Alonso's points advantage: too much or not?

[Schummy]

(This post has commentaries about some statistical calculations about FA, MS and KR chances to be WDC this season. So it "probably" is not too funny, except for those freakies who likes to lose time doing sudokus )

Currently (after GP Europe), FA enjoys a 13 points advantage over MS and 21 over KR. A long part of the season is still in the future, 13 GPs are there to be fought. But the question is, is FA's advantage big or it is relatively no significant?

Strangely , I have done some calculations to try to look into this question.

pnt gap ppr
FA 44 -- ----
MS 31 13 1.00
KM 23 21 1.62

MS has to recover at a ratio of 1 point per race (ppr) and KM needs recover 1.62 points per race. But those ratios are deceiving the difficulty of the task, if is not so easy to recover it *on average*.

In order to a better appreciation of the level of difficulty (or easiness) MS and KM have to deal with, it's better to calculate the equivalent recovery as if it was in just one race. It is to say, how many points they have to recover if there was only one GP.

It is possible to calculate it supossing drivers don't have significant "trends" or "streaks" along a season. Surprisingly, this is approximately right, because most of perceived "streaks" of good or bad results can be explained by random luck (but *sometimes* there are real trends along a season).

We just need to find the ration between the points gap and the square root of number of resting Gps, and it will be the points to recover as it were only one race resting.

pnt gap por
FA 44 -- ---
MS 31 13 3.6
KR 23 21 5.8

It means MS overscoring FA in the whole season is so difficult (or so easy) as MS getting 3.6 points advantage in one race over FA (por). It is perfectly acheivable, but not too easy. In KM case, he would needs the equivalent of gaining 5.8 points over FA in one race. Not easy.

In order to be a bit more concrete, I have tried to convert those figures in probabilities of it happening. In the past three years (with the new scoring system) champions and sub-champions have scored with a standard deviation of about 3.5 points (per race). With this datum and supossing FA, MS and KR are going to enjoy a similar form and car in the rest of the season, I have done 10000(!) simulations of the resting 13GPs and I have got they can win the WDC with these probabilities:

FA ---> 71%
MS ---> 22%
KM ---> 7%

So KM is in a nearly critical position. His chance to be WDC is small and, thus, he will need an advantage (better car, for example) or a heavy good luck to get the title. MS is in a slightly better position and he has the tyre factor to gain an advantage, but anyway FA is having a clear advantage by the moment.

Again, it is deduced by supossing those three drivers are going to have a similar form/car along rest of the season. If some team makes a breakthrough os a driver suffers any problem these probailities are, naturally, going to change.

[daniel1985]

All it takes is one DNF from Alonso and the gap will be closed. Surely he won't finish every single race of the year

[Gore]

Ah, but equally, one DNF for MS/KR will have the opposite effect. The impact of unreliability is captured by Schummy's simulations - although the constant assumed standard deviation imposes that all three drivers' will suffer an identical degree of unreliability (in the long term), which may, on the limited information availble, be an optimistic assumption for KR.

This is interesting work Schummy: I'd only been thinking of the situation in terms of "points per race" (your first analysis). I don't entirely follow your second analysis, however, in particular the intuition behind the ratio of the points gap to root of the remaining races. Would you mind explaining that bit again (I was never much good at stats!)?

Cheers.

[goodhorsehymn]

Originally Posted by daniel1985

All it takes is one DNF from Alonso and the gap will be closed. Surely he won't finish every single race of the year

That's what Massa is for

[Menelaos]

Originally Posted by daniel1985

All it takes is one DNF from Alonso and the gap will be closed. Surely he won't finish every single race of the year

hmmm, that's nice, one guy puts in a few hours work and gives us an entire page of great statistics and we ruin it all with argument?

Very nice stats!

[Andrew2001]

Originally Posted by daniel1985

All it takes is one DNF from Alonso and the gap will be closed. Surely he won't finish every single race of the year

This is gunna sound pretty bad, but it would not suprise me to see Alonso cruise to his second title, and the real battle come down to Raikkonen and M.Schumacher for 2nd place. I hope that does not happen, as I desperately want to see McLaren finally pull it off this year.

[Bononi]

When was the last race Alonso have a DNF ?

[Bleu]

Originally Posted by Bononi

When was the last race Alonso have a DNF ?

Depending on what is race start, it is Indy or Canada 2005. After that he has had one non-points-finish in Hungary.

[BootsOntheSide]

Considering how many failures Fisichella has had, Fernando may well be due one. Anyway, if you've got the fastest car and equal reliability, 1 point per race is fairly easy to overcome - if Michael won every remaining race with Fernando 2nd, he would lead by 13 points - he'd have the title sealed with a race to go, or alternatively he could have a mechanical failure and not lose the title.

[Kirk]

I would be surprised if McLaren were able to keep pace but Ferrari will be pulling out all the stops to get MS another WDC.

Last weekend we witnessed a rather desperate strategy of Massa using up his tyres to fetch extra data for his teammate (who was able to save his for the race). That is something one MIGHT expect in the very late season but now?

Sadly, FM seems to be another sacrificial lamb to the Ferrari cause!

As for Alonso. He is very consistent, isn't he. Does anyone get the impression of a certain smugness, though?

