## Our defense, plus minus, and how I look at it.

After reading Stephen Whyno's grades today, and seeing the plus/minus stat being reference again for grading I decided to take a look at something. We all know defensive pairs face different levels of competition, and have different team on ice shooting and save percentages (luck), but we never really try to calculate their effects on +/-. The advanced stats fans on this site are always quick to point out if a player is getting lucky or unlucky based on above or below average shooting % or save % compared to their teammates, but I haven't seen any of us try to quantify that number for comparison. Below is an extremely simple math exercise in a crude attempt to normalize the effects of competition and luck on a the defense's +/- per 60.

The Thought Process:

We are all familiar with +/-, and we are all familiar with +/- per 60 minutes, which was my starting point for this exercise. I wanted to take that and normalize it for luck and quality of competition in a very quick and dirty way. I figured the best way to do so was to calculate the teams average shooting % and save %, then apply those numbers to each players individual shots for and shots against per 60 to get a normalized goals for and goals against per 60. My logic behind this was that applying the teams average %'s would take out all of the luck involved in differences between on ice shooting and save %. Now you might argue that luck isn't a total explanation of the differences, and I agree, but I also feel that quality of competition is also playing a role in the different on ice shooting and save %. As you can see from the link as QualComp decreases, the on ice save % increases. The trend isn't as strong for on ice shooting %, but the general negative correlation still applies. The idea is that normalizing the shooting and save % is then also taking some of the quality of competition difference in to account. I realize this is not a perfect normalization as there are factors I can't model even if I wasn't just trying to do this quickly, but I feel like this normalization offers a truer representation of the players +/- per 60 relative to his teammates if they all played in the same situation. This could be completely off base, and feel free to give feed back for improvements, but I thought it was an interesting look.

Data/Calculations:

All data is at 5 on 5 hockey, and it appears that the source I used was a game behind the latest totals.

If you go to behindthenet.ca you can find all the data I used for this exercise. +/- per 60 is calculated by taking a players goals for per 60, and subtracting their goals against per 60 (while on ice of course). The teams shooting % for each player is calculated by taking goals for and dividing it by the sum of goals for per 60 and saves for per 60. The teams save % for each player is calculated by take goals against per 60 and dividing it by the sum of goals against per 60 and saves against per 60; then taking the result and subtracting it from 1. The average for the team for both shooting and save % was just the sum all of the respective per 60 numbers for each player, as opposed to just the individual's number, with the same formulas. Once the averages were calculated, they were then reapplied to the individual's numbers to back out their normalized +/- per 60. To get goals for per 60, I took the team average shooting % and multiplied it with the sum of the individual's goals for and saves for. To get goals against per 60, I took the teams average save %, multiplied it with the sum of the individual's goals against and saves against, then took that number (normalized saves per 60) and subtracted it from the sum of the individuals goal's against and saves against. Once I had goals for and goals against per 60, you just take the difference to get the normalized +/- per 60.

Results:

Before attempting to normalize for luck, the defensemen's +/- per 60 looked like this:

1. Meszaros: 2.07
2. Carle: 1.47
3. Pronger: 1.27
4. O'Donnell: 0.93
5. Timonen: 0.92
6. Coburn: 0.65

Once I applied the team average shooting and save % to each individuals shots on net, the results were quite different:

1. Pronger: 1.56 (delta of +0.29)
2. Carle: 1.55 (delta of +0.08)
3. Coburn: 1.30 (delta of +0.65)
4. Timonen: 1.26 (delta of 0.34)
5. Meszaros: 1.12 (delta of -0.95)
6. O'Donnell: 0.52 (delta of -0.41)

The normalization helped Coburn, Timonen, and Pronger the most, while hurting Meszaros and O'Donnell the most. That is not really surprising when you look at the one ice shooting % and save % for those players, and isn't a revelation of this exercise, rather something obvious. The whole point was to see how they would compare to one another in order to get a better idea of their true value at 5 on 5. I think this helps to provide a clearer picture of that, but obviously it's not perfect. There is no true normalization for quality of competition other than it seems that worse competition results in a higher save %, which then is accounted for in the same way luck is, by using the team's average, rather than the individuals. Also, the players role dictates their value in this analysis, meaning it isn't Meszaros's fault that he is playing against poor competition, he may perform just as well as Coburn or Carle if the roles were switched, and there isn't really a way to account for that in this exercise. Rather, this exercise gives you a good idea of each players value in terms of the popular +/- stat when normalized for luck and competition, which I realize is basically just an analysis on shots, and how luck plays a huge role in plus minus.

Any feedback, criticism, and ideas for improvement are welcome. I'd like to figure out a way to not make this so shots driven, and actually useful, rather than just a long way to show the effects of luck on +/-.

This item was written by a member of this community and is not necessarily endorsed by <em>Broad Street Hockey</em>.

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