Alternative history: 2012 championship without misfortune

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Stradivarius
1
Joined: 24 Jul 2012, 19:20

Re: Alternative history: 2012 championship without misfortun

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I think that the drivers' and teams' strategical approach should be part of an evaluation like this. I originally wrote this example when looking at the differences between Hamilton and Button, who have very different qualities as race drivers. But it is equally valid for the teams who also have (to some extent) the ability to trade reliability for speed or vice-versa. Similar to the qualities of Hamilton and Button, McLaren had more speed than Ferrari last year, but Ferrari had better reliability and in the end they scored almost the same ammount of points.

First of all, a driver's approach to racing should be (and probably is in most cases) a result of both his own abilities and his knowledge and judgement about the reality of racing. Hence, when a driver like Button has a more careful and controlled approach than Hamilton, it is most probably not a coincidence. Button exploits the fact that during a full f1 season there is a lot of points to gain through other's misfortune or mistakes, provided that he is still in the race. So Button makes sure he stays in the race and picks up what his opponents leave behind, like a patient chess-player. While Hamilton, on the other hand, goes all in and pushes to the limit at all times. Some times this means Hamilton scores a lot more points than Button, but some other times it means that Button scores more, when Hamilton is unlucky, or makes a mistake. What we are doing here, is giving Hamilton back all the points he looses, while we are removing the points that Button gains, which doesn't quite give a 100% realistic picture.

Of course, if Hamilton is fastest and leads the race when his car breaks down through no fault of his own, it makes sense to give him full compensation. But when Hamilton and Hülkenberg crash and Button takes over the lead (and the victory), as happened in Brazil, it does not make that much sense. I am not trying to put the blame on Hamilton for what happened, but he did try to defend his position and he may have been less careful than Button would have been. When you choose to battle with someone, there is always a risk that you will suffer without being at fault. It is my impression that Hamilton's driving is normally more risky than Button's. That's why we often see Hamilton involved in collisions. It is not always his own fault, but he still has to pay the price. He takes up the battle and doesn't yield, while Button seems to be more careful. In many races Hamilton gains from his approach, but in Brazil last year he lost, while Button gained.

But more important than the above mentioned risk which the driver can influence himself, a driver who is placed 8th has basically 7 times higher probability of gaining a place through other's mechanical failures than a driver who is placed 2nd, simply because there are 7 cars ahead of him whose dnf would benefit him, compared to only one car ahead of the 2nd placed driver. And of course, when you are placed 1st, you have nothing to gain from mechanical failures or other incidents. This means that this way of compensating for luck doesn't treat different drivers equally in terms of rewarding them for their qualities. It basically rewards speed more than it rewards consistency when comparing to reality.

As mentioned, a driver's approach to racing is not purely a result of his choise. It is probably also influenced by his abilities. Button is probably not able to go as fast as Hamilton, even if he decided to take more risks. But Hamilton is probably also not able to be as consistent and make as few errors as Button (at least not without going even slower than Button), so their differences are not only due to risk evaluation. But let's imagine it was and consider a simplified example: (For the record, it doesn't really matter whether or not the difference between the drivers is a result of strategical choices and risk evaluation, as long as we take as given that Hamilton is quicker than Button, while Button makes fewer mistakes.)

Let's assume that Hamilton is always fastest and will win every race he finishes, because of his willingness to take more risk. But because of his risky driving, he makes a mistake in one out of 5 races that results in retirement. Button, on the other hand, never makes any mistake and finishes all races. If it was only the two of them (or if McLaren had a superior car that no one else could beat), and Hamilton retires in 20% of the races, Hamilton would win 16 races and have 4 dnfs during a season with 20 races. Button would win 4 races (those races where Hamilton retires) and in addition have 16 second places. In this case, Hamilton's strategy (ability) would give him 400 points and Button's strategy (ability) would give 388 points. So in an ideal world (under these simplified conditions) Hamilton does best.

But let's introduce some mechanical errors: Let's say that both drivers have an engine failure some time during the season. Hamilton's engine failure would most probably cost him a win and 25 points, in which case Button would probably (unless his engine failure occurs in that very same race or one of the 4 races where Hamilton makes a mistake) inherit the lead and gain 7 points. Button's engine failure, however, would not affect Hamilton. Hamilton would gain nothing, while Button would probably loose 18 points (or possibly 25 points).

Let's evaluate the possible outcomes and their probability (again simplifying by some assumptions): Let's say that Hamilton makes a mistake in the first 4 races of 20, just to keep track of those races in a simple way (it doesn't really matter when it happens).

We then have 5 possible outcomes:

First: Hamilton has an engine failure in one of the first 4 races, before he has time to make his mistake, and Button also has an engine failure in one of the first 4 races. In this case Hamilton will loose nothing, while Button will loose 25 points. The probability for this is 4%, assuming that the engine failures are independent events. (Which is not quite true as some tracks and some weather conditions are harder on the engines, but nevertheless gives a good idea for this example.)

Second: Hamilton has an engine failure in one of the first races, before he has time to make his mistake, while Button has his engine failure in one of the final 16 races. In this case Hamilton will loose nothing, while Button will loose 18 points. The probability for this is 16%.

