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Personal matters Equation can compute player's true impact on a teamPosted: Monday November 26, 2001 11:14 PMUpdated: Tuesday November 27, 2001 4:24 AM
By Marc Foster and Chris Apple, special to CNNSI.com Last week, we explained how the +/- system doesn’t go far enough to explain the impact of a player on the ice, in that two players each with +2 could have very different impacts towards a team’s chance of winning. Instead, we’re using some of the same raw data combined with ice time to compute a player’s actual winning (or losing) impact on a team. We start with the goals scored both for and against the player’s team while he is on the ice. While we could look at just even strength goals, we have chosen to examine all goals scored. We have decided this for several reasons, but primarily, we want to directly tie Personal Pythagorean numbers to the team numbers as explained in a previous column. Since the team figures are for all goals, and in theory the sum of the player figures should equal the team figures, we have chosen to keep this consistent. Once we have the goals for and against, we plug them into the Pythagorean equation to derive a Personal Pythagorean Winning Percentage. Then we take a players’ ice time and convert it to games played by dividing the total minutes by 300 (five players on the ice times 60 minutes). Having completed that, we take the time on ice games played and multiply it by the Personal Pyth% to calculate the wins that can be attributed to that player. We’ll leave as an exercise to the reader how the losses are compiled. This week, we take a look at the data and analyze some of the results. We left in the +/- data for comparative purposes and to show what happens when all goals are incorporated.
As you can see, there is a fair bit of bias at the top that is easy to explain. In this system a top defenseman can be at an advantage in that they typically get about 40%-50% more ice time than the average forward. Players who see a lot of powerplay time are also usually at an advantage. That some pairing up of teammates occurred wasn’t a major surprise, but we didn’t expect five Rangers to crack the top 15.
If you spend a lot of time killing penalties, you may find yourself on this list. To be fair, we want to look at this in even strength situations in the future. You may also see the odd defenseman (no, we’re not calling Rob Blake "odd") in there as well. While Blake’s Pyth% is below .500 it isn’t horrific, but he’s accumulated enough ice time to actually lead the Avalanche in both PythWins and PythLosses. Several other players accomplished the same feat for their teams. We have yet to examine the issue we addressed at the beginning, what about players around the same +/-? What is their impact? If a group of players are at Even, then it usually becomes a matter of ice time. We had hoped to find examples of players with Even +/-, but with a Pyth% that was not .500 (due to the impact of power plays and penalty killing), but having played just a quarter of the season examples were few and far between. We do expect to find them as the season progresses. Mailbag Last week after we originally explained how to use the Pythagorean equation with individual player data, we received a few emails like the following: “I'm not sure why it was necessary to bring the Pythagorean theory into play when a simple ratio of GF/(GF+GA) seems to be an adequate method of applying scale to the problem. The Pythagorean equation would unfairly skew the data towards the player with fewer games played.” We appreciate the thought, but the skew comes from the ice time. A player with low GF/GA numbers isn’t being treated unfairly in that they could just as easily be 4 GA and 1 GA as they could be 1 GF and 4 GA. The difference in Pyth% is .941 to .059, but if the player has seen little ice time, then the total impact of that high or low Pyth% is minimized. Also, we want to tie this to total team Pythagorean numbers. At the team level, the equation is an excellent predictor of winning percentage, with an average season error of just three points (or 1.5 games) per team. Using the basic equation (i.e., not squaring the GF and GA) is not nearly as accurate. For a team scoring 300 GF and 250 GA, the difference is .590 vs. .545, a difference of 7.3 points. Coming next week We've looked at weighting goals and assists by the situation in which they were scored. In this next week's column we'll look at these numbers once again, only from the goaltenders perspective. Which goaltenders have under/over performed? Is Dominik Hasek’s 2.42 goals against average as bloated as it appears? We'll look and see how weighing goals against average shakes up the league’s leaderboard... 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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