F1 2019: Some stats regarding the title chase

[Schummy]

After 6 GPs, I think there are already data to make a number of significant assumptions about this season's title.


The following conclusions are "based" on an indicator that could be named "One-Race Gap" or something like that.


WARNING! The next part is a sort of explanation of the ORG indicator
Please, jump ahead if you are not interested in freaky things.

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ORG is the gap in points to overcome in just one race that is equivalent to the actual gap in points with N races to go. For example, according to this indicator, a 20 points gap with 16 races to go is equivalent to a 5 points gap with one race to go. ORG is built using the assumption that the two drivers involved in the gap are going to perform similarly well in the remaining races and that the performance in those races are nor going to have any relevant "trend" or "streak" (that is what F1 usually shows in actual data). In fact, ORG is ultimately based in the simple additive property of variances.

====================================================



Ok, enough of boring details. Let's pass now to... boring numbers .


Current (2019/06/04) data about gaps in points respect the leader (Lewis Hamilton):

    Gap   ORG  
BOT -17   4.4  
VET -55  14.2  
VER -59  15.2  
LEC -80  20.7  
GAS-105  27.1

So, for example, Vettel has a 55 points gap to Hamilton with 15 races to go. It is equivalent to a 15.2 gap with one race to go. Obviously, putting it this way one realizes Sebastian Vettel has a very tough task to overcome that gap. In a somehow naive point of view one could think that 15 races to go means there are still 375 points to take and 55 points is only a fraction of it. But that is not how probability works in real world.


(An "interesting" case is Gasly. His ORG is 27.1, that is literally impossible to achieve in one race, but actually his 105 gap with 15 races to go is possible to be done. The reason for this "discrepancy" is ORG is an approximate probabilistic model, not a perfect exactness. In fact, according to historic F1 scores, a 27.1 ORG value means somewhat less than 1% of probability of being overcome, i.e. extremely unlikely, but not impossible.)


In a (perhaps) intuitive way, ORG = 10 means approx a probability of 10% of remount that gap. So, ORG >= 10 means driver has a small chance to surpass the points leader (Hamilton). ORG = means approx a 1% of chance to overcome that gap; for me it means that it's very unlikely to happen.


In conclusion of this extremely raw and rough post, only Bottas is in a not hard position to fight with Hamilton. Moreover, only 5 drivers has a likely chance to be champion (from Hamilton to Leclerc). In fact, Leclerc is in a desperate position and Vettel and Verstappen are already in a tough place.


It is not a enjoyable thing, it means current season is, mostly, decided, at least in a great part.



There is an escape route in this barren scenery: if Ferrari or RedBull suddenly improves, then the ORG assumption of similar future performances between drivers will be broken and probabilities will be less severe.

Sorry for this lengthy, thick post.

[Born Racer]

Thanks, Schummy. Nice to see this analysis.

So, this probability backs up the idea that Ferrari or Red Bull drivers simply will almost certainly not beat Mercedes if the cars stay the same. They depend on closing the gap to Mercedes.

[Aysedasi]

No, don't apologise - I love the whole thing......

[chillibowl]

Originally Posted by Schummy

So, for example, Vettel has a 55 points gap to Hamilton with 15 races to go. It is equivalent to a 15.2 gap with one race to go....

im assuming just a typo but i should be reading this as VET's ORG is 14.2 and VER's ORG is 15.2?

interesting way to boil it down to one race like this.

also i tend to agree...given LH's remarkable record of consistency combined with Merc's unbelievable reliability i feel like the season is already done and dusted. but there is a reason they still have to run the races so lets hope LH's deal with the devil has come to an end!

[Schummy]

Thank you very much to both!


I hope to follow this particular stat in other future GPs. My (somewhat comic) problem is I watch all sessions of GP weekends (FP1, FP2, FP3, Qualy, Race) delayed in internet and I usually watch the proper race on Thuesdays or Wednesdays!

So, I am always late with GPs!

Yeah, Seb and Max, realistically speaking, depends on their teams' shape respecting Mercedes's. Otherwise, only bad luck/decisions by Lewis/Bottas/Mercedes, can give them a slight hope.


Another interesting point is teams' championship...

[Schummy]

Sorry, chillibowl, our messages crossed in time and I didn't see yours!


