I'm trying to make a model for forecasting the results of games with multiple win conditions.
For example, we may have a game where the first player to score a certain number of points wins, or the player with the most points after a time limit is reached wins. Say we have a point limit of 5 and a time limit of 10 minutes. If neither player scores 5 points in 10 minutes, then scores like 3-2 or 1-2 are possible. However, if a player reaches 5 points, then the score may be 5-0 or 5-4 in a shorter amount of time than 10 minutes.
One way of approximating results for this is using a poisson model, estimating ranking variables for each player, then simply censoring predictions that have wins over the limit. A poisson model isn't applicable in this case though, because if the limit is reached then the duration of the game is shorter, so scores of 5-2 should be more likely than 5-4.
Another case I'm interested in is where there is a limit on point difference, rather than absolute number of points.
Are there any existing statistical models that account for multiple win conditions like this?
