# How to set up a regression for Adjusted Plus Minus with no offense and defense?

So here is the backstory:

• This is a game with two teams
• The outcome of the game is that one of the teams wins and the other loses
• There is no offense and defense
• We can use tug of war as an analogy (the game is actually paintball)

My question: I’m trying to identify the relative contributions of each player. Adjusted Plus Minus (APM) seems to be the best way to do this.

However, players can switch between teams so I’m curious how to track individual players since a win for one team is a loss for the other.

In the above, players are put on “offense” or “defense” but that doesn’t apply here.

For example, do I need to create dummy variables for when a player is on the winning or losing team?

Or should I run a separate regression for each player? Eg for each player, run a regression where the dependent variable is the outcome of whatever team that player was on.

Happy to add more detail if it helps.

The situation you are describing would be a subset of typical Adjust Plus/Minus calculations.

One way to set this regression up would be to set "Team 1 Winning" as the dependent variable. This target variable would be 1 sometimes and 0 sometimes.

Then, create a large matrix of dummy variables (this could be a sparse matrix) with all players represented. Players on team 1 would be represented with a 1, players on team 2 would be represented with a -1, and players not represented in the given game would be a 0.

This could then be solved using a logistic regression to estimate player effects. Given that colinearity would be likely in the dataset, a penalized regression approach would likely give more valid results.