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I’m somewhat ashamed to admit it: I was a late convert to shot-based metrics. While the Corsi number has been a subject of interest in the online community for a several years, it was only last year that I began seriously considering Corsi numbers as an alternative to an adjusted plus-minus. The benefits of Corsi are numerous: they rely on a much larger sample than plus-minus, between 12X and 25X depending on whether you also include missed and blocked shots, which means that Corsi numbers are much more reliable and less noise-prone. They also naturally factor out the effect of goaltending, which causes plus-minus to be even more team-dependant than it already is.
However, Corsi numbers also have their weaknesses. While Corsi is useful as a proxy for territorial advantage, it does not factor in the quality of the shots being generated or allowed. My historical preference for plus-minus stemmed from the fact that a player may be doing several subtle things right that will, in the long-term, show up in his plus-minus. This remains true: however, the long-term can be several seasons or even longer, and most of us would prefer a metric that allows us to judge a player before he has retired, not after. The classic bugaboo of Corsi is Scott Gomez: a player who generates a large number of low-quality shots, thus artificially inflating his Corsi without generating a commensurate number of scoring chances. Corsi is also influenced by game score, as trailing teams generate more shots.
The online community has addressed this problem: track scoring chances explicitly. I like this approach a lot, and those who discard it because it is subjective are attacking a strawman: to a large extent, all statistics in hockey are subjective. However, it is not being done for all teams, and has certainly not been done for any previous seasons, making its usefulness for large-scale analysis limited. Therefore, I decided to use another approach. The main factors that affect shot quality (distance, rebounds, game situation, game score) are well known. Simply weight each shot by its expected chance of resulting in a goal, do the difference of for and against as in Corsi, and voila! Delta, the love-child of Corsi and plus-minus, is born.
Establishing shot quality is actually rather straightforward: the gold standard for this research, so far, is the work of Ken Krzywicki (warning: pdf)and I have used a shot quality model that is very similar to his, with the only extra factor I added being the game score, as teams with the lead generate higher quality shots.
Using this process, we can establish raw Delta scores, which simply represent what a player’s plus-minus would have been with average goaltending on both teams, average shooting ability on both teams, and neutral luck. Thus emerges Delta’s first acid test: is Delta a better predictor of plus-minus than Corsi is? Luckily the answer is yes, otherwise you probably wouldn’t be reading this right now. The correlation coefficient last season between plus-minus and Delta was 0.528, while it was 0.475 between plus-minus and Corsi. While this may not seem like a big difference, over hundreds of players last year the difference is very significant. For 2007-08 the numbers were 0.569 and 0.540 respectively.
For now, I will look at all Delta numbers uniquely at 5-on-5. As a quick look, here are the top 20 players in the league by raw Delta last season:
Top 20 raw delta
Player Pos Team Delta
ZACH PARISE L njd 16.0
MARC-EDOUARD VLASIC D san 15.3
MILAN MICHALEK L san 14.5
ALEXANDER SEMIN L was 14.3
MARC METHOT D cls 14.2
PATRICK O'SULLIVAN C lak 14.2
JAROSLAV SPACEK D buf 14.1
COREY PERRY R ana 14.1
JOE PAVELSKI C san 13.7
ERIC STAAL C car 13.4
ROB BLAKE D san 13.4
MIKE GREEN D was 13.4
RYAN GETZLAF C ana 13.3
RYANE CLOWE L san 12.8
JAMIE LANGENBRUNNER R njd 12.7
DAN BOYLE D san 12.6
JOE THORNTON C san 12.3
DAYMOND LANGKOW C cgy 12.2
JOHAN FRANZEN C det 12.1
RYAN SMYTH L col 12.0
Obviously, as with any raw number, there are large team effects at work here, with 7 Sharks, 2 Devils, 2 Capitals and 2 Ducks in the top 20.
Having established a raw benchmark that has some value, we can now apply the golden rule of hockey statistics, as per the Oilogosphere: context is everything. In terms of influencing Delta, the most important factors are the number of faceoffs taken in the offensive and defensive zone, and the percentage of faceoffs that your team wins. A lost faceoff in the defensive zone leads to an expected goal differential of -0.02 over the next 50 seconds (roughly the length of a shift), while a won faceoff in the offensive zone is the opposite. We can now correct Delta to produce DeltaS (for Situation), which gives Delta working in a zone-neutral environment.
