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Anyway, the question has often plagued me as to what makes an MVP over a player that had a really good year. To this end I have tried a number of different models over the past couple years, but recently I came across the ideas of classification trees and "bagging". Classification, or decision, trees have become popular in the media recently. Instead of trying to explain what such a tree is, here is an example (along with some props thrown to FlowingData.com). The basic idea is that you classify each individual by one variable at a time into one of three options: group A, group B, or no decision yet. At each fork in the tree, with the exception of the last fork, one of the two options is no decision. This seemed like an interesting idea to use for MVP voting, among other baseball applications that I have tried to model at some point, such as HOF status. In fact, that may lead to another post.

By now, most people are fairly familar with Bill James' Expected Wins (referred to as XW) formula, but for those who are not, a quick description:

• (Expected Winning Percentage) = ( (Total Runs Scored)^1.82 ) / ( (Total Runs Scored)^1.82 + (Total Runs Allowed)^1.82 )
• Step 2: Multiply expected winning percentage and by the unmber of games played to get expected wins estimate

The beauty of this process is that a fairly simple formula gives very accurate results. In the table and images at the bottom of this article you will see that this gives surprisingly accurate results. For the 2007 and 2008 seasons, the average error made by the XW formula is 0.0411 wins, and half of all errors are between about -2.5 and 3 wins. The idea of the XW statistic is to see how much teams have over- or under-performed throughout the season. Whether one attributes this difference in performance to randomness or skill of the team/ manager/ players to win close games is a personal decision. Most tend to assume any difference is due to luck, but I don't know if I fully agree with that assessment.

From its introduction, I have been wary of the XW procedure. The XW formula treats every run a team scores throughout the course of a season equally. This, we all know, is not true. Some runs are more important than others. This does not just include runs that win (or lose) crucial games , but crucial runs within games. In almost every case, a team's 10th or 12th run of a game means much less than a teams 3rd or 4th run of that game since they would most likely win with or without that, say, 12th run. I felt that the XW formula did not account for this difference in importance.

Enter Randomized Wins.