Third: Hamilton has an engine failure in one of the final 16 races, while Button has an engine failure in one of the first 4 races. In this case Hamilton will loose 25 points, while Button will loose a net 18 points (he will loose 25 points when he retires, but he will gain 7 points when Hamilton retires). The probability for this is 16%.

Fourth: Both Hamilton and Button have an engine failure during the last 16 races, in the same race. Hamilton will loose 25 points, while Button will loose 18 points. The probability for this is 4%.

Fifth: Both Hamilton and Button has an engine failure during the last 16 races, but in different races. Hamilton will loose 25 points, while Button will loose a net 11 points (he will loose 18 points when he retires, but then he will gain 7 points when Hamilton retires). The probability for this is 60%.

Of course, I have chosen the numbers conveniently to demonstrate a point here, but when we introduce random unreliability resulting in one extra dnf for each driver under these circumstitions, Button will suddenly be the most likely champion. The fifth outcome is the most probable one, and it will see Button end up with 377 points, while Hamilton will end up with 375 points. In this case, if you compensate for luck by looking at what would happen without the engine failures, you will favour Hamilton in front of Button, because Hamilton will get back the points that he looses no matter what and he will be champion no matter what happens to Button. But this wouldn't be a realistic compensation of luck, because it assumes an "ideal world" which is a very unrealistic assumption. Also, if Hamilton is compensated with 25 points for his engine failure, there is a small error due to the fact that he might have done a mistake himself and lost points later, if the engine failure hadn't occured. The statistical expectancy value of how many points they will loose from their engine failure will be 20 for Hamilton and 14.08 for Button.

If we look away from these numbers for a moment and just think about the principles that governs this evaluation, it is evident that Button's approach seem to spread the risk more than Hamilton's approach. Hamilton is more vulnerable to technical problems (in fact to any problem that may arrise, whether it is his own fault or not), because he generally finishes fewer races without running into trouble, when comparing to Button. And if something happens to Hamilton's car in a race where he has not made any mistakes himself, he will usually loose a very good place. If something happens to someone else, chances are that they are already behind Hamilton and Hamilton doesn't gain from hit. Button, however, usually has more to gain and less to loose from non-ideal events.

To sum up, Hamilton was undoubtedly unlucky last year, as we see a very big difference between his score and the calculated score when compensating for misfortune. But this difference is not necessarily very accurate and should be taken as an indicator, rather than an accurate measure of the situation, especially when comparing very different drivers like Hamilton and Button or Alonso. A mechanical failure or another type of DNF which is not the driver's own fault, is likely to hurt Hamilton more than Button and that has nothing to do with luck or misfortune, as long as it is quite normal to have at least one DNF during a full season, which is not the driver's own fault.

beelsebob
85
Joined: 23 Mar 2011, 15:49
Location: Cupertino, California

Re: Alternative history: 2012 championship without misfortun

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The problem with all that is that it's predicated on the idea that one driver is more likely than another to --- something up seriously. Looking at the driver's performances last year, Hamilton was in fact more consistent than button - button's failure to score was mostly down to his complete inability to drive the car in the middle of the season (effectively a string of --- ups), not due to mechanical disaster. Hamilton meanwhile only had one incident (with maldonado in valencia) that you could reasonably argue was down to him fighting too hard (and even that one can be argued both ways).

Stradivarius
1
Joined: 24 Jul 2012, 19:20

Re: Alternative history: 2012 championship without misfortun

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beelsebob wrote:The problem with all that is that it's predicated on the idea that one driver is more likely than another to --- something up seriously. Looking at the driver's performances last year, Hamilton was in fact more consistent than button - button's failure to score was mostly down to his complete inability to drive the car in the middle of the season (effectively a string of --- ups), not due to mechanical disaster. Hamilton meanwhile only had one incident (with maldonado in valencia) that you could reasonably argue was down to him fighting too hard (and even that one can be argued both ways).
It is true that Hamilton was more consistent than Button last year, so when I mentioned this I was refering to the 3 years they have been together at McLaren, not 2012 exclusively.

Looking at 2012 alone, I agree and I have also written that Hamilton was indeed unlucky. I would agree that it is a coincidence that he only beat Button by 2 points. But if you compensate for misfortune in the way that is done here (giving Hamilton additional 152 points for bad luck, and Button only 9), you are making an unrealistic assumption that nobody will ever run into trouble. Since Hamilton usually both qualified better and raced in front of Button, it is natural that Button has a higher probability of gaining positions and points than Hamilton due to an arbitrary drivers' misfortune. If Hamilton is running 3rd and Button is running 7th, there are 3 cars between them, and if one of them hits problems, Button will benefit, but Hamilton won't. That isn't luck, but rather a predictable pattern. So when Hamilton is compensated with 143 points more than Button, this is not a realistic compensation. What you could do is to give Hamilton back 25 points for each of his retirements from the lead that he couldn't have avoided himself, but then you would also have to do the same for Button. In that case, I suppose you would see that Hamilton would have beaten Button by around 50 points last year, and that would be enough to put him ahead on the total over 3 years. But the difference would still be relatively small. You couldn't say with (statistical) confidence that either of them were better or worse than the other. Driver performance varies over time and from one track to another, so a small difference in points isn't enough to outshine the "background noise".