[Driver] Team Mates Comparison 2012

[alc]

I really like this stuff. We should thank Schummy for his work, and it provides a great context for the line-up debate. How about Force India?

[Schummy]

I would not like to be "Forced" to do it ;-)

But it would be interesting.

[Schummy]

==========================================================================================
        AUS MAL CHI BAH SPA MON CAN EUR GBR GER HUN BEL ITA SIN JAP KOR =  TOT  lead  prb%
==========================================================================================
HAM-BUT 100 111 000 111 -01 111 111 110 101 000 111 000 111 100 000 111 = 28-19 (HAM)  76%   Advantage
VET-WEB 011 000 000 111 111 000 111 100 010 111 111 001 110 111 111 001 = 29-19 (VET)  81%   Advantage         
SCH-ROS 100 111 000 000 000 110 000 001 111 111 000 101 101 100 111 011 = 23-25 (ROS)  11%   Similar
ALO-MAS 111 111 111 101 111 111 101 111 101 111 111 100 011 111 100 101 = 39- 9  ALO  100%   BUSTED!
RAI-GRO 011 111 100 001 001 011 010 011 111 111 011 111 --- 011 011 101 = 30-15  RAI   96.4% Almost Busted
PER-KOB 000 111 000 101 100 -11 011 011 100 000 111 000 011 101 000 111 = 23-24 (KOB)  00%   Equal
==========================================================================================

Raikkonen is nearing the total busting of Grosjean in this stat. Vettel and Hamilton are ahead of their team mates but don't trounce them yet. It means data don't completely discard Vettel or Hamilton are ahead just by hazard.

Lotus and Sauber's team mates are extremely close.

[Born Racer]

Thanks for the update as always Schummy.

It's interesting that Perez is off to McLaren while Kobayashi may be scratching around looking for an F1 drive, despite their close proximity in the stat-based analysis. People talk about the old "lies, damned lies and statistics" thing, but the true lies here are the mistaken perceptions of the teams sometimes. Does Perez deserve a McLaren drive? Perhaps he does. But does Kobayashi deserve to be out of F1? Almost definitely not.

Conversely, Raikkonen is almost totally busting Grosjean, but on pace, the maligned Frenchman has been similar.

[Marbot]

Originally Posted by Born Racer

Conversely, Raikkonen is almost totally busting Grosjean, but on pace, the maligned Frenchman has been similar.

It's not just about pace, obviously.

[Schummy]

Really, crashing, crashing and crashing doesn't make any good at your results. In this particular set of stats, when one crash early in a race both final result and fastest laps are damaged.

About Perez-Kobayashi, Born Racers's thoughts are acute. Vast different roads ahead for those two barely different drivers. I don't know many drivers who can sub Kamui in a F1 seat. But budget and a non-top team can be a hard combination.

Perez can have some advantages, though. He seems strong in tyres and racecraft. He is very young (22 vs 26) and he is a bit less experienced than Koba, so probably he can have a bit more development in next seasons.

But IMO, Koba is above the median of the F1 field. It is never going to happen but I would find fascinating a team with Schumacher and Kobayashi, comparison wise. Peter, before you bow out, are you listening?

[Born Racer]

I too sense that Perez has the better potential, but I feel Kobayashi's been a tad sidelined. That said, Perez has banged in the big results, which is judgement day.

Originally Posted by Marbot

It's not just about pace, obviously.

Of course. I guess I just feel that Grosjean has been somewhat ignored after some high profile binnings. His pace vis-a-vis Raikkonen has been sterling. Raikkonen's a formidable driver and Grosjean will come good.

[Schummy]

Median differences between team mates in qualifying.

VET-WEB 0"11
HAM-BUT 0"30
ALO-MAS 0"35
GRO-RAI 0"06
ROS-MSC 0"02

The qualifying data can be gotten in any F1 page, but I have gotten them from F1Matrix.it , where they are well exposed and resumed. The medians have been calculated by myself. As it has been done by hand, there can be some error.

The team mates are pretty close, except Ferrari and McLaren. Interestingly, the gap ALO-MAS is almost the same as the gap HAM-BUT. Of course, Button has had better races than Massa.