You are right about the typo, Seb's ORG is 14.2 Thanks!


Yes, it seems Lewis has a very positive chance to add another title... but who knows what Bottas can achieve in the remaining races. If they are relatively balanced, the title could be decided by random events, always present in F1 and motorsport in general.

[wnut]

Originally Posted by Schummy

Sorry, chillibowl, our messages crossed in time and I didn't see yours!


You are right about the typo, Seb's ORG is 14.2 Thanks!


Yes, it seems Lewis has a very positive chance to add another title... but who knows what Bottas can achieve in the remaining races. If they are relatively balanced, the title could be decided by random events, always present in F1 and motorsport in general.

Thanks for the work Schummy! Interesting analysis.

Mercedes engine upgrade is due in Canada, so I think that Hamilton will be in a much stronger position wrt RBR and Ferrari.

[Schummy]

wnut, glad to see you again! (Also, I hope you enjoy the "traditional" team mates comparison for 2019).


It's terrible to say but I hope Mercs has a few reliability issues with its engine upgrade or something like that, for the sake of the championship's interest.



It's the "curse" of teams who do a great job: we tend to hate their (deserved) dominance. A sweetener for this dominance is the fact that Mercedes was the last team of the great Niki Lauda, so it is not so bad if they go on winning.

[jimclark]

Originally Posted by Schummy

according to this indicator, a 20 points gap with 16 races to go is equivalent to a 5 points gap with one race to go.

Please PM me....how do you arrive at these figures?
20/16 equiv. to 5/1? (1.25=5? )
'Truly interested in your derivation. I create indicators re: the stock market and I just don't get it....

[crmalcolm]

Originally Posted by jimclark

Please PM me....how do you arrive at these figures?
20/16 equiv. to 5/1? (1.25=5? )
'Truly interested in your derivation. I create indicators re: the stock market and I just don't get it....

I am interested too, and from my own experience I attempted to explain it as follows:

Hamilton has scored 137 points from 6 races, so his average score is 137/6=22.83
This is identified as Hamilton Mean (HM)
His score in each race is given the notation HS.
His deviation (HD) from HM so far reads:
18-22.83= -4.83
25-22.83= 2.17
25-22.83= 2.17
13-22.83= -4.83
26-22.83= 3.17
25-22.83=2.17

His expected score (HE) at the moment is 22.83.

Putting each deviation into the calculation below:
((HS-HD)^2) = gives a string of results
23.33
4.71
4.71
23.33
10.05
4.71

So his variance is the square root of the sum of all of these figures,
70.84/70.84 = 8.42 ie, Hamilton's results can expect to be 8.42 away from 22.83.

Applying the same set of calculations for Bottas gives:
120/6=20 (BM)

His results are:
26-20= 6
18-20= -2
18-20= -2
25-20= 5
18-20= -2
15-20= -5

Calculated in the formula gives:
36
4
4
25
4
25

So his variance is the square root of the sum of all of these figures,
98/98 = 9.90 ie, Bottas's results can expect to be 9.90 away from 20.


His variance is 1.48 away from Hamilton's and his expected result is 2.83.

I see it as Bottas needs to improve on his expected result by 2.83, and improve his variance by 1.48.

1.48+2.83= 4.31 points to make up in one race.


This may be all a load of nonsense calculation but I have attempted to work out why Bottas is 4.31 (by my calculation) behind Hamilton in terms of improvement required.

[Skam85]

my brain hurts.

[Schummy]

Oh, it was an unexpected series of calculations!

I replied a PM to jimclark with my ORG explanation, but here goes an explanation regarding your calculations and ORG.

Variance is the average (mean) of the squared deviations. So, Bottas's would be: 98/6 = 16.33. Variance itself is not directly related to any expectations around the mean, as variance is expressed in squared unit of measurement. Standard deviation I think is what you were referring to, it is the square root of variance. So Bottas's is 16.33^0.5 = 4.04. In gaussian distributions it means Bottas's score has approx 95% of expectations to be between 20-2·4.04 and 20+2·4.04 (i.e. in the interval (11.9,28.1)).

But, under the conditions formerly said, ORG is easiest to calculate (and deduce):

ORG = Gap/sqrt(n), with n= races to go.

