[Driver] Virtual World Championships

[Schummy]

[[WARNING: extreme nonsense ahead. Please jump to the tables below. You has been warned!]]

Sometimes random events happen and change the outcome of a race or WC. For example, that (in)famous exploding tyre in Mansell's car in Adelaide's finale; that season three drivers ended in three points. Or the nut popping out of Mansell's rear wheel in front of live TV in Hungaroring, making Nigel to lose 12 points to Piquet (Piquet won the title by 12 points with less wins).

One of my favs random events was Monaco'84. It was widely accepted that, the race had not been stopped, Prost would have lost the win. But the funny side of it is that Monaco's win caused the lost of title for Prost. He got half of 9 points for the stopped race, but he had got full 6 points for the not stopped race: +1.5 points... Prost lost the title by 0.5 points...

Or perhaps the random outcome of the event at Suzuka's Casio chicane between "those" two celebrities. Or the incredible finale in the last lap of 2008. Or the convoluted random combinations in 2007, with three drivers in just one point... The list goes on and on...

So, why I'm telling all that? The point is: if we could repeat a season with the same drivers and cars and the same general context, the outcome of the title could be different and perhaps another driver could win the title. It is like the Many-Worlds concept in Quantum Mechanics or the Logically Possible Worlds in Philosophy

Blah, blah, blah, I know What I try to say is it's reasonable to explore how past WCs could have been and to evaluate the past titles according to it.

In statistic we can create "alternative worlds" by mean of "bootstrapping". Basically it is to run a virtual season where "races" are chosen randomly among the races that really happened. For example, perhaps a race like Valencia doesn't happen again or maybe there are two races like Singapur. If we run many virtual reruns for a given past season (let's say 2005) we can see what percentage of times Alonso, Raikkonen or Schummy could have won that title.

The percentage of (virtual) titles are in the following tables:

Percentage of Virtual Titles:

2003: 
SCH 43%
RAI 38%
MON 18%
BAR  1%

2004:
SCH 95%
BAR  5%

2005:
ALO 79%
RAI 21%

2006:
ALO 73%
SCH 26%

2007:
RAI 35%
HAM 31%
ALO 28%
MAS  6%

2008:
HAM 47%
MAS 41%
RAI  5%
KUB  5%

2009:
BUT 67%
VET 23%
BAR  6%
WEB  3%
HAM  1%

2010:
VET 29%
ALO 29%
WEB 18%
HAM 20%
BUT  4%

Now the resume of percentages of titles along those seasons:

Percentage of VT along the seasons:
     03  04  05  06  07  08  09  10
SCH  43  95   0  26   0   -   -   0
RAI  38   0  21   0  35   5   -   -
MON  18   0   0   0   -   -   -   -
BAR   1   5   0   0   0   0   6   0
ALO   0   0  79  73  28   1   0  29
HAM   -   -   -   -  31  47   1  20
MAS   -   0   0   0   6  41   0   0
KUB   -   -   -   0   0   5   0   0
BUT   0   0   0   0   0   0  67   4
VET   -   -   -   -   0   0  23  29
WEB   0   0   0   0   0   0   3  18

A horizontal bar "-" means the driver was not in F1 that season.

Adding the percentages along the seasons we get a sort of "total virtual titles" for each driver (MS is not put because he has many more titles in the past seasons, so his count would be not complete in this table). It is interesting to see how the number of Virtual Titles agrees pretty well with the real number of titles. The number of active seasons if written as well.

Virtual Titles (and number of active seasons):
ALO 2.10 10 *********************
HAM 0.99  4 **********
RAI 0.99  9 **********
BUT 0.71 11 *******
VET 0.52  4 *****
MAS 0.47  8 *****
WEB 0.21  9 **
MON 0.18  6 **
BAR 0.12 18 *
KUB 0.05  5 ·

And lastly, the "density" of Virtual Titles, i.e. number of VTs per active season. It shows the level of success taking in account the number of seasons. The most important difference is Vettel's position in this table.

Virtual Titles per active season:
HAM 0.248 *************************
ALO 0.210 *********************
VET 0.130 *************
RAI 0.110 ***********
BUT 0.065 *******
MAS 0.059 ******
MON 0.030 ***
WEB 0.023 **
KUB 0.010 *
BAR 0.007 *

In general terms I agree with those numbers. I feel Alonso is the overall best driver and perhaps Lewis is the most brilliant. Vettel is aproaching those two but he is not there yet. Button is IMO the best of the rest and Webber sadly is below them (although last season was very good for him). Kimi is right there with LH or SV and Massa is below Button and perhaps ahead of Montoya (let's not forget Massa's best years). Finally Barry and poor Kubica are at the end of this top ten list. Supposedly this season could have been a good chance for Kubica...

One last word of "advice". All those numbers refers to performances of drivers with their particular cars in those years. It doesn't measure the "intrinsic" quality of drivers, but the quality of the pair driver-car.

[dyewat808]

Interesting concept - am I right in thinking that the so-called "Crashgate" scandal would be another example?

Very interesting, it would be nice to see how many alternative seasons people can come up with. Presumably you have to stick to events that happened in specific races and not just conjure up magical results - you have to stick with what would seem the most logical outcome?

[JeremySmith]

Schummy great stuff as always, lateral thinker...

[Schummy]

Originally Posted by dyewat808

Interesting concept - am I right in thinking that the so-called "Crashgate" scandal would be another example?

Very interesting, it would be nice to see how many alternative seasons people can come up with. Presumably you have to stick to events that happened in specific races and not just conjure up magical results - you have to stick with what would seem the most logical outcome?

The generation of "alternate seasons" is an automated process done by the "statistical bootstrapping", a known method. I don't choose what scenarios can happen and what not. My only (few) choices are "technicalities" about what type of bootstrapping to use and so on. So, those results are not subjective in that sense.

[Schummy]

Originally Posted by JeremySmith

Schummy great stuff as always, lateral thinker...

Really brilliant minds think alike

(Translation: we, the number freaks, like tables with many digits)