Probabilities of Win

[Schummy]

(Warning: post basically about two tables of data! )

The title is wide in its meaning, ii is not just "probability of win a race" or "probability of win the title", it depends on the type of calculation I can bring here in, hopefully, several posts in the remain of the season.

In this case it is about the estimated probability of a driver ending the season above other driver in the final classification.

It is done using some probabilistic calculations using current data of the season. Although the details can be intricate (i.e. boring) my goal is that it can be somewhat curious/interesting to look at.

I have done two scenarios. In the first one, I suppose future races with the average performance of past races for each driver. It favors those drivers who have got many points, and penalize those with a weak beginning of the season. In short, this first case is maintaining the present status quo of performances.

    VER LEC PER SAI RUS HAM
VER  --  88  98  99 100 100
LEC  12  --  75  93  98 100
PER   2  25  --  78  89  96
SAI   1   7  22  --  60  92
RUS   0   2  11  40  --  92
HAM   0   0   4   8   8  --

For example, Verstappen has a probability of 98% of ending ahead Perez and Russell has a 11% probability to beat Perez.

Essentially, VER is only threatened by LEC; LEC is threatened by PER and maybe SAI;PER is threatened by SAI and RUS; SAI is by RUS and maybe HAM and RUS perhaps threatened by HAM.

Of course they are other ("lesser") drivers who could have a go to those last positions.

Now the second scenario. In this case it is supposed that all the drivers will have in the future similar performances. It is a supposition that helps drivers currently with less points (for example, Mercedes supposedly will match Red Bull and Ferrari's pace, or Sainz will get similar performances than Leclerc, etc). In short, this table is supposing the performance will be similar in the future for all drivers.

    VER LEC PER SAI RUS HAM
VER  --  73  88  91  97  96
LEC  27  --  63  78  87  94
PER  12  37  --  65  73  82
SAI   9  22  35  --  55  77
RUS   3  13  27  45  --  77
HAM   4   6  18  23  23  --

The structure is similar to the former table, but the span of "menaces" for positions is wider. One can see the probabilities of lesser drivers against leader driver are higher than before. For example, VER can be challenged by LEC, PER and maybe SAI, LEC could be threatened by anybody until HAM.

There is a "minor" dissonance in those calculations: the past data include two GP with sprint race added points while (I think) in the rest of the season there are not more sprint races. I did a little check about it and the impact is not very significant.

[Born Racer]

Thanks for the work, Schummy. Clarification - there is one more sprint race, in Interlagos.

[Schummy]

Thanks for that detail!



Naively, I used Forix's future GP weekend schedules to get an idea but I suppose they just project a standard schedule in local time, or something like that(?)


(Forix is great but one should not misuse it :-) )

[Schummy]

Updating the table of probabilities after Paul Ricard.

    VER LEC PER SAI RUS HAM
VER  --  85  93  95  99  98 
LEC  15  --  55  72  76  85 
PER   7  45  --  67  72  80 
SAI   5  28  33  --  51  71 
RUS   1  24  28  49  --  75 
HAM   2  15  20  29  25  --

(Calculations don't take in account in Brazil there is a sprint race, but the impact of it is still small. It will be greater when we are in the few last GPs.)


One more slip by Charles and suddenly we could find ourselves with a dead Championship.

On a brighter side of things, the 2nd positions is still very open!

This table is done supposing that, from now on, those drivers are going to perform approx at the same level between them. Probably Verstappen is going to perform better than others on average, so his probabilities are arguably even higher.

[Moneyseeker]

Never mind, apparently Ferrari see no reason why they can't win the remaining ten races...

Sent from my SM-T580 using Tapatalk

[Schummy]

They can do it... the problem is it is extremely improbable :-D

The lesson of the data is that the current gap from Leclerc to Verstappen is reaching a hard level.

A simpler way to monitor it is the One-Race-Gap measure: it is the gap divided by the square root of remaining number of races. Currently is 63/sqrt(10) = 19.9. The ORG is approx proportional to the probability to overcome that gap in the remaining races. As a rule of thumb, when it is above 25, the situation is practically impossible.

The ORG is not a "magic" formula, it is based in the properties of variances in probability theory.

One can calculate the ORG to follow the situation of drivers respecting the leader and the likelihood of contending for the title.

[Schummy]

More calculations (before GP Belgium).

I have done a number of calculations about the expected evolution of the championship in the final 9 races (ignoring the remaining sprint race).

The next table try to show many of those calcs: (sorry if the characters in the table are small, I am afraid it can be more cumbersome if I put them bigger).

     Pwin Podium Pzero  m     s    EFP  CP   ETP  sTP   Interval  Ptitle
VER  48%   65%    24%  15.7  10.5  141  258  399  31.6  336  463  99.83%
LEC  19%   37%    29%  10.7   9.1   96  178  274  27.4  219  329   0.13%
PER   7%   40%    29%  10.2   8.0   92  173  265  24.0  217  313   0.04%
SAI   7%   37%    35%   9.4   8.2   84  158  242  24.6  193  291   0.003%
RUS   1.2% 32%    18%  10.2   5.9   92  156  248  17.7  213  284   0.001%
HAM   1.2% 34%    18%   9.4   6.0   85  146  231  19.8  191  270  <0.0002%

Explanation:
Pwin = Probability of winning the next race.
Podium = Prob of getting a podium position (including 1st).
Pzero = Probability of getting 0 points.
m = average (expected) points per (future) race.
s = standard deviation of points per race.
EFP = Expected points in the next 9 races.
CP = Current points.
ETP = Expected total of points at the end of the season.
sTP = Standard deviation of points at the end of the season.
Interval = interval of points at the end of the season (95% of confidence)
Ptitle = Prob of getting the World Champion title.

By now it is enough! I will add other things in another post.

[Schummy]

Second part. The same calculations BUT supposing everyone of the 6 leading drivers will perform at the same level (same probability for win, for podium, for getting zero points,...). I.e., after summer break, Verstappen/RedBull will not be dominant, Ferrari will be less unreliable and Mercedes will be at the level of the other two teams.

     Pwin Podium Pzero  m     s    EFP  CP   ETP  sTP   Interval  Ptitle
VER  14%   41%    26%  10.9   8.5   98  258  365  25.5  305  407  97.5%
LEC  14%   41%    26%  10.9   8.5   98  178  276  25.5  225  327   1.2%
PER  14%   41%    26%  10.9   8.5   98  173  271  25.5  220  322   0.80%
SAI  14%   41%    26%  10.9   8.5   98  158  256  25.5  205  307   0.22%
RUS  14%   41%    26%  10.9   8.5   98  156  254  25.5  203  305   0.17%
HAM  14%   41%    26%  10.9   8.5   98  146  244  25.5  193  295   0.07%

Even with this "egalitarian" supposition about future performances, Max has still 97.5% probability to getting the title while Leclerc has just 1.2%.

Those percentages take in account the "random events" (i.e. luck) that, sooner or later, play a role in races. What they don't take in account are changes in performance that cars (or drivers) can have in the last part of the season. It is clear that Leclerc/Ferrrari needs a better level against Verstappen/RedBull to aspire to be a real contender. Luck, by itself, will not be enough (as the former calculations show).

[Aysedasi]

Originally Posted by Schummy

.....after summer break, Verstappen/RedBull will not be dominant, Ferrari will be less unreliable and Mercedes will be at the level of the other two teams.

After qually yesterday, this scenario seems very unlikely!

[Schummy]

Indeed!!