In short, it is based in that standard deviation of a sum of n identical uncorrelated random variables is sqrt(n) times the s.d. of one of those variables.

So, ORG(Botas) = 17/15^0.5 = 4.4 (15^0.5 is the square root of 15).

I hope this messy explanation is useful, crmalcolm :-)

PS:

A "funny" consequence of this is one can try to estimate a probability for Bottas overcoming this deficit using past results in the season. For example, in how many possible races Bottas would get more than 4.4 points than Lewis? (knowing the first 6 races). So we would pass from a ORG to a probability.

[Schummy]

I have looked the Teams' Championship situation and the ORG analysis doesn't throw anything interesting: it says Ferrari and RedBull have a difficult chance to win the title and McLaren cannot win it LOL . That's nothing new, certainly!

About Drivers' Champ, we can deduct some "things to do" for the drivers if they want to be in contention for the title. Describing as "difficult" if ORG is 10 or more and "unlikely" (as in "freaky" ) if ORG is 25 or more, currently Bottas is comfortably in the title chase but Vettel and Verstappen have it difficult and Leclerc is nearly unlikely to do it (a freaky chance).

For Canada:

Bottas will enter in a difficult position if he loses 22 points respecting Hamilton (Lewis wins and Valteri has a disastrous result).

Vettel can go back to a normal position as title contender if he gains 17 points to LH (Hamilton has to have a very bad day and Vettel has to have a good one).

Verstappen will go back to be in a normal contender position is he gets 19 points over Hamilton (read Vettel's comentary...)

Leclerc cannot go back to a normal contender position, but he could fall into the Hades of being out of the championship if he loses a further 17 points to Lewis (i.e. another bad day in the office).

Gasly could get back into life (although with extremely tough chance) if he gains 9 points to Hamilton.

Nobody else can go back to life even winning the race and Hamilton crashing in the first corner (which is not very unlikely in Canada...).

LOL those non Mercedes drivers need Lewis Hamilton to have a problem to gasp a bit of air.

[wnut]

Originally Posted by Schummy

wnut, glad to see you again! (Also, I hope you enjoy the "traditional" team mates comparison for 2019).


It's terrible to say but I hope Mercs has a few reliability issues with its engine upgrade or something like that, for the sake of the championship's interest.



It's the "curse" of teams who do a great job: we tend to hate their (deserved) dominance. A sweetener for this dominance is the fact that Mercedes was the last team of the great Niki Lauda, so it is not so bad if they go on winning.

Very glad to see your posts too Schummy, was missing your valuable contributions.

[Schummy]

New gaps after Canada:

    Gap   ORG  +10  +26
HAM 162    
BOT -29   7.8   -8  ---
VET -62  16.6  +25  ---
VER -74  19.8  ---  -17
LEC -90  24.1  ---   -1

I will remind you that an ORG > 10 is difficult to overcome (approx < 10% of probabilities) and an ORG > 26 is practically unrecoverable (< 1%).

Bottas is still on the hunt but if he loses more than 7 points in the next race he will be in a difficult position.

Vettel goes on losing chances. Even if he wins the next race and Lewis doesn't score, he will be almost in a difficult situation. Vettel looks as the boxer who is a bit groggy at the moment.

Max Verstappen is nearly finished in terms of title. If he has a bad day next race, he will be definitively out.

Leclerc is just in the edge. Losing points respect Hamilton will push him over the cliff.

Regarding the Teams' Championship, the situation is even more grim for Mercedes's rivals.

     Gap   ORG  +44
mer  295        
fer -123  32.9  -36
rbr -171  45.7  +12

Here the point without return is ORG > 44. Red Bull just lost its last hopes in Canada (realistically speaking, I doubt they had any hope anyway).
However, the more interesting point is Ferrari is going firmly in the direction of nothingness in just a few more GPs.

If they lose 36 points in the next race, the title will be over with >99% probability. The same if they lose 30 in the sum of the next TWO races or if they lose 23 in the sum of the next THREE races. In all those scenarios Ferrari would be out of the title race.

[wolfhound]

On the constructors front by my calculations Mercedes could have the championship by Singapore or Russia if the two top teams keep up their current scoring averages.

