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This time, it's personal
Updated: Tuesday November 20, 2001 12:43 AM
By Marc Foster and Chris Apple, special to CNNSI.com Is there anyone out there with an undying love for the +/- stat? No? We think everyone out there has some sort of issue with it. Many think it's unfair to penalize a player for the actions of his other teammates, but is not and argument since players benefit just as easily under the same circumstances. Besides, hockey is a team sport; so most individual stats are indirectly linked to the actions of one's teammates. But our problem with +/- is that it does nothing to address scale. Say you have two players with a +/- of +6. Which +6 is more impressive, the one earned in 80 games or the one earned in 65 games? Let's make it easier and say the +6 is earned in two games. Now it becomes obvious, for players with the same plus, the one earned in fewer games is the more significant. For someone in the minus it's the opposite -- the more games the better. But why stop with game played to measure the impact? Can't we do the same with time on the ice? Of course, and it allows us to do some very interesting things. But first, we need to look at the raw stats used for +/-, then revisit our friend the Pythagorean equation. In any league that records +/-, what is actually recorded are the jersey numbers of everyone on the ice when a goal is scored. That the goal is powerplay or even strength is also recorded, so that for +/- only the even strength goals are used. At the end of the game, the total GF and GA for each player are then tallied, and difference calculated to determine the +/- for the game. But for our latest toy, we really don't care about the +/-. It's this GF and GA that are important. We can plug these into the Pythagorean to create what we call a Personal Pythagorean Equation (PersPyth%). The first thing we notice is that if someone has 55 GF and 50 GA, and another has 25 GF and 25 GA, their +/- will be the same (+5), but their PersPyth% will be different (.548 vs. .610). So that’s the first step, determining the Personal Pyth%. It should be noted that we could calculate this three ways. First, we can just use even strength goals. Second, we can use special teams’ goals. Third, we can use all goals. Using just special teams goals can be perilous, however, if you're dealing with a player who spends significantly more time on the power play than on the penalty kill (or vice verse). But using the even strength goals to determine the PersPyth% doesn’t do anything more to address the issue of scale than does +/-, so now it's time to look at ice time. By incorporating ice time, we can actually determine the wins and losses that might be directly attributed to a specific player. The number of skater-minutes in a regulation game is 300 -- five players times 60 minutes. Certain adjustments for overtime and shorthanded minutes could be considered, but we don't think they're significant, and keeping the number of player-minutes at 300 prevents us from making 30 individual calculations to satisfy the difference for each team. It really doesn't matter if we're looking at this from an even strength or from a total goals/minutes situation, a full game is still 300 minutes and remaining calculations for either system differ only in context. So let's create an example. Say we've got a defenseman who in 20 games has played 560 total minutes. That works out to 1.866 complete games. In that time, his team has scored 36 goals while he was on the ice, and allowed 24. That's a .692 PersPyth% for all minutes played. Take that times the 1.866 games played, and you've got a player with a Personal Win-Loss Record of 1.30 - 0.56. If 420 of those minutes were even strength, with 25 GF and 20 GA, that's 1.4 even strength games played with a .610 even strength PersPyth% for a win-loss record of 0.854 - 0.546. Now, those people who have some of the more traditional issues with +/- are not going to be totally happy. Since Personal Pythagorean numbers are derived from the same raw data as +/-, the same caveats of “unfairness” still apply. Still, we feel this method goes a long way towards addressing the issue of scale, which was our point to begin with. Next week we’ll take a hard look at the data. In the meantime, those of you salivating for stats may feast upon updated numbers for Scoring Efficiency, Weighted Goals, and Weighted Assists.
Marc Foster is a research analyst in Fort Worth, Texas. Chris Apple is a database analyst/Internet specialist in Lincoln, Neb. Together, they operate HockeyResearch.com, and hope to one day elevate statistical research in hockey to the level seen in other sports.
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