Tuesday, August 29, 2006

False Normalization of 1920's Assists

During the off season I have looked at some hockey sabermetrics questions. One problem is adjusting scoring from different eras to produce a top 10 goal scoring seasons and a top 10 assist scoring seasons list. One method to do this comes from the hockey outsider (Peter Albert) and I am exploring his results.

The adjusted goal scoring list gave pretty good results, with Brett Hull leading the way. It tended to have too many players from years where the quality of play is lower (like expansion years) and it had none from the original six era. Because of this, I suggest it needs a quality of opposition adjustment but I am uncertain that existing statistics allow a reliable method to do this.

The adjusted assist list is different. It has Wayne Gretzky on it four times and the other six entries are all players from the 1920's. In the 1920's assists were different from today. Forward passing was slowly being allowed into the game. In 1929/30 it was first allowed within the offensive zone (but not across the blue line into the offensive zone as that would be offside). Thus there was less passing in the attacking zone. Any pass had to be a pass backwards. The official scorers were very stingy with assists. They tended to give out a maximum of one assist per goal - and only if the pass clearly led to the goal. As a result there were significantly less assists. Players who got a good number of assists tended to get them from drop passes and cross ice passes that were slightly behind them. The nature of their assists was different from that of today. The number of players who got these assists was less than it is today. Some players who were goal scorers tended to shoot instead of pass in these situations and rarely got assists. As a result, a player could have an assist total in the teens and lead the league.

Is that achievement really the same as a 100 plus assist season in more modern times? With this adjusted assist system it is viewed as such. Is it even logical to believe that the best assistmen of all time are a bunch of guys who were not allowed to use forward passes in the offensive zone and then nobody else until Wayne Gretzky came along sixty years later? No. This is a false normalization.

A false normalization occurs if player's totals are normalized against their era, when they clearly have very different totals from very different eras and it appears after normalization that in one era, an achievement is worth a lot more than the same achievement in another era and this difference is unreasonable.

As an example we can look at the best two seasons of all time in the adjusted assist list. Number one is Wayne Gretzky who in 1985/65 scored 163 assists for the Edmonton Oilers. Number two is Cy Denneny who in 1924/25 scored 15 asists for the Ottawa Senators. Denneny's assist total is normalized upwards two times by significant amounts. It is normalized upwards once because he only played 28 games (compared to Gretzky's 80) and a second time because assist frequency was so much lower in his era. After normalization, Gretzky has 129 normalized assists and Denneny has 128. Each real assist by Gretzky translates to 0.79 normalized assists and each real assist by Denneny translates to 8.5 normalized assists. Therefore each Denneny assist is worth 10.8 Gretzky assists. Is that reasonable? Could one assist really be worth more than ten times as much in one era then it is in another era? Afterall each assist ony leads to one goal regardless of era. Could that goal be ten times more valuable? Obviously not.

The problem is one of normalization. It is the wrong way to approach this problem. Unfortunately, it is the only approach where a framework exists to try to approach it. I suggest approaching it with a different framework - unfortunately one that is probably not entirely possible given the nature of hockey stats. Despite the fact that the method is not entirely possible, it is instructive to look at the way it would be approached.

Assist scoring produces goals. One method to approximate how many goals it produces comes from goals created formalism. This is merely an approximation and with better statistics about how the goal was created, we could probably break it down better. Anyway, we need to know how many goals were created by the assists of a player in question. Once we have that number, we can translate it into wins. Since wins correlate with goals scored (neglecting complications like shootouts and points for losing in overtime, a team's winning percentage is very well approximated by their goals scored squared divided by goals scored plus goals allowed squared - this is often referred to as the Pythagorean Formula - not to be confused with right angle triangles), we can turn the number of goals created into a number of wins created by those goals. Then we can compare the wins created into different eras. The wins created need to be normalized once by the number of games played to do this. This will reduce the false normalization where one assist is worth ten times as much as an assist in another era. There is no way one assist can be worth that much more even taking into account schedule length. Now after this is all done, we must correct one more time for the quality of opposition. It is easier to get assists or win games in a lower quality league. There is likely no clear way to undertake this step as it requires a way to quantify precisely the quality of opposition in different eras. Following this method there is no way six of the ten best assist seasons would come from the 1920's before forward passing was fully allowed.

In the 1920's few players got assists. A select handful was capable of getting them in double digit numbers. That select handful gets falsely normalized to be equivalent to 120 to 160 assist seasons of Wayne Gretzky. There is no way that 15 assists is the same as 160 assists. The 160 assists lead to far more wins.

Another example of this sabermetric problem can be found in baseball. Prior to Babe Ruth (the deadball era), there were very few homeruns. Sometimes people produce some normalization to say that a 10 home run season was as good or better than a 60 home run season. Its not. It doesn't produce nearly as many wins for a team.

Given the current framework of hockey sabermetric calculations it is necessary to normalize to compare different seasons. This leads to problems particularly with assists. Players from the 1920's before the full implementation of forward passing who were capable of getting a few assists (maybe a double digit number) normalize to be as good as somebody who gets 100 plus assists in later years. This doesn't make sense. It doesn't make sense that several players in the pre-forward passing era could get have better assist seasons than Bobby Orr or Mario Lemieux or Adam Oates.

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