

4 Jun 2019, 12:50 (Ref:3907847)

#1

Subscriber
Veteran
Join Date: Jul 2001
Location:

Somewhere near 2nd Lagrangian point 
Posts: 3,183

F1 2019: Some stats regarding the title chase
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 "OneRace 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.
======================================================
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):
Code:
Gap ORG
BOT 17 4.4
VET 55 14.2
VER 59 15.2
LEC 80 20.7
GAS105 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.



4 Jun 2019, 13:16 (Ref:3907858)

#2

Race Official
Veteran
Join Date: Mar 2005
Posts: 7,513

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.



4 Jun 2019, 13:17 (Ref:3907859)

#3

Retirement Club Member
20KPINAL
Join Date: Oct 2001

Lymington, New Forest, England 
Posts: 32,357

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


__________________
Free as a bird now......
0/218

4 Jun 2019, 16:40 (Ref:3907907)

#4

Veteran
Join Date: Mar 2005
Posts: 6,479

Quote:
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!


__________________
What shall we use to fill the empty spaces, where waves of hunger roar?
Shall we set out across the sea of faces in search of more and more applause?
Shall we buy a new guitar? Shall we drive a more powerful car?

4 Jun 2019, 16:49 (Ref:3907910)

#5

Subscriber
Veteran
Join Date: Jul 2001
Location:

Somewhere near 2nd Lagrangian point 
Posts: 3,183

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...



4 Jun 2019, 18:12 (Ref:3907925)

#6

Subscriber
Veteran
Join Date: Jul 2001
Location:

Somewhere near 2nd Lagrangian point 
Posts: 3,183

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.



5 Jun 2019, 04:40 (Ref:3907988)

#7

Veteran
Join Date: Jun 2009
Posts: 7,269

Quote:
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.



5 Jun 2019, 05:18 (Ref:3907991)

#8

Subscriber
Veteran
Join Date: Jul 2001
Location:

Somewhere near 2nd Lagrangian point 
Posts: 3,183

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.



5 Jun 2019, 09:21 (Ref:3908006)

#9

Veteran
Join Date: Oct 2000

Champion Porsche/Audi territory 
Posts: 1,522

Quote:
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....


__________________
"Those were the days my friends. We thought they'd never end..."
jimclark

5 Jun 2019, 16:50 (Ref:3908087)

#10

Veteran
Join Date: Apr 2007
Posts: 4,187

Quote:
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:
1822.83= 4.83
2522.83= 2.17
2522.83= 2.17
1322.83= 4.83
2622.83= 3.17
2522.83=2.17
His expected score (HE) at the moment is 22.83.
Putting each deviation into the calculation below:
((HSHD)^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:
2620= 6
1820= 2
1820= 2
2520= 5
1820= 2
1520= 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.


__________________
"It was really frustrating to stay behind slower cars, it ended up to be a fairly boring race for me."
"Wasn't fair! I brake for animals, Lewis doesn't"

6 Jun 2019, 02:06 (Ref:3908201)

#11

Veteran
Join Date: Oct 2003
Posts: 2,072

my brain hurts.


__________________
Part time wingman, full time spud.

6 Jun 2019, 02:44 (Ref:3908204)

#12

Subscriber
Veteran
Join Date: Jul 2001
Location:

Somewhere near 2nd Lagrangian point 
Posts: 3,183

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 202·4.04 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.



6 Jun 2019, 07:16 (Ref:3908217)

#13

Subscriber
Veteran
Join Date: Jul 2001
Location:

Somewhere near 2nd Lagrangian point 
Posts: 3,183

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.



9 Jun 2019, 02:03 (Ref:3908692)

#14

Veteran
Join Date: Jun 2009
Posts: 7,269

Quote:
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.



12 Jun 2019, 03:09 (Ref:3909471)

#15

Subscriber
Veteran
Join Date: Jul 2001
Location:

Somewhere near 2nd Lagrangian point 
Posts: 3,183

New gaps after Canada:
Code:
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.
Code:
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.



Thread Tools 

Display Modes 
Linear Mode

Posting Rules

You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts
HTML code is Off