Here is the list of players whose DeltaS most benefits from the adjustment:
Top 20 DeltaS adjustments
Player Pos Team Delta DeltaS Adj
NICK SCHULTZ D min -13.1 -8.2 4.9
ZBYNEK MICHALEK D pho -9.0 -5.0 4.0
KURT SAUER D pho -9.0 -5.1 3.9
KIM JOHNSSON D min -7.6 -3.8 3.8
STEPHANE VEILLEUX L min -7.9 -4.2 3.7
MARTIN SKOULA D min -5.0 -1.7 3.3
BRENDAN WITT D nyi -12.4 -9.3 3.1
JAY BOUWMEESTER D fla -8.4 -5.4 3.0
CAL CLUTTERBUCK R min -5.6 -2.6 3.0
MIKE RICHARDS C phi 1.1 3.9 2.8
JAMES SHEPPARD C min -5.9 -3.2 2.7
JEFF CARTER C phi -3.8 -1.2 2.6
JAY MCCLEMENT C stl -3.9 -1.4 2.5
KARLIS SKRASTINS D fla -7.9 -5.7 2.2
RADEK MARTINEK D nyi -3.1 -1.0 2.1
JERRED SMITHSON C nsh -5.3 -3.2 2.1
SCOTT HANNAN D col -8.5 -6.4 2.1
MARTIN HANZAL C pho -2.9 -0.9 2.0
KYLE BRODZIAK C edm -3.0 -1.0 2.0
RICHARD PARK R nyi -8.5 -6.5 2.0
Longtime followers of Corsi will recognize most of the players on this list: mostly defensive defensemen who tend to start almost all their shifts in the defensive zone. In fact, Mike Richards stands out from this list as the only player with high offensive talent (apart from Carter, and debatably Bouwmeester), and the only player with a Delta that was initially positive. This begs the question: given that most of the DeltaS values above are still negative, am I undercompensating? I believe the answer is no, though I’m willing to be convinced. The reason these players are on the list is that they ONLY start in the defensive zone, which means they have little offensive skill. A player with little offensive skill usually will not generate an overwhelming shot advantage for his team.
Obviously, the starting zone of faceoffs is not the only factor that influences a player’s result. The strength of his teammates and strength of his opponents also factors in. Compensating for teammate strength is fraught with peril, and I will address it at a later date, but for now we will steal a page from Gabriel Desjardins’ book and compensate for the average of the opponents’ DeltaS: in effect, a DeltaS-based QualComp. The only difference between this methodology and traditional QualComp is that we are compensating for players’ absolute DeltaS, not their DeltaS as compared to their team.
The magnitude of this effect is smaller than that of faceoffs: you can start 70% of your shifts in the defensive zone, but you can’t start 70% of your shifts against Getzlaf (except in the playoffs, but that’s a story for another day). We now have DeltaSO (for Opponents). Here is the list of players who had the greatest adjustment to their DeltaSO, which in effect means the greatest QualComp weighted by ice time:
Top 30 DeltaSO adjustments
Player Pos Team Delta DeltaS DeltaSO Adj
ZBYNEK MICHALEK D pho -9.0 -5.0 -3.1 1.9
DAN HAMHUIS D nsh -9.9 -8.6 -6.9 1.7
KURT SAUER D pho -9.0 -5.1 -3.5 1.6
GREG ZANON D nsh -6.6 -5.3 -3.8 1.5
SHEA WEBER D nsh -0.6 -0.8 0.6 1.4
MIKKO KOIVU C min 1.7 1.5 2.8 1.3
LOUI ERIKSSON L dal 2.5 3.3 4.5 1.2
DUNCAN KEITH D chi 6.7 6.5 7.7 1.2
BRENT SEABROOK D chi 5.5 5.3 6.5 1.2
RYAN SUTER D nsh -1.2 -1.2 0.0 1.2
NICK SCHULTZ D min -13.1 -8.2 -7.0 1.2
SHANE DOAN R pho -5.6 -4.0 -2.9 1.1
TREVOR DALEY D dal -0.7 -0.1 1.0 1.1
JEAN-PIERRE DUMONT R nsh -2.6 -3.5 -2.4 1.1
DAVE BOLLAND C chi 2.7 4.4 5.5 1.1
STEPHANE ROBIDAS D dal 3.3 4.7 5.8 1.1
ANTTI MIETTINEN R min -7.5 -6.6 -5.5 1.1
KIM JOHNSSON D min -7.6 -3.8 -2.8 1.0
MARTIN HANZAL C pho -2.9 -0.9 0.1 1.0
ANDREW LADD L chi 9.1 10.8 11.8 1.0
WILLIE MITCHELL D van 3.1 3.7 4.7 1.0
SCOTT HANNAN D col -8.5 -6.4 -5.5 0.9
NICKLAS GROSSMAN D dal -11.0 -9.9 -9.0 0.9
ANDREW BRUNETTE L min 3.0 2.8 3.7 0.9
NICKLAS LIDSTROM D det 10.5 9.7 10.6 0.9
RYAN GETZLAF C ana 13.3 12.4 13.3 0.9
BARRET JACKMAN D stl -0.5 1.3 2.2 0.9
JAMES NEAL L dal 1.1 0.7 1.6 0.9
DAVID LEGWAND C nsh 0.6 0.9 1.8 0.9
SAMI SALO D van -0.2 -0.4 0.5 0.9
The composition of this list is quite different from the previous one. While the previous list had defense-first players, this one features more two-way defensemen and power-vs-power players. Seeing both Duncan Keith and Brent Seabrook in the top 10 is not a surprise, as they are widely considered among the top two-way defensemen in the league, and were found to face the toughest quality of competition as measured by Corsi, and finding Nicklas Lidstrom, Mikko Koivu and Ryan Getzlaf is good validation as well. I extended the list to 30 players because the top 20 positions consisted entirely of players from 5 teams. Astute readers will notice that this list is composed entirely of Western Conference players, showing that the Western Conference teams were stronger, based on Delta, than the East.
