Many people who look at hockey statistics focus on these scoring rates as a measure of performance. Alan Ryder used the difference in scoring rates of players from some marginal scoring rate to determine how much value a player added. I also focus on scoring rates to determine value. Problem is most people in hockey know that players get tired and tired players aren’t as good as fresh players.
There are a number of things to consider when looking at scoring rates, the most commonly mentioned two: who are the other 4 players on the ice with the given player and who are they playing against. However, what might be more significant than both of those issues is how much they play.
Let’s say there are two players who are identical in every way. Let’s say one gets 10 minutes of ice time and the other gets 20 minutes of ice time. Which player’s scoring rate will be higher? At this point the answer should be obvious the 10 minute player shouldn’t do worse under identical conditions as the player with 20 minutes as he’ll likely be a few seconds faster and have a little more jump. So, how does increased ice time affect scoring rates?
Short Mathematical Discussion
Determining the cost of additional ice time is not trivial. A regression on ice time and scoring rates is generally positively correlated, that is to say players with more ice time have higher scoring rates because coaches play the better players more often, but if you give the same player more ice time his scoring rate will fall. So I had to look at how individuals did with extra ice time.
I ran a regression with 4 variables: power play time [pp], penalty killing time [sh], even strength time [ev] and (power play time/1.5 + penalty killing time + even strength time) [adjusted ice time]. You can see the adjusted ice time variable lowers the value of power play time as I feel that the power play is generally easier than even strength play. This is simply my opinion. The response was how many goals the player was on the ice for in that game (for all situations), I’ll call these pluses. All ice time variables are measure in terms of hours per game.
A player will play in the neighborhood of 70-80 games a season and my model has 4 variables with very small domains, that is to say that ice time will vary by only a couple of minute per game. Due to this, some coefficients can become quite “strange” and aren’t very meaningful on the individual player level as many players do better with more ice time, which could be because they are paired with better players when they get more ice time. But, I’m not trying to discover an individual player’s fatigue pattern; instead I am looking for a trend in the NHL. So I take an average of all the coefficients to get an average coefficient.
I separated forwards and defenseman:
Pluses/game = 4.0 * ev + 7.0 * pp + 3.0 * sh– 4.5 * adjusted ice time2
Pluses/game = 3.6 * ev + 6.6 * pp + 3.4 * sh– 2.8 * adjusted ice time2
Time measured in hours.
There is significantly less cost for a defenseman in terms of extra ice time and this makes sense.
How does this effect even strength scoring?
The math part.
The reason the equations are as complicated as they are is because there are two types of effects: fatigue factor and a different scoring rate. On the power play you get the benefit of an increased scoring rate and a cost of additional ice time. For penalty killing you are hit with a lower scoring rate and the additional ice time.
In other words the cost of an additional hour of ice time per game is 4.5 goals for per hour. So, an additional minute (one 60th of an hour) is equal to: -4.5/60 = -0.075 goals for per hour. So the difference between a 10 even strength minute player and a 15 minute even strength player is about 0.375 GF/hour. So a player who has a scoring rate of 2.1 with 15 minutes is equivalent to a player who has a scoring rate of 2.5 with 10 minutes. That’s quite a big difference when you start thinking about it.
In order to make this analysis more real I calculated how the average player would do with a given player’s ice time and compared that to how they actually did. The comparison calculated a percentage better (or worse) than average (labeled ‘P’ on the table below). A score of +100 is equivalent to doing twice as well as the average player would do with the given amount of ice time. A score of -83.5 represents playing at 16.5% (= 100+(-83.5)) of expected. Doing poorly on this metric makes you a bad offensive player, but that does not make the player bad, they can easily make up the differences by providing defense. There are other things to consider including the standard line mate problem and opposition issues. And I should note injuries and luck play their part as well.