This is what I predicted for the Hungarian Grand Prix:
I was intrigued by the percent at full throttle graph, so I did a regression on m/s and percent at full throttle in dry qualifying and used that model to predict future qualifying results based on track length and percent at full throttle. This is under the assumption that car quality has been constant throughout the season though.
I used f1fanatic.com for track length and throttle percent figures, as it was the only site that had them for every track (bar Sochi).
This is what I got for Hungary with f1fanatic's 59% full throttle:
Mercedes: 1:17.632
Red Bull: +0.698
Williams: +0.736
Ferrari: +0.980
McLaren: +1.148
Force India: +1.419
Toro Rosso: +1.499
Lotus: +1.904
Sauber: +2.432
Marussia: +3.379
Caterham: +3.905
Using UBS' 49% this is projected:
Mercedes: 1:23.551
Red Bull: +0.652
Ferrari: +0.941
Williams: +1.180
McLaren: +1.364
Toro Rosso: +1.583
Force India: +1.618
Lotus: +2.131
Sauber: +2.728
Marussia: +3.637
Caterham: +4.319
The 2nd projection seems more reasonable considering that Hamilton's pole from 2013 was 1:19.388.
The model predicts that Mercedes will have at least 0.5s gap to their closest competitor at every GP bar Italy and Brazil where Williams will be closer (+0.242 and +0.362 respectively). Williams will have at least 0.3-0.4s down to the 3rd best team at every GP bar Hungary and Singapore where they will drop to 4th best team.
Most teams apart from RBR have been catching up to Mercedes though (esp. Williams) so it could become closer than that.
These are the actual results compared to what the model predicted:
So while the model was surprised by the general pace of the field, it was actually quite accurate in predicting the gaps to Mercedes. Only two teams were more than 0.4s off the prediction (Williams 0.541s faster, and Lotus 0.491s slower).
It was also quite accurate in predicting the order of the teams, though it switched around two pairs of teams (Williams/Ferrari and Lotus/Sauber).
Key: Actual/Predicted
1. Mercedes/Mercedes
2. Red Bull/Red Bull
3. Williams/Ferrari
4. Ferrari/Williams
5. McLaren/McLaren
6. Toro Rosso/Toro Rosso
7. Force India/Force India
8. Sauber/Lotus
9. Lotus/Sauber
10. Marussia/Marussia
11. Caterham/Caterham
As the season goes on, the model should become more accurate as the data sample increases.
This is the prediction for Belgium (7004m, 72% full throttle):
The gaps are larger because of the long lap. Williams are predicted as being 0.42% slower than Mercedes in Belgium whereas Red Bull was 0.59% slower in Hungary (and was predicted to be 0.78% slower).
The predicted pole time is of 1:53.613 is 6.040s slower than Button's 2012 pole time, suggesting that the 72% full throttle might be a conservative estimate. I think the prediction will be off in terms of absolute times, but it will be interesting to see how accurate the predicted gaps to Mercedes will be.
These are the predicted gaps to Mercedes for the rest of the season (in terms of absolute lap time):
I will continue to post the comparisons between the model and the actual results in this thread after each race. I will also update the model with the new data after each race to improve the predictability.