Me again, here is an example of a performance file for Australia 1998
[Team #00]
Name=Williams,Mecachrome
Performance=765,775,2789
First Driver=1,Jacques Villeneuve,14465,263,15151,263
Second Driver=2,Heinz-Harald Frentzen,14704,263,14951,263
[Team #01]
Name=Ferrari,Ferrari
Performance=780,790,2300
First Driver=3,Michael Schumacher,15162,263,15073,263
Second Driver=4,Eddie Irvine,14644,263,14620,263
[Team #02]
Name=Benetton,Playlife
Performance=765,775,4973
First Driver=5,Giancarlo Fisichella,14601,263,14868,263
Second Driver=6,Alexander Wurz,14420,263,14430,336
[Team #03]
Name=McLaren,Mercedes
Performance=790,800,3693
First Driver=7,David Coulthard,15255,263,15286,263
Second Driver=8,Mika Hakkinen,15304,263,15304,263
[Team #04]
Name=Jordan,Honda
Performance=740,750,5538
First Driver=9,Damon Hill,14717,263,14763,263
Second Driver=10,Ralf Schumacher,14796,263,14766,263
[Team #05]
Name=Prost,Peugeot
Performance=755,765,15627
First Driver=11,Olivier Panis,14441,263,14040,263
Second Driver=12,Jarno Trulli,14537,263,14077,263
[Team #06]
Name=Sauber,Petronas
Performance=760,770,8888
First Driver=14,Jean Alesi,14371,263,14591,488
Second Driver=15,Johnny Herbert,14445,263,15008,263
[Team #07]
Name=Arrows,Arrows
Performance=690,700,16384
First Driver=16,Pedro-Paulo Diniz,14247,681,14184,263
Second Driver=17,Mika Salo,15153,263,14588,263
[Team #08]
Name=Stewart,Ford
Performance=725,735,9189
First Driver=18,Rubens Barrichello,14497,263,14462,263
Second Driver=19,Jan Magnussen,14217,263,14038,263
[Team #09]
Name=Tyrrell,Ford
Performance=700,710,16384
First Driver=20,Ricardo Rosset,13635,1687,14071,263
Second Driver=21,Toranosuke Takagi,14811,263,14767,263
[Team #10]
Name=Minardi,Ford
Performance=700,710,10018
First Driver=22,Shinji Nakano,14256,431,14128,263
Second Driver=23,Esteban Tuero,14580,263,14192,263
What are assumptions I made?
1. Reference value is 800bhp and 15406 grip (Hakkinen).
2. I used real engine powers from different sources (statsf1.com except Playlife and Honda which I found doubtful).
3. Variance of 263 corresponds to 0.6% in qualifying on average during the season. Yes, for different track it's different, but I prefer using the same variance across the season. 0.6% comes from GP4-qualifying distribution and my real calculations (based on 2020) of prediction error of driver result (SD=0.171%), so the delta max-min is about 0.58-0.59%, I rounded it up to 0.6% and it seems pretty realistic.
4. What if variance is different from 263? This means a driver has shown a very bad/good result on this exact circuit relative to his own performance throughout the season. In this case the variance is calculated differently:
4.1. His mean value was assumed to be his season mean +1SD for bad results.
4.2. Then the lower bound was assumed equal to his actual performance, the upper bound was calculated like if he had the same upper bound with variance of 263.
4.3. The difference between UB and LB is the new variance.
The same principle if a driver scored better (like Irvine in Monza). Here you can see only drivers that I adjusted up: Wurz, Alesi (qualifying), Diniz, Rosset, Nakano (race)
5. Generally speaking, I "restored" performance of early retired drivers (here Takagi, Diniz, Ralf Schumacher, Magnussen, Barrichello, Nakano) based on 2 things: their average race to qualifying gap (season) and field average race to qualifying gap (current track) in 50/50. The same principle was used for the entire field in rainy races like Silverstone and Spa.
6. For qualifying I used best weekend time instead of qualifying time. This changed A1-ring and partly Monza (Irvine was the best).
And it behaves pretty realistic in qualifying: poles mostly scored by Hakkinen/Coulthard/Schumacher. Eddie is among Williams and Benetton drivers. Alesi is somewhere in between Damon and Ralf. And Rosset totally sucks. No surprises like Barrichello in top-6 (unless it rains).
What I did not expect:
1. Race pace is quite different. There is obviously more impact of grip factor on lap times than in qualifying.
Irvine is assumed to perform better than Williams and Benetton, but he is outscored by both despite higher reliability. The reason is that Ferrari has a more powerful engine, so it is compensated by a lower grip. In qualifying he does slightly better than Williams-Benetton drivers, but in race it is not the case although the values I've given are superior to those of Mecachrome-powered drivers.
SO, BASICALLY THE CONCLUSION: AN APART RACE CONDITIONS CORRELATION IS NEEDED
(based on 1998 strategies of course, mostly 1 pit-stop, sometimes 2)
2. Grip has even more impact on a wet track (but this I knew long ago). Not critical for overall results as we have few rainy races and bad drivers are bad in rain conditions as well.
3. Bonus: if you start a non-championship race from the end of the grid, the starting grid is more chaotic than after a real qualifying. I've encountered Panis starting 3rd for example (although he was good in Brazil, he wasn't expected to be higher than 8th). My only explanations is that random generator makes only 1 simulation instead of 4 in real qualifying. Obviously you have more discrepancy (about 3 times).