In one of the earliest Puck Prospectus articles, my colleague Timo Seppa pointed out how weak a stat Plus/Minus (+/-) is, with its main detraction being that it is team-dependent. I couldn’t agree more: the league leaderboards of Plus/Minus always consist of players from a handful of top teams, and players with a lot of ice time on bad teams end up with disastrously bad Plus/Minus ratings. However, there is some validity to the statistic. After all, if your team scores goals and doesn’t allow anything while you are on the ice, that’s good, right? Historically, top Plus/Minus players have tended to be among the greatest two-way players of all time: Bobby Orr, Larry Robinson, Wayne Gretzky, Ray Bourque, Chris Pronger and Nicklas Lidstrom have all been among the top players in Plus/Minus for many years. If only we could extract the signal from the noise, we would have a valuable metric of player value. Here, I propose to do exactly that with a new statistic, RPM.
The most fundamental problem with Plus/Minus is obvious: it is highly affected by team strength. Ergo, if we want to fix it, we could simply define an “adjusted +/-“ that is Plus/Minus minus some team factor. Many people have thought of this; it’s a standard statistic that stats people come up with (a variant of this showed up in Klein and Reif’s Hockey Compendium, one of the earliest hockey stats books). However, one quickly notices that Plus/Minus is affected not just by team strength, but by ice time. While historical ice time numbers are almost impossible to come up with, pluses and minuses are not. We can simply calculate the total team pluses and minuses and subtract a portion of them from our players’s Plus/Minus. An example will illustrate this nicely: last year’s Plus/Minus leader was Pavel Datsyuk of the Detroit Red Wings, who is justifiably lauded as an excellent two-way player, with a + 41, consisting of 84 pluses and 43 minuses. The Wings had a total of 839 pluses and 604 minuses. This means that Datsyuk, who was on the ice for 127 even-strength goals, should have expected to be at + 20.6. Hence, Datsyuk’s adjusted +/- would be 41 – 20.6 = 20.4.
However, this would mean that the average adjusted +/- on every team would be 0. Intuitively, this makes no sense. Players on better teams should have better adjusted +/- on average. The problem with the above approach is that we have factored out the entire team, including the player himself. When you are on the ice for a goal for or against, you should, on average, get 20% of the credit (or blame) for it. To correctly adjust Plus/Minus, we must not subtract out the team’s entire performance, but rather 80% of the it, letting the player himself get credit for the remaining 20%. In Datsyuk’s case this means his adjusted +/- is 41 – 20.6 * 0.8 = 24.5.
A player may play with very good or very bad linemates, and this is hard to factor out from his Plus/Minus without going into game logs in detail. There is another player who has an immense impact on a player’s Plus/Minus: the goaltender. Players playing on a team with excellent goaltending will see their Plus/Minus artificially inflated by their goalie’s great job at keeping the puck out of the net. For example, let's take the best goaltender in the NHL this year, which has been Tim Thomas. Look up the NHL’s +/- leaders and tell me if any of his Bruin teammates have benefited from his goaltending.
The impact of a team’s goaltending can and should be factored out of a player’s adjusted +/-. At this point, I will start calling our new stat RPM, because we have moved beyond the traditional definition of adjusted +/-. The quality of the opposing goaltender, like the quality of the opposing team, is less of an issue because teams play games against various opponents of various strengths. The quality of opposing goaltending will tend to even out in the long run as opposed to your own goaltender who is the same guy or pair of guys every night.
Finally, we must compensate for one last weakness of +/-: it counts shorthanded goals scored as pluses and shorthanded goals against as minuses. This artificially penalizes power-play players and boosts penalty killers, while we are really looking at a measure of even-strength play. If you have access to the exact number of short-handed pluses and minuses, simply subtract them out. Otherwise, you can estimate based on a players power-play goals for and against, how many shorthanded goals he was on the ice for and subtract those from the even-strength pluses and minuses. In Datsyuk’s case, we estimate he was on the ice for 1.3 short-handed goals for and 3.7 short-handed goals against. Thus, his new pluses and minuses are 82.7 and 37.3 respectively. Once we factor in goaltending and team strength, we find Datsyuk’s RPM for 2007-08 to be 27.9, which would have placed him 4th in the league.
This is all good, you say, but where’s the beef? What are the results it provides and are they of any use? I will let you judge for yourselves. Here is the leaderboard of RPM for the current season, 2008-09, including games up to last week:
Player Team Pos +/- RPM
1 Pavel Datsyuk Red Wings F + 33 25.6
2 Alexander Semin Capitals F + 25 24.9
3 Mark Streit Islanders D + 8 23.7
4 Travis Zajac Devils F + 36 23.1
5 Mike Green Capitals D + 23 23.0
6 Evgeni Malkin Penguins F + 19 22.5
7 Patrik Berglund* Blues F + 16 22.1
8 Nicklas Lidstrom Red Wings D + 29 20.4
9 Blake Wheeler* Bruins F + 36 20.1
10 Zach Parise Devils F + 30 19.8
11 David Krejci Bruins F + 34 19.5
12 Nikolai Zherdev Rangers F + 7 18.5
13 Martin St. Louis Lightning F + 6 18.3
14 Willie Mitchell Canucks D + 30 17.6
15 Tomas Holmstrom Red Wings F + 19 17.0
16 Daniel Alfredsson Senators F + 10 16.7
17 Loui Eriksson Stars F + 12 16.6
18 Joe Thornton Sharks F + 20 16.6
19 Marian Hossa Red Wings F + 22 16.3
20 Stephen Weiss Panthers F + 15 15.9
21 Alexei Ponikarovsky Maple Leafs F + 6 15.7
22 Jamie Langenbrunner Devils F + 27 15.7
23 Chris Kunitz Mighty Ducks, Penguins F + 14 15.7
24 David Perron Blues F + 9 15.5
25 Duncan Keith Blackhawks D + 30 15.4
26 Stephane Robidas Stars D + 10 15.4
27 Michael Ryder Bruins F + 26 15.4
28 Aaron Johnson Blackhawks D + 19 15.3
29 Martin Havlat Blackhawks F + 23 15.1
30 T.J. Oshie* Blues F + 12 15.1
While there are some similarities between this list and the +/- list, they are clearly not the same. The most striking difference is that the RPM list is not dominated by players from the same teams. While three of the top 5 Plus/Minus spots were taken by Bruins, here the top Bruin comes in 8th place and Dennis Wideman, despite his +32 rating, doesn’t even rank (his RPM is 10.6). Meanwhile, players like Mark Streit and Martin St.Louis, who have posted decent numbers on weak teams, are among the league’s elite in this ranking. Our friend Pavel Datsyuk heads the list, just ahead of the impressive Alexander Semin. Overall, RPM seems to be doing its job: extracting the information available in +/- to judge players without being drowned by the team effects that its sister stat is subject to.
One last thing to notice from the above list: the top 3 defensemen on it, Streit, Green and Lidstrom, should be the three finalists for the Norris trophy this year as the NHL's best defenseman if the voters don’t mess anything up.
This concludes our introduction to RPM. In a few weeks, I’ll look at the historical results of RPM and figure out if we can use it to estimate players’ true strength over the last 40 years.
Tom Awad is an author of Hockey Prospectus.
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