Finally, here is the list of top players by DeltaSO:
Top 30 DeltaSO
Player Pos Team Delta DeltaS DeltaSO
ZACH PARISE L njd 16.0 15.6 15.3
MARC-EDOUARD VLASIC D san 15.3 14.6 14.5
COREY PERRY R ana 14.1 13.2 14.0
PATRICK O'SULLIVAN C lak 14.2 13.5 13.6
MARC METHOT D cls 14.2 13.8 13.6
JAROSLAV SPACEK D buf 14.1 14.2 13.6
ERIC STAAL C car 13.4 13.5 13.5
RYAN GETZLAF C ana 13.3 12.4 13.3
MILAN MICHALEK L san 14.5 13.3 13.2
JOE PAVELSKI C san 13.7 13.3 13.1
RYAN SMYTH L col 12.0 12.7 13.0
JOHAN FRANZEN C det 12.1 12.2 12.8
ROB BLAKE D san 13.4 12.6 12.3
ALEXANDER SEMIN L was 14.3 13.2 12.2
JAMIE LANGENBRUNNER R njd 12.7 12.4 12.1
ANDREW LADD L chi 9.1 10.8 11.8
RYANE CLOWE L san 12.8 11.9 11.7
DAYMOND LANGKOW C cgy 12.2 11.6 11.5
CHRIS KUNITZ L ana 10.5 10.1 10.8
TRAVIS ZAJAC C njd 11.3 11.1 10.8
BRIAN RAFALSKI D det 10.6 9.8 10.7
NICKLAS LIDSTROM D det 10.5 9.7 10.6
JOE THORNTON C san 12.3 10.6 10.6
MARTIN HAVLAT R chi 10.0 9.8 10.4
DAN BOYLE D san 12.6 10.6 10.0
MIKE GREEN D was 13.4 11.1 10.0
ANZE KOPITAR C lak 9.4 9.3 9.9
KYLE QUINCEY D lak 10.9 9.6 9.9
MARIAN HOSSA R det 10.1 9.4 9.7
ERIC FEHR R was 10.7 9.9 9.3
Mostly solid players and few surprises. While Eric Fehr was the player that most jumped out to my eyes, he’s been a +24 over the past two seasons with limited ice time, so perhaps it’s not a fluke after all. There has been no correction for teammate strength, so this list still exhibits a good-team bias.
And, since there is as much to be learned from the trailers as well as the leaders, the bottom 20:
Bottom 20 DeltaSO
Player Pos Team Delta DeltaS DeltaSO
ILYA KOVALCHUK L atl -15.9 -14.6 -14.5
ROD BRIND'AMOUR C car -12.2 -13.8 -14.5
JASON STRUDWICK D edm -13.7 -13.4 -13.8
JORDIN TOOTOO R nsh -12.5 -13.0 -12.2
JOHN MITCHELL C tor -10.4 -11.4 -11.9
DEREK MORRIS D pho -10.7 -10.9 -10.4
LUKE SCHENN D tor -9.9 -10.1 -10.4
JAY PANDOLFO L njd -9.0 -9.8 -10.3
VERNON FIDDLER C nsh -11.8 -10.8 -10.1
ETHAN MOREAU L edm -11.4 -10.7 -10.1
TODD WHITE C atl -11.6 -9.9 -9.7
ANDREI MARKOV D mon -10.3 -9.5 -9.4
NICKLAS GROSSMAN D dal -11.0 -9.9 -9.0
BRENDAN WITT D nyi -12.4 -9.3 -9.0
VILLE PELTONEN L fla -10.1 -8.7 -8.9
DUSTIN BOYD C cgy -8.1 -8.6 -8.9
SAKU KOIVU C mon -9.0 -8.7 -8.8
STEVE STAIOS D edm -9.3 -8.8 -8.7
NICLAS HAVELID D atl -9.8 -8.5 -8.7
KRIS DRAPER C det -7.5 -8.4 -8.7
While I doubt any NHL executives will take my statistics into account, this list goes some way towards explaining why I think the team that signs Kovalchuk will have overpaid. If Kovalchuk’s shooting percentage wasn’t off the charts, he’d be quite a liability to his team. I’d be curious to hear from my Oiler readers, who tend to be numerically astute, if the three Edmonton names on this list make sense to them. There’s also a mild bias against defensive forwards, with Jay Pandolfo and Kris Draper making the bottom 20.
That concludes my initial tour of Delta. For any of my readers who feel like crunching the numbers themselves, feel free to contact me and I will e-mail you a spreadsheet of full Delta numbers for the 2008-09 season.
Tom Awad is an author of Hockey Prospectus.
You can contact Tom by clicking here or click here to see Tom's other articles.
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