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Eighth-grade math helps hockey
Updated: Tuesday October 16, 2001 12:55 AM
By Marc Foster and Chris Apple, special to CNNSI.com One of the things we hope to accomplish through this column is to elevate the level of statistical analysis in hockey to the level seen in baseball. In baseball, the science of stats is called sabermetrics, after SABR, the Society for American Baseball Research. While hockey has a similar organization called the Society for International Hockey Research (SIHR), this is yet to be called "sihrmetrics" or "sirmetrics." "Hockeymetrics" has been bandied about but it hasn't caught on yet. We're open to suggestions. Anyway, back to the stats. Bill James, the Dean of Sabermetrics, has a simple tool to measure if a team over- or under-achieved for a given season based on the total runs scored and allowed. Ideally, a team that scores 800 runs and allows 800 runs should finish with a winning percentage at exactly .500. But what about teams who score 850 and allow 700? James came up with the following equation to handle this: Pythagorean Winning Percentage
RF^2
Conveniently, the same equation works just as well for hockey. We can substitute runs for goals to nearly the same effect, giving us: Pythagorean Winning Percentage
GF^2
There is one small difference, however. Depending upon the era, adjustments need to be made to the exponential factor. In the early days of hockey (prior to 1942), when scoring was at a premium and the best goalies recorded shutouts nearly every other game, the factor is 1.63. In the Original Six era (1942-67), the final factor used is 1.92. In the Era of Expansion (from 1967 to present), 2.03 minimizes the total error, but is close enough to 2.0 to use the latter for everyday use. Once the Pythagorean Winning Percentage (Pyth%) has been calculated, it can be multiplied by the number of possible points earned in a season to easily evaluate how the team performed in comparison to theory. This also allows a statistician to derive the average error -- how the equation performed in relation to reality. The average error for the first era was 3.01 points, second era 3.33 points, and for the current era 3.61 points. It may appear that the equation is losing its effectiveness over time, but one must also remember that more games are played today than in the past. The modern error for an 82-game season is about 2.2 percent, while the early period error for seasons of 48 games or less is at least 3.76 percent. One problem with the current use of the equation exists, though; regulation ties. The equation is based on the concept that all games are created equal. In the past, they were since exactly two points were on the line every night, creating a hockey equivalent to the First Law of Thermodynamics -- matter and energy cannot be created nor destroyed. Regulation ties screwed this up. Without a diatribe about what an abomination the new scoring system is, simply stated: it makes working with this equation more difficult. This resulted in last season's chart examining stats in both the original format and one in which all regulation ties are counted as losses. Looking at last season, the top and bottom of the rankings are of some interest. The table is sorted by the real system difference, but removing the regulation ties reveals some sharper splits in the data. Carolina, Detroit, Boston, Colorado and Phoenix all outperformed the equation by two wins or more, while New Jersey, Toronto, Montreal and Florida all underperformed by three to four wins each. It is interesting to note that although Montreal finished well out of the playoffs, had the standings reflected this equation, the Canadiens would actually have been less than five points out. Perhaps they’re already making up for it early this season. It may never be quantitatively determined why one team swings up whereas another goes down. While a correlation for team average age came up empty, there was a strong correlation, however, between team age and overall performance. On the subjective side, it could be anything from coaching to an abundance of lucky (or unlucky) breaks. James has some ideas on multiple season trends for teams, but many of those come from a time when rosters were much more static than today. Our Web site compiles a nearly complete history of Pythagorean records dating back to the start of the NHL broken up by both season and franchise. We’ll also be returning to this topic around the middle of the season to see where teams stand.
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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