Friday, 24 October 2014

Puckerings archive: Win-Things Theory (18 Oct 2002)

What follows is a post from my old hockey analysis site (later It is reproduced here for posterity; bear in mind this writing is over a decade old and I may not even agree with it myself anymore. This post was originally published on October 18, 2002.

Theory: Win-Things
Copyright Iain Fyffe, 2002

The most common perspective put forward on win theory can be summarized as follows:

Before a game begins, each participating team has a 50% chance to win (a .500 expected winning percentage), ceteris paribus. As the game progresses, and as each team does things that affect their chances of winning or chances of losing, the expected winning percentage of each team changes. For instance, if a team scores a goal after 5 minutes of play, their percentage may change to .550, and the opponent's would therefore be .450, since the percentages necessarily sum to one.

At the crux of this theory lie two ideas: (1) before a game begins, a team's winning percentage is .500, and (2) a team does two types of things that affect its chances of winning: good things (which we'll call "win-things") and bad things (which we'll call "loss-things".)

As a team, you have no significant control over what your opponents do. Therefore, at least from an analytical perspective, you can assume they will do an average number of things to win. At the beginning of a game, you have not yet done anything to win, and have no guarantee that you will do so. Therefore, your expected winning percentage before a game is not .500, but .000.

Teams try to win games, they do not try to lose them. Therefore a loss-thing is merely a failed attempt at a win-thing. Just as darkness is merely the absence of light, loss-things are merely the absence of win-things. Therefore win-things are what matters, and this is why I refer to this theory as Win-Things Theory.
The idea that you cannot control your opponent's actions is carried throughout the thoery. For instance, in the traditional theory, scoring a goal is a very good thing (i.e., it has a high Win-Things value). Under Win-Things Theory, whether or not a shots actually produces a goal is irrelevant to the shooting side. The Win-Things were produced by the shot itself, with a higher-quality shot producing more Win-Things. Conversely, the opponent's Win-Things on the play depend on whether or not the shot is stopped. Stopping the shot produces Win-Things about equal to the Win-Things resulting for the other side by taking the shot. Not stopping the shot produces no Win-Things (it does not produce Loss-Things).

It should be noted that the .000 beginning expected winning percentage applies only to one-team analysis. In two-team analysis, where the actions of both teams are considered, the expected percentage would depend on the Win-Things each team has accumulated. But generally speaking, one-team analysis is more useful in analyzing what contributes to winning, by assuming opponents to be average in all regards.

Traditional theory focusses much attention on expected winning percentage. Win-Things Theory does not. The point is not to get your expected winning percentage up; the point is to accumulate more Win-Things than your opponents. Since you cannot control how many Win-Things your opponents accumulate, the best way to ensure this is to accumulate as many Win-Things as possible.

This theory supports Bill James' Win Shares system for baseball, which I have adapted into the Point Allocation method for hockey. Win Shares has been criticized for not considering "Loss Shares". Using this new theory, Loss Shares are irrelevant, and the criticism is therefore invalid. Opportunity should still be considered, but fortunately in hockey games are timed, while in baseball the opportunities vary greatly from game-to-game, based on a multitude of factors.

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