Another interesting point is the minimal gap between Grosjean and Kimi, against a popular perception. Minimal gap too in VET-WEB even if there is a perception that Seb is much better qualifier than Mark.

[Schummy]

Ok, ok, I show the rest of teams

PER-KOB 0"13
MAL-SEN 0"67
DIR-HUL 0"01
RIC-VER 0"24
GLO-PIC 0"35
KOV-PET 0"24
DLR-KAR 0"51

• Big gap against Senna. He is not good in qualifying, he is not that good in races. So...
• Big gap in HRC, but we knew it already, I suppose.
• Good gap in Caterham, Marussia and Toro Rosso.
• Extreme equality in Force India and small gap of Perez over Koba.

[Mr V]

Originally Posted by Schummy

The team mates are pretty close, except Ferrari and McLaren. Interestingly, the gap ALO-MAS is almost the same as the gap HAM-BUT. Of course, Button has had better races than Massa.

Another interesting point is the minimal gap between Grosjean and Kimi, against a popular perception. Minimal gap too in VET-WEB even if there is a perception that Seb is much better qualifier than Mark.

I suppose it doesn't matter what the gap is, if a driver constantly outqualifies his team mate, be it by 1/10th or 1 second, he's the better qualifier?

[Schummy]

Problem is every driver has a lap time variance, so it's virtually impossible to outqual consistently by 0"1. What we can do is to estimate the average gap between them. Another estimation of the average gap is the relative score, but this loses more information because we don't know by how much one was beaten. Putting it in another way: if one knows the lap times then one can know the score, but if one knows the score then one cannot deduct the lap times. Laptimes have more info than scores,

Anyway, with just 20 or less races (in a season) always there is a degree of uncertainty in the estimation.

If a driver's lap times are not skewed around the average (a reasonable approx hypothesis) then the driver with best average has >50% probability of outscoring his rival. Or inversely, a driver who outscore his rival, has a better average with >50% probability. In resume, both stats are directly related.

Sorry, all this looks a joke, a bad headache, lol.

[wnut]

Originally Posted by Schummy

Problem is every driver has a lap time variance, so it's virtually impossible to outqual consistently by 0"1. What we can do is to estimate the average gap between them. Another estimation of the average gap is the relative score, but this loses more information because we don't know by how much one was beaten. Putting it in another way: if one knows the lap times then one can know the score, but if one knows the score then one cannot deduct the lap times. Laptimes have more info than scores,

Anyway, with just 20 or less races (in a season) always there is a degree of uncertainty in the estimation.

If a driver's lap times are not skewed around the average (a reasonable approx hypothesis) then the driver with best average has >50% probability of outscoring his rival. Or inversely, a driver who outscore his rival, has a better average with >50% probability. In resume, both stats are directly related.

Sorry, all this looks a joke, a bad headache, lol.

Schummy, what happens if you eliminate the largest 2 variances, say for technical issues or sickness, and then do your calculation?

[Schummy]

Originally Posted by wnut

Schummy, what happens if you eliminate the largest 2 variances, say for technical issues or sickness, and then do your calculation?

Yes, dropping worst/best results is a good technique to avoid "outliers" (extremely good or bad results). Another technique is calculating the median instead of the average. Median is the middle number in an ordered series, average is adding every number and dividing by the amount of them. So average is affected by strange data but median is not (almost).

On a side note, I think I remember simulations show it is more fair a WDC where one can drop some bad results. "More fair" in the sense that the best driver has more probability of getting the title.

