What is the mathematical term for the technique of calculating Wins Above Replacement?

Question

"WAR" is an advanced statistic that combines several individual statistics for a baseball player,and then compares them to a given standard.

To put it one way, Player A is defined as a point in multidimensional space, where each dimension represents an independent baseball statistic (at bats, doubles, stolen bases, etc.). Player X is another point in the same multidimensional space. The relative "Wins Above Replacement" is an attempt to reduce the differences between the two player/points into one single quantity. Or, you could say that WAR is an attempt to quantify the "distance" between a player's "point" and some specified origin.

Is there a mathematical term that might define what WAR is trying to do? Somehow, in my limited knowledge of advanced mathematics, I'm thinking that the term "eigenvalue" fits the bill.

Mathematicians: Am I on to something here, or am I just blowing smoke?

M · Accepted Answer

Sports deals with probabilities, not certainties. The appropriate concept is expected value, which is probably (pun intended) what you were actually thinking about. You get something like:

Expected Value E(X,N)
Expected Value above replacement is E(X,N) - E(R,N)

where:

E(X,N) = N if (average) team would expect to win all N games player X was in
E(X,N) = 0 if (average) team would expect to lose all N games player X was in

E(X,N) = M if (average) team would expect to win M of N games player X was in
E(R,N) = K if (average) team would expect to win K of N games replacement player R was in

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What is the mathematical term for the technique of calculating Wins Above Replacement?

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