[chunterer]

Hmmm, it's unlikely that either driver will win or finish second in all the remaining races.

Alonso was the master of percentage playing last year, doing exactly what was required of him (Montreal where he crashed and Hungary where he had problems aside).

However if Renault start to push the envelope to counter the threat, that will surely mean reliabilty and/or driver consistency will have more of a premium. There might be a car breakage or the odd mistake leading to a dnf or 2 which could alter the balance.

And if McLaren also enter the fray properly that could also effect the amount of points on offer. As Alonso said he'd prefer one driver to battle rather than 3 or 4?

[deejay]

I can certainly see Mclaren taking race wins this year - although not threatening the championship as a whole. But if the Mclarens can get between MS and Alonso a couple of times it could be enough to disrupt things.

[Notso Swift]

although the constant assumed standard deviation imposes that all three drivers' will suffer an identical degree of unreliability (in the long term), which may, on the limited information availble, be an optimistic assumption for KR.

[JohnSSC]

I appreciate the effort you put into this Schummy! Very nicely done.

I think that what the numbers demonstrate is that the pressure is on Alonso to not DNF, not finish off the podium, etc as his lead is not at all "safe" or insurmountable.

Should another team up their performance to become a factor it will make an already interesting season more comlicated statistically and much more entertaining!

[Bononi]

Originally Posted by JohnSSC

Should another team up their performance to become a factor it will make an already interesting season more comlicated statistically and much more entertaining!

In that case the pressure is on McLaren. I can't see Honda yet becoming the third force, except if Mclaren fails to raise their game during the season.

[BootsOntheSide]

Martin Brundle touched on a key point during the Nurburgring race - Renault have a lot more teams competitive on their tyres. So far Renault have been the fastest Michelin team every time, and Ferrari the fastest Bridgestone, other than possibly Malaysia. However, when Michelin are on top, you can expect McLaren and perhaps Button's Honda to finish ahead of Ferrari, whereas none of the other Bridgestone teams have shown any sign of being able to beat Renault, so Renault could get a 3-4 result (behind a Ferrari 1-2) even if Bridgestone have a big advantage one weekend. That might make Michael's task tougher.

Alonso finishing every race seems unlikely, but it can be done, if the team is on top of performance enough to not need to push the marginal components 100%. Alonso having a 71% chance of winning the title seems like quite a good estimate.

[RT]

The form that Ferrari is showing may just force Renault to push the envelope to avoid the prospects of a "death of a thousand cuts" (e.g. those two points per race). If that is the case and Renault is forced to the limits of performance, then the likelihood of DNF's will markedly increase for Renault. The difference is that now they will really have to push the limits and one DNF will have a large effect on the way things look.

[Menelaos]

Alonso isn't "too" far ahead at the moment, even from Kimi, not to mention Schumi. The thing is, both Kimi and Schumi must be fighting for wins if any of them wants to be able to catch Alonso, else we'll just see the same play as last year. Alonso will settle for podiums each race and leave Schumi and Kimi break their cars trying to win races.

[Marbot]

Lies,damn lies and statistics.

[JohnSSC]

Well there is a wild card for both Renault and McLaren.

Alonso is leaving. Kimi is likely to leave. How probable is it that they will be given the latest gizmos late in the season when they could possibly take the knowledge of said gizmos elsewhere?

Even if Michael decides to retire, Ferrari will pull out the stops for him. I do not see that happenning at Mc or Renault. Michael could have an advantage there by the 2/3 point of the season.

[Dutton]

Originally Posted by JohnSSC

Well there is a wild card for both Renault and McLaren.

Alonso is leaving. Kimi is likely to leave. How probable is it that they will be given the latest gizmos late in the season when they could possibly take the knowledge of said gizmos elsewhere?

Not being involved in the finer information/details/testing of said new gizmos figures, but why would they not put them on the car?

That would be sabotaging their title bids.

That makes no sense at all.

[Hein]

Originally Posted by JohnSSC

Well there is a wild card for both Renault and McLaren.

Alonso is leaving. Kimi is likely to leave. How probable is it that they will be given the latest gizmos late in the season when they could possibly take the knowledge of said gizmos elsewhere?

Even if Michael decides to retire, Ferrari will pull out the stops for him. I do not see that happenning at Mc or Renault. Michael could have an advantage there by the 2/3 point of the season.

I kinda was thinking the same thing! Does make a lot of sense, does'nt it?

[Dutton]

Originally Posted by Hein

I kinda was thinking the same thing! Does make a lot of sense, does'nt it?

How does it make sense to not put the latest stuff on one of your cars? It makes no sense at all.

[browney]

One of the dissadvantages of the current point system is that it is hard to crawl back championship leads. I hate points systems where there is not a large points gap to the winner because of this. The FIA made the change to stop someone dominating the championship, but I think that it actually promotes it. Anyone else agree with this?

(P.S it's not as hard as clawing back a lead in V8 supercars! That's be like having a point gap of 10 - 9.9 - 9.8....)

[chunterer]

Yeah but i also bet they were banking on a lot more teams battling for those closer together points differences - to keep it close right down to the wire.

We're almost at that stage now really, with tenths not seconds covering a handful of teams then it's down to the drivers and strategists to maintain that pace over a whole race...