Here I've found what I wanted to find about variance:
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www.grandprixgames.org]
Suddenly, all the remarks and my own observations (about skill bonus of 60 per 100 variance) make a perfect sense.
25% of the variance is attributed before the start of the weekend, 75% in each session, in qualifying even for each run.
What is then the bonus due to variance?
Well, it depends. The mean value of uniformly distributed variable between 0 and 1 is equal to 0.5. So theoretically every 100 of variance must lead to +50 in driver skill.
But it is valid if you make only one qualifying attempt. Making several qualifying attempts means the best time is retained.
And the best of 2 uniformly distributed random variables between 0 and 1 is not equal to 0.5. It's 2/3.
The best of 3 such variables is =3/4. The best of 4 =4/5.
This means your driver skill increases with the number of qualifying attempts and strives to 1.
Though we should never forget about the weekend part of the variation. It's independent from the number of qualifying runs and its mean value = 0.5
So:
1 flying lap: bonus = 0.25*0.5+0.75*0.5=0.5
2 flying laps: bonus = 0.25*0.5+0.75*2/3=0.625
3 flying laps: bonus = 0.25*0.5+0.75*3/4=0.6875
4 flying laps: bonus = 0.25*0.5+0.75*4/5=0.725
On the other hand, it practically never reaches 0.725. I don't know if it's because I have few data (so the error is considerable, even 100 drivers attempts(or 5 qual x 22 drivers) will not give you enough data to decrease the error below 2%). But maybe there's another factor: fast cars can simply stuck behind slower cars, so when their random value is high, they cannot always convert their high driver skill into a good lap time.
One important consequence:
Your standard deviation drops with the number of runs.
Probability density function of a driver skill for 1 lap qualifying = 1. This means his max skill can be equally everywhere between 0 and 1.
For 2 laps it's equal to 2x (I omit here the weekend part). This means your driver is more likely to be at the right end of the variance.
For 3 laps it's 3x^2, for 4 laps it's 4x^3.
The mean will tend to 1, the field will be concentrated on the right side, but you'll still have some drivers on the left side with huge gaps to the leaders.
These lap times are so bad not because of mistakes, this is how the distribution is programmed. If you simulate 1 run with the same bhp, driver skills, variance*, you will definitely see high density at the top and low density at the bottom. And sometimes you have a higher standard deviation of lap times at lower variance values because the density on the left side is so low that you can have a bad driver at variance 500 and not have it at variance 1000. 1 run with 22 drivers is in this case insufficient to draw conclusions.
* Though variance must be high enough to distinguish it from internal variance which differs from circuit to circuit. And obviously don't forget the weekend part which is good for 25% of driver performance.
And: this counts for qualifying only, not for race. For race it's obviously 0.5.
Consequence #2: there's no need in higher variance for race. It's already de facto higher because several qualifying attempts artificially reduce variance. And if it's a 1-lap qualifying, its results are probably even random as race results.