  37 = 0.97  1  +0.03
HAM   0   0  16   0  46  30   0   0   0   0 = 0.92  1  +0.08
BUT   0   0   4  69   0   0   0   0   0   0 = 0.73  1  +0.27  4
MAS   0   0   0   0  45   5   0   0   0   0 = 0.50  0  -0.50  3
WEB   0   0  19   5   0   0   0   0   0   0 = 0.24  0  -0.24  5
BAR   0   0   0   8   0   0   0   0   3   2 = 0.13  0  -0.13
KUB   0   0   0   0   4   0   0   0   0   0 = 0.04  0  -0.04

The number within the table are percentages of title (probability of get the title in a counterfactual world). Adding it we get VT = Virtual Titles, i.e. the titles the driver is expected to have according to his past probabilities of title. RT is the real number of titles owned. Dif is obviously the difference between reality and expectation; positive means the driver has been lucky, negative means, of course, that he has been unlucky. Rank is the rank of anomaly respecting expectations.

In short, Alonso "should" have 2.60 titles and Vettel "just" 2.05. So, Vettel has been lucky in the "cosmic lottery" that decides who is lucky and who is not; on the other side, Fernando has been unlucky. They are the two drivers more influenced by luck; third notable case is Massa, obviously unlucky. The rest has got pretty much what was expected for them.

In the next post I'll add some minor details.

[Schummy]

The next table shows the "anomalies" (good or bad luck) in every year. A positive anomaly means the driver was lucky in that year, getting a title that perhaps he could have not got. Negative means he was unfortunate because he didn't get the title but he could have got it.

 
     12  11  10  09  08  07  06  05  04  03
VET +48   0 +66 -19 
ALO -47   0 -27   0   0 -28 +25 +17   
RAI  -1   0   0   0  -5 +63   0 -17   0 -37
HAM   0   0 -16   0 +54 -30   
BUT   0   0  -4 +31
MAS   0   0   0   0 -45  -5

Basically almost everyone has been lucky some times and unlucky other times, but not necessarily in the same amount.

The most notable instances of (good or bad) luck regarding titles are:

1) Vettel in 2010: He got the title against a close package of candidates. Bootstrap calculations shows had only a 34% probability of being WDC (the others shared the remaining probability).
2) Raikkonen in 2007: this is a well known case. Kimi was fortunate because the title race was extremely close between three drivers. Basically they played a virtual roulette.
3) Hamilton in 2008: Another well known case. Poor Massa.
4) Vettel in 2012: His (other) close title against Alonso.
5) Alonso in 2012! : The reverse side of the former event. This is the unluckiest case in the whole table.
6) Massa in 2008: Obvious, I suppose.

[Razzzor]

Interesting but not proof going by MSC ending up on only 25% chance for 2006... without the engine blow and puncture in the last 2 rounds, he WOULD have been champion.