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- TL;DR Summary
- Combination of two probabilities such that outcome of 2nd probability increases outcome of the 1st probability.

I am trying to determine the likelihood of a driver winning a race based on an associated rating as well as the team he drives for.

The probability that Driver A beats Driver B =

The probability that Team A beats Team B =

How do I combine these two probabilities, where the outcome is an increase in Driver A's probability of winning?

The point is that Driver A is a better driver than Driver B, but the team he is racing for produces a better car. Thus, Driver A's probability of winning increases. If Driver A and Driver B switched cars, then Driver A's probability of winning decreases.

It may be the case that the proper way to implement the team's effect is to actually insert its probability into the equation between the drivers. In that case, I am using a standard Elo calculation.

Driver A Rating =

Driver B Rating =

(Driver B - Driver A) | (1241 - 1543) = -302

(Result / 400) | (-302 / 400) = -.755

(1 + 10

(1 / (1 + Result)) | (1 / (1 + 0.175792)) = 0.8504,

The probability that Driver A beats Driver B =

**.8504**The probability that Team A beats Team B =

**.7576**How do I combine these two probabilities, where the outcome is an increase in Driver A's probability of winning?

The point is that Driver A is a better driver than Driver B, but the team he is racing for produces a better car. Thus, Driver A's probability of winning increases. If Driver A and Driver B switched cars, then Driver A's probability of winning decreases.

It may be the case that the proper way to implement the team's effect is to actually insert its probability into the equation between the drivers. In that case, I am using a standard Elo calculation.

*Example:*Driver A Rating =

**1543**Driver B Rating =

**1241**(Driver B - Driver A) | (1241 - 1543) = -302

(Result / 400) | (-302 / 400) = -.755

(1 + 10

^{Result}) | (1 + 10^{-.755}) = 0.175792(1 / (1 + Result)) | (1 / (1 + 0.175792)) = 0.8504,

*or an 85% chance of beating Driver B.*