January 15, 2007

Plus Minus Graphs II

David Johnson provided a neat suggestion that the plus minus graphs should include the team along with it. 1 problem with doing this is that the X axis is time played and the Y axis is plus minus. Any given team will have more even strength time than any player so graphing the numbers together would just make the individual graph portion a small part at the beginning with a very long portion for the team data. So instead I scaled the team data down by the same percentage the player plays on a per game basis. So that the slopes are the same and the length of both curves are equal and each segment represents a game played.

Instead of graphing the team data as it is, I decided to remove the ice time and plus minus data of the given player so that the two are relatively independent of each other. This closely mimics that of Behind the Net On-Ice/Off-Ice statistics. However it only looks at the games they were involved in (where as behind the net takes the entire season average).

So to get me started I'll use Jovanovski as an example. A top defenseman on a terrible team, as you can see below, Jovanovski has done quite well in his circumstances. Even though Jovanovski has played on a relatively bad team he's managed reasonable numbers.
  • Individual (blue) Slope (red): 0.54 ±/HR
  • Team (grey-red) Slope (light pink): -0.76 ±/HR
  • Difference: 1.3 ±/HR
I found this one to be possibly the most interesting, Thomas Vanek. The rest of the team has significantly upward sloping team curves, but Vanek has managed to be the one player who makes all the other players look average. A difference of 2.09 isn't the best in the NHL, since he's on a good team, but the score is quite good.

  • Individual (blue) Slope (red): 2.47 ±/HR
  • Team (grey-red) Slope (light pink): 0.38 ±/HR
  • Difference: 2.09 ±/HR
As far as I'm concerned this is the most drastic difference in the NHL and this is Jagr. A difference of 3.43 is quite remarkable, although you can see Jagr hasn't been doing as well in recent games as he has in the past, but the team is getting better.
  • Individual (blue) Slope (red): 1.63 ±/HR
  • Team (grey-red) Slope (light pink): -1.81 ±/HR
  • Difference: 3.43 ±/HR
A number of things to remember is that: The difference scores are not really measures of skill, they probably remove some effects and are therefor better measures of skill that other alternatives. For example, Shanahan in New York, suffers from the fact that when he's not on the ice Jagr is, so he is certainly worse than Jagr, but that doesn't make him a bad player.

I'm not sure who's responsible for making Phoenix so bad, but Morris and Scatchard certainly aren't the best two players in the NHL, but on a bad team both of these players are making the team look average.
Morris: ($3.9M)

Scatchard: ($2.1M)
And if anyone is wondering who is responsible for Philadelphia's -1.71 ±/HR you need not look any further than Calder ($3M):

The rest of these graphs can be found on my website by clicking on a players name.


Anonymous said...

When people look at my player rankings and see Tom Preissing ranked so high people question them. But using your numbers he has a difference of 4.01/HR ( which perfectly explains why he does so well in my rankings. As does Vanek. As does some guy named Travis Roche for Phoenix. While Jovanovski has a difference of 1.3/HR, Roche has a difference of 2.88/HR.

Anyway, the numbers are quite interesting and can be used as a rudementary even strength rating system.

JavaGeek said...

It's not just for even strength, I've almost finished the PP and SH versions.

Earl Sleek said...

I suppose, but I guess what this neglects is context, as in somebody's got to be playing tougher minutes, and somebody's got to be playing easier minutes.

Why rate a player who has tough minutes against the easy minutes that he isn't playing? Or vice versa?

Behind the Net has a lot of these good "5-on-5 context" ratings.

For note: Preissing rates 289 / 555 in quality of teammates and 543 / 555 in quality of competition. He's not facing the Jagrs of the world.

Vanek and Roche are playing against slightly tougher competition (Vanek: 401 / 555; Roche: 494 / 555) but with much better teammates (Vanek: 56 / 555; Roche: 32 / 555).

Long story short--I'd expect these players' teams, given the nature of their minutes, to have better performances when they were on the ice as opposed to when they were off the ice. Your graphs, though, don't show me this discrepancy in teammates or opposition (the implication is +/- should be the same whether you face the Jagrs or not).

I don't really know how to express this well, but I wouldn't go dropping the Jovo's of the world in order to develop more Roche's.

JavaGeek said...

Line mates: I'll write something longer later, but the "behind the net" Teammate ratings depends on the given players plus minus so it's no surprise that NYR top all makes it to the top. Havlat ranked #58 in terms of line mates? In other words Jagrs line mates look good because Jagr helped them get a lot of plusses. I'm not sure if this rating is of any use.

If you consider strength of opposition:
Max: 0.23
Min: -0.20
Sd: 0.07
Avg: 0.015

Obviously I don't know the cost/benefit of these scores, but if your opposition averages +0.23 I'd expect that to be the cost of playing against those players, which in most cases is small enough to ignore. So while the numbers are interesting, I'm not sure if there's a huge impact.

As to Roche:
23% shooting %: is this his true shooting percentage? (3 goals, 2 of which were scored when Jocanovski wasn't on the ice) It's unlikely (basically impossible) for him to continue scoring that many goals. I also suspect that 1.3GA/hr 5-5 is not what his true rate is (probably between 2 - 2.5). So the problem isn't the equations and graphs it's the data. That is to say Roche has been extremely lucky so far.