[Schummy]

Updating after India:

================================================
        AUS MAL CHI BAH SPA MON CAN EUR GBR GER 
================================================
HAM-BUT 100 111 000 111 -01 111 111 110 101 000 
VET-WEB 011 000 000 111 111 000 111 100 010 111      
SCH-ROS 100 111 000 000 000 110 000 001 111 111 
ALO-MAS 111 111 111 101 111 111 101 111 101 111 
RAI-GRO 011 111 100 001 001 011 010 011 111 111 
PER-KOB 000 111 000 101 100 -11 011 011 100 000 
================================================

================================================
HUN BEL ITA SIN JAP KOR IND =  TOT  lead  prb%
================================================
111 000 111 100 000 111 101 = 30-20 (HAM)  80%   Advantage
111 001 110 111 111 001 111 = 32-19 (VET)  90.8% Almost busted
000 101 101 100 111 011 010 = 24-27 (ROS)  22%   Similar
111 100 011 111 100 101 111 = 42- 9  ALO  100%   BUSTED!
011 111 --- 011 011 101 111 = 33-15  RAI   98.7% Almost busted
111 000 011 101 000 111 100 = 24-26 (KOB)  11%   Similar
================================================

Basically two groups: teams with a big difference between team mates (Ferrari, Lotus(!), Red Bull); teams with great equality (Sauber, Mercedes). McLaren shows advantage for Hamilton but a bit less than in Red Bull's case.

Grosjean bad result is a consequence of his naughty antics in races ;-) . Kobayashi's fate is painful looking at this stat, he is basically doing the same work than Perez, as pointed out by Born Racer.

[phoenix]

Originally Posted by Schummy

Yes, dropping worst/best results is a good technique to avoid "outliers" (extremely good or bad results). Another technique is calculating the median instead of the average. Median is the middle number in an ordered series, average is adding every number and dividing by the amount of them. So average is affected by strange data but median is not (almost).

Or, you could keep the worst and best and use the geometric mean to reduce their effect - i.e. the mean of the squares?

[Schummy]

The geometric mean is the exponential of the mean of the logarithms. It damps the effect of greatest numbers (worst laps) but can amplify the effect of smallest numbers (best laps). Usually is a better alternative than the simple mean when data is positive; it is not usable with no positive data. In this case it cannot be used for gaps; we would have to calculate the gm for driver 1 and for driver 2 and then calculate the gap.

But gm suffer from freakish data (anomalously big or small numbers), anyway. Usually dropping best/worst data is safer.

BTW, the square root of the mean of squared data is the quadratic mean. It has the opposite effect to gm, i.e. it amplifies the effect of the greatest numbers (worst laps), with catastrophic results in our case. It would not be calculated with the gaps (a mix of negative and positive numbers plays havoc with it), but separately to each driver's laps.

[Mr V]

Originally Posted by Schummy

The geometric mean is the exponential of the mean of the logarithms. It damps the effect of greatest numbers (worst laps) but can amplify the effect of smallest numbers (best laps). Usually is a better alternative than the simple mean when data is positive; it is not usable with no positive data. In this case it cannot be used for gaps; we would have to calculate the gm for driver 1 and for driver 2 and then calculate the gap.

But gm suffer from freakish data (anomalously big or small numbers), anyway. Usually dropping best/worst data is safer.

BTW, the square root of the mean of squared data is the quadratic mean. It has the opposite effect to gm, i.e. it amplifies the effect of the greatest numbers (worst laps), with catastrophic results in our case. It would not be calculated with the gaps (a mix of negative and positive numbers plays havoc with it), but separately to each driver's laps.

Your taking the mick now !

[Schummy]

It looked so pedantic :'-( :-)

[Taprobane]

I still think this would all be much more relevant without fastest laps included...

[wnut]

Originally Posted by Taprobane

I still think this would all be much more relevant without fastest laps included...

Given that the guys are now setting fastest laps on the last lap/s of the race if you are eliminated early you will probably lose out twice, also violates the old saying "win as slow as possible".

Often the lower finishing driver sets the fastest lap.

This is a Schummy question!

[Schummy]

I include in the table all the info, it is up to each take or drop the parts that seem relevant or not :-) .
Total scores is just a resume, the real info is the matrix itself.

Fastest race laps is less meaningful this season because of the combination between not refuelling and tyre composition. Usually drivers care their tyres along the race, except perhaps some laps. FLs are usually done without fuel load, in the last laps, depending on your race situation and tyre age/composition.

Anyway, it is not totally meaningless, you still have to be quick without fuel and with your given tyres. It is just less interesting than in other seasons because there are too many irrelevant variables in it. So it gives less info over total performance, there is more "noise" and less "signal".