## New Formula for 2-Leg-Games

The current method of calculating two-leg games takes into account the aggregate result, increases its weighting and subtracts the result of the first leg. Please see here for details.

However, there are some issues that I have with that method:

- Once the second leg is played, the first becomes irrelevant
- The workaround for two single victories seems (and is) constructed
- The expectancy of losing or winning Elo points in the second leg is not 0

The way it should be in my eyes is rather:

- Winning or losing Elo points based on one game only
- The expectancy of losing or winning Elo points should be 0 in every match

The first leg should be considered as a standard game, I do not see a reason in changing that.

The second leg however depends very much on the first leg. Winning, drawing or losing the second leg only is irrelevant, but what matters is to qualify for the next round. Qualifying should earn you points, not qualifying should make you lose points, based on the probability of qualifying. Just what are the probabilities for that?

We will for this purpose refer to the probabilities from the

Poisson/Elo-Model. By using this model, it can be quite accurately calculated what the probability of qualifying for the next round is.

This probability replaces the one from the Elo Formula in order to determine how many points will be exchanged per game. Practically, this means that if you carry a large lead from the first leg, then qualifying does not earn you many Elo points as this is the expected result. Losing however will cost you a lot of points. The expectancy of losing or winning Elo points is zero.

This new method will be applied to all games and will take the away goals rule into account in games where it applied. Penalty shootouts will count as draws.

*Created: 23 Mar 2013 - Modified: 20 Jan 2013*