[Schummy]

Sorry for not replying earlier :-)

Yes, in terms of absolute impossibility, at current rate (updated after France), Mercs would get the title in Japan or Mexico, as you said.

(BTW, in general terms, the numbers of GPs to get the title with absolute certainty would be: n = GPTG/(1+Gap/(44*GPs)), where GPTG is races to go, Gap is current points gap and GPs is number of races already done)

But in terms of very high probability (>99%, almost certainty) the future is much bleaker: Red Bull is already out of the title and Ferrari can be out in the very next race.

Something very, very fundamental has to change for Ferrari can remount the 140 deficit it currently has. Probably it doesn't have any precedent in F1 past, but I have not looked into it. (In Drivers's Championship we have the case of Raikkonen's title...).

[Schummy]

New gaps after GP France:

     Gap   ORG  +10  +25
HAM  187
BOT  -36   9.98  -1  ---
VET  -76  21.1  ---  -15
VER  -87  24.1  ---   -4
LEC -100  27.7  ---  +10

     Gap   ORG  +44
mer  338        
fer -140  38.8  -16
rbr -201  55.7  ---

Now even Bottas is in a difficult position (approx 10%) to overcome the gap. Leclerc is out and Vettel and Verstappen are almost out of the title (<1% is out of the title for me, it is a ORG of 25 or more).

If Verstappen doesn't get more points than Hamilton in the next race he will be "officially" out (ORG > 25). Same with Vettel if he loses 11 points. Respecting Leclerc, he has to recover 14 points to Lewis to come back to life (altough very probably to no avail).

In the teams' table, only Ferrari has a chance to fight Mercedes, and this chance is small. If Ferrari loses the next race, it probably will be out too. I remind you that, in this discussion, a <1% chance is not a realistic chance to get the title.

[Schummy]

Gaps after Austria:

Drivers
     Gap   ORG  +10  +25
HAM  197
BOT  -31   8.9   -3  --- Contender
VER  -71  20.5  ---  -12 Almost out
VET  -74  21.4  ---   -9 Almost out
LEC  -92  26.6  ---  +10 Out

Teams
     Gap   ORG  +43
mer  363        
fer -135  38.97   -8 Almost out
rbr -194  56.0   --- Out

Ironically, Vettel and Leclerc are in a slightly worse position than before even if they got more points than Hamilton. It is due to now there is one less race to go and then the significance of a given gap is bigger.

Botas is in the limit as contender, if he loses 3 points to Lewis in the next race, he will pass to be "Struggling", i.e. less than 10% chance to overcome the gap with Hamilton.

Leclerc would need gain 10 points to Hamilton (always in the next race) to get into a minimal likelyhood of getting the title. Meanwhile, Verstappen and Vettel will be out of title chase (with at least 1% of chance) if they lose 12 and 9 points, respectively, with LH.

About teams championship, Ferrari has slightly worsened its chances (due to the same reason as formerly mentioned) and it is nearing the limit for being out of the championship. If they lose 8 points to mercs, they will "achieve" that. Of course RedBull is already out.

In short, things are not exactly exciting respecting titles this season.

[alc59]

Well done Schummy on an intriguing analysis. It's a bit of an ask, but how does the technique look when applied tp a previous season or two?

[Schummy]

alc59: sorry for not replying before (-_-)'

I have used this procedure since years ago, in F1 and in MotoGP, to get an idea about how the championship was going in realistic terms. The method has worked nicely.

Retrospectively, I applied it to older WDCs too; the most striking case is Raikkonen's title in the (in)famous McLaren self-debacle (Alonso-Hamilton). Kimi was in the edge of being statistically "discarded" and yet got the title in an extraordinary set of circumstances. Actually, it is not a rare event considering the whole picture of F1 history. There have been 69 seasons, so is probabilistically reasonable that a "rare" championship happens.

(Gore details:
More concretely, Raikkonen was at the 1% chance point and however he got the title. What is the probability of not getting any 1% event-championship in 69 seasons? Applying a binomial distribution that probability is 50%! Thus, is very reasonable to have such an exceptional event as Kimi's title.)

[Schummy]

Update of ORGs after Germany.

