Saturday, August 12, 2006

Adjusting Scoring From Different Eras

One problem in sabremetrics and hockey is how to compare scoring stats from one era to another. There are several strategies that have been used. I have introduced one used by Darryl Shilling and another used by Total Hockey. Today I will introduce a third method. Its conceptually similar to the other two, but shows the differences that can occur with slightly different methodology. It also gives me an opportunity to introduce a great sabremetrics site the hockey outsider (Peter Albert). This adjusted scoring method is his way of comparing players between different eras.

The first variable that influences scoring statistics from one era to the next is schedule length. In the early days on professional hockey, teams played as few as 16 games in a regular season. Today they play 82. Obviously, the more games a player plays the more chances he has to score. To adjust this, a statistic is multiplied by a schedule adjustment of 82/games played. For example, in a 50 game season it is multiplied by 1.64.

The second variable that influences scoring statistics from one era to another is the level of offence. In some eras, teams scored more goals per game than in others. A player from a higher scoring era would appear to have higher scoring numbers than a similar player in a lower scoring era, despite the fact they are similar. To adjust for this, a player's statistics need to be adjusted for the scoring rate in his era. This is complicated further, especially in the early days of hockey, where one high scoring player could account for a large portion of the goals in a league. In order to account for this, the player whose stats are being adjusted needs to have his offensive contribution subtracted from the league. This is done by subtracting the "goals created" by a given player from the league stats. In this analysis, a slightly different formula is used for goals created than in the Daryl Shilling goals created analysis. Here the formula used is
Goals Created = 1/2 * (Goals + Assists * League Goals / League Assists).
The intent of the formula is the same, but it is a slightly different approach. To adjust for the scoring rate in an era, statistics are next multiplied by a level of offense adjustment of 6.4/(League Goals - Player's Goals Created). Here 6.4 is taken as a value to approximate the longterm average of goals per game in professional hockey.

The next adjustment is that of assist frequency. In the early days of professional hockey there are very few assists per goal. That reduced player's offensive totals relative to today where there are more assist per goal handed out. This adjustment is 1.55/(League Assists/ League Goals). 1.55 is taken as a value to approximate the longterm average of assists per goal in professional hockey. Obviously this adjustment is not necessary when comparing goal scoring only, but when comparing assists or points from different eras it is.

The final adjustment is that of icetime. In the early days of professional hockey, it was no uncommon for a player to play the entire game. Today there are four lines that are often given relatively even ice times. To adjust playing time from one era to the next, it is necessary to adjust average playing times for a player of that time. Individual players will be different from the averages, but in the earlier days of hockey, there is no record of how much playing time a player had. Today, there are 60 minutes in a standard NHL game. There are 18 non-goalies competing for icetime and five players are on the ice at any given time. So 60 * 5 / 18 = 16.7 minutes per player per game. This analysis assumes no shorthanded situations or goalies getting pulled and no overtime, so it is not exact, but it gives a number quite close to the average ice time per player. Ice time will vary for forwards vs. defencemen (defenders tend to get more ice time in a game), but again this complication is ignored. In a given era, the same calculation can be carried out. 60 minutes * number of skater positions on the ice / number of skaters on a roster (= era adjusted ice time per player). The roster size changed over time and in the very early days so did the number of skater positions since they had a seventh man on the ice called the rover. This ice time adjustment is 16.7 / Era adjusted ice time per player.

With these four adjustments we can attempt to compare statistics from different eras. This does not capture all the possible era adjustments that might exist. The biggest one missing is that of quality of opposition. In some years, the NHL wa better than in others. It was easier to score in the weaker (for example expansion or war) years than in the higher quality years, since you had weaker players to beat in order to score. This is a large adjustment that is missing. It is missing, because it is extremely hard to find an independant measure for the quality of a professional league in a given season. I will soon post giving some results of this analysis.

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