Can we improve WPA?

One of the ways of evaluating baseball players is WPA. Currently available at Baseball Reference, WPA basically evaluates the player's contribution as the difference between the team's probability of winning before the player's appearance and the team's probability of winning after the player's appearance. The same thing can be done for runs, as RE24.

There are two main problems with WPA.

1) It is evaluated against a league average. League-average players, regardless of their playing time, are given the same result. Most evaluation systems use a replacement level comparison in order to avoid this problem.

2) Players are dependent on the game situation in which they appear. So if a player comes to bat in the eighth inning of a tie game, a homerun will have a great impact on WPA. But if the player comes to bat in the eighth inning of a 13-2 game, a homerun will have little impact. I understand that some analysts do not like to tie player evaluation to leverage.

With respect to the latter issue, I disagree with the view that evaluation should be stripped from leverage in order to create a traditional linear weights-type measure. The point of any evaluation is to measure a player's contribution to his team wins. The timeliness of a hit or out matters as much to team success as the kind of hit or out.

I haven't seen any attempts to deal with the former issue, and it is what I wanted to address here. One solution to the problem is to include a replacement level evaluation in WPA. The idea is that the player is evaluated against a hypothetical replacement level player who would be appearing in the same situation. Again, the player will be evaluated on the basis of the difference between two game states; we'll call them the pre-state and the post-state. The post-state value is the same as it would be under the traditional WPA, as the team continues on with its other players. The pre-state is the value that a typical replacement level player would contribute to the game state facing the player. One way to do this part would be to assume a replacement level player hits a single in a certain percentage of his appearances, strikes out in a certain percentage, etc. One would aggregate these results in order to determine that a certain game state had a value based on a replacement level player's expected performance. We would evaluate the real player's contribution as the difference between a) the pre-state value for a replacement level player and b) the post-state value.