Probability of Win

[Schummy]

Last season I did this kind of calculations in the first part of the champioship. So... here we are again.

It is a rough estimation of the probability of win in the next race (or in any particular race in the season), just using the info in the past races (of the season).

First, the results: probability of win (next race), and estimated future wins (rest of season)

    PW%  EFW
FA  21%  2.9
FM  19%  2.7
KR  17%  2.4
LH  10%  1.4
XX*  2%  0.3

Ferrari  36%
McLaren  31%
Anyother  4%

As can be seen, FA, FM and KR are more or less at the same level, and Lewis "Hype" Hamilton is a bit behind (yet?). XX is not a new chinese driver at all, it is just a mark for any other driver.

Ferrari and McLaren have a very similar probability of win, taking in account the circunstances so far.

Now the gory, tasteless details

Two considerations are taken. Firstly one has to calculate the "estimated wins" (EWs) one driver has got. EWs is more or less the number of wins, except that second positions are considered equal a 1/4 of a win (this particular fraction is approximative, and can be updated along the season). So, to let a total of 1 "win" per race, real wins have to be valued as 0.8 and 2nd positions as 0.2.

Secondly, EWs has to be "faded out" as races are becoming more and more old as time pass by. So, last GP is valued 100%, second last is valued 95%, third last is 90% (more precisely 0.95*0.95), etc. Thus, for example, a win in the last GP is a bit more signifricant than a win in the second last one (in terms of prediction for the next race). This number 0.95 is an actual aproximation of the real data from F1 in the last seasons (although it is difficult to know precisely).

With all this nonsense, we can calculate EWs for each driver. After that, and including a suitable a priori "before the season" probability of win (PW) for each driver (in this case merely a 5% PW for everyone), we reach to a forecasted PW for the next race for each driver.

This table has the info:

    Positions  Estimations       EW        PW
               0.90 0.95 1.00 
FA  2  1  -  = 0.2  0.8  ---  = 0.94 wins  21%  
FM  -  -  1  = ---  ---  0.8  = 0.80 wins  19%
KR  1  -  -  = 0.8  ---  ---  = 0.72 wins  17%
LH  -  2  2  = ---  0.2  0.2  = 0.39 wins  10%
XX* -  -  -  = ---  ---  ---  = 0.00 wins   2%

Team     PW
Ferrari  36%
McLaren  31%
Another   4%

[Marbot]

And what if it rains?

[Inigo Montoya]

Great stuff as usual Schummy. keep it coming

[Marbot]

Yes,great stuff,but what if..........

[Schummy]

Originally Posted by martyn bott

And what if it rains?

If it rains all this is unprecise, because wet races need its own set of data, and we don't have any at the moment, and probably we will not ever have enough data along the season

So... go on dancing for rain Unpredictability is the best gift for us!

[Sev]

Nice metric Schummy, but I do have one problem with that.

Those numbers do not add up to 100%, not even close; which should clearly be wrong.

Even if you assume "XX" or "Another" to be each other team individually (which I'm assuming it's not), you get weird numbers, and frankly McLaren/Ferrari win more than that % of GPs.

I think the scoring system is good, but it definately needs to be normalizable; otherwise it doesn't really represent anything.

[Schummy]

Originally Posted by Sev

Nice metric Schummy, but I do have one problem with that.

Those numbers do not add up to 100%, not even close; which should clearly be wrong.

Even if you assume "XX" or "Another" to be each other team individually (which I'm assuming it's not), you get weird numbers, and frankly McLaren/Ferrari win more than that % of GPs.

I think the scoring system is good, but it definately needs to be normalizable; otherwise it doesn't really represent anything.

I advice you to buy another calculator, or buy new batteries for it

FA+FM+KR+LH = 67%, the resting 33% is divided between the other 18 drivers and... you get 2% (rounded to integer). It's not so hard

[Sev]

I stand corrected :O

To then again ask a more sensible question, you said you used this metric all through last year; how well did predictions match up to reality?

[Schummy]

In fact I was lazy enough to only make the first rounds . Anyway, I have to redo it for last season to get convinced about the 1/4 coeficient for 2nd position. I'll try the best coef possible and I'll see how it does.

I eventually will put it here in this thread (if I don't get tangled with others stats, that is ). Please, check here some day in the future!

[Inigo Montoya]

Based on last year, is there a statistically significant effect of a driver being on his first or second race of an engine?

If so, is it worth it to include a factor which takes this into account?

[Schummy]

I have not examined it. But if I found some data source for engine "cycles" along 2006, I could look at it. Probably if it is significant then it would be worthy to include, because with few GPs the effect has to be pretty large (to be significant).

It is even more pertinent to a reliability table I'll try to do in the next days. Probability of mechanical failure *should be* related to engine age.

[Inigo Montoya]

I guess in your reliability table, you will see not only engine failures, but gearbox, etc, which are not related to engine age.

Anyhow, thanks for your work on this. I always look forward to your stats

[Schummy]

Engine is one of the (main) factors in reliability, so I hope it (age) shows in total mechanical reliability.

Another element of interest (and not related {ummm...} to this issue) is "driver reliability". It is difficult to proof definitively that someone is prone to accidents, in just a season, but it makes another interesting column in the (future) table