     Gap   ORG   +10  +25
HAM  225
BOT  -41  12.97  +11  ---  Difficult
VER  -63  19.92  ---  -12  Difficult
VET  -84  26.6   ---   +9  Out
LEC -105  33.2   ---  ---  Out

     Gap   ORG  +43
mer  409        
fer -148  46.8  +19  Out
rbr -192  60.7  ---  Out

Bottas is in a difficult position (<10% chance). Verstappen is still in the title's hunt but in an even more difficult situation than Valteri. The two Ferraris are out (<1% chance).

In terms of short time evolution, Bottas can get out of his difficult position if gains 11 points above LH in the next race. Verstappen will be out of the championship if he loses 12 points to Hamilton in Hungary. Vettel could go back to the title race if gets 9 points above Lewis in this next race.

Respecting teams, Ferrari and Red Bull are out of the championship but Ferrari can recover to a (very difficult) title option if they win 19 points over Mercedes in this GP.

[Schummy]

Hungary has been "tragic" for Bottas: from a pretty difficult position to an almost out of contention position. Basically, he is out, from a probabilistic point of view (perhaps around 2% of chance).

     Gap   ORG   +10  +25
HAM  250
BOT  -62  20.7   ---  ---
VER  -69  23.00  ---   -2
VET  -94  31.3   ---  +24
LEC -118  39.3   ---  ---

     Gap   ORG  +43
mer  438        
fer -150  50.0  +29
rbr -194  64.7  ---

Bottas and Verstappen still minimally resist on the title hunt but both Ferraris are utterly busted...

For the next race:
If Verstappen loses 2 points against Lewis he will be out as well. If VET wins and HAM has a disaster, Seb will go back to title contention (but an extremely unlikely contention anyway).

In teams champ, the only thing worthy to say is if Ferrari amass 29 points over Toto's team in Spa, they will have the privilege of to have an extremely marginal chance for the title (about 1% perhaps).

In practical terms, both titles are decided but both 2nd positions are still well in fight.

[Schummy]

With the ORGs (One Race Gaps) previously calculated we could estimate the probabilities of any driver beating any other driver at the end of the season. The following table shows those probabilities for each pair of drivers (one versus another). The last column is an estimation of the final probabilities to get the title.

     HAM  BOT  VER  VET  LEC
HAM   --   99  100  100  100  = 98%
BOT    1   --   69   93  100  =  2%
VER    0   31   --  100  100  =  1% 
VET    0    7    0   --   92  =  0%
LEC    0    0    0    8   --  =  0%

For example, Bottas has 93% of probabilities of getting ahead of Vettel in the championship.

The first 5 positions in the championship are pretty much decided, except 2nd-3rd that are still to be decided between Bottas and Verstappen (69% against 31%).

Vettel is out of the final podium already, except, curiously, he has some chances of overcome Bottas (7%), but doesn't have chances against Verstappen(!). Leclerc is pretty much buried in 5th place... but, however, has a small 8% chance of jump ahead Vettel for the 4th final position.

Frankly, a bit sad for Ferrari to be "fighting" for 4th-5th, positions. At the end of the day, however, perhaps they were lucky that Red Bull chose Gassly for the weberish second Red Bull...

[Schummy]

Update after Italy, with only 7 races to go.

GAP ANALYSIS

For title:
-----Gap ORG
HAM 284
BOT -63 23.8
VER -99 37.4
LEC -102 38.6
VET -115 43.5

For 2nd:
--- Gap ORG
BOT
VER -36 13.6 (~6%)
LEC -39 14.7 (~5%)
VET -52 19.7 (<1%)

For 3rd:
--- Gap ORG
VER
LEC -3 1.1 (~50%)
VET -16 6.1 (~18%)

I have extended a bit the analysis to add the fight for 2nd and 3rd positions... mostly because the title hunt is not very exciting, due to the prevalence of Hamilton (and Mercedes).

For title there is just the slightest hope for Bottas.

For runner up, Bottas is favorite, of course but Verstappen and Leclerc has a (difficult) chances, that I evaluate aprox about 5-6%. Vettel has also a chance but, according to past results, is a lot harder.

For third, there is an expected hard fight between the no-mercs drivers. Verstappen and Leclerc are virtually tied and Vettel still has a sizeable chance (if his brain finally engages... ).