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Frequently Asked Questions: Advanced Statistics
What are the Advanced Statistics?
Starting with the 2006-07 season, they were:
What is +/-?
Plus/Minus is the net number of goals scored (for and against) while a player is on the ice in a 5-on-5 (or any other even-strength)
situation. Invented by the Montreal Canadiens in the 1950s, it was first officially kept as an NHL statistic in 1967-68.
On this site, Plus/Minus is shown as a rate stat, net goals per 60 minutes of a player's ice time.
What is On-Ice/Off-Ice +/-?
It's the difference between the team's plus/minus rate when a player is on the ice and when he's off the ice.
Why subtract the Off-Ice +/- from regular +/-?
Hockey's a team game; a good two-way player on a bad team (Peter Forsberg, Ryan Smyth in 2006-07) will have a lower +/-
than most players on a good team like Detroit or Nashville. That's obviously not an accurate reflection of Forsberg and
Smyth's performance because they'd have a much higher +/- over the course of a season with a good team. Plus/minus
relative to the rest of the team's performance is a more accurate reflection of a player's ability to score and prevent goals.
The top 20 players in the league (minimum 25% even-strength icetime) are shown below. This list incudes many of the best
offensive players and pairings in the league, as well as players on bad teams who still do a good job of scoring and
preventing goals.
| Name | Pos | Team | # | On/Off +/- |
| PREISSING | D | OTT | 42 | +2.79 |
| VANEK | F | BUF | 26 | +2.61 |
| ALFREDSSON | F | OTT | 11 | +2.25 |
| JAGR | F | NYR | 68 | +2.21 |
| KUNITZ | F | ANA | 14 | +1.97 |
| GAGNE | F | PHI | 12 | +1.92 |
| MALIK | D | NYR | 8 | +1.78 |
| STRAKA | F | NYR | 82 | +1.68 |
| SELANNE | F | ANA | 8 | +1.65 |
| WEIGHT | F | STL | 39 | +1.62 |
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| Name | Pos | Team | # | On/Off +/- |
| PRONGER | D | ANA | 25 | +1.61 |
| ZETTERBERG | F | DET | 40 | +1.60 |
| DATSYUK | F | DET | 13 | +1.60 |
| CROSBY | F | PIT | 87 | +1.58 |
| SEDIN | F | VAN | 22 | +1.57 |
| LIDSTROM | D | DET | 5 | +1.55 |
| CAMMALLERI | F | L.A | 13 | +1.54 |
| VISNOVSKY | D | L.A | 17 | +1.48 |
| HEATLEY | F | OTT | 15 | +1.45 |
| SEDIN | F | VAN | 33 | +1.45 |
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What about the impact a player's teammates and opponents have on his +/-?
Those are listed here: Strength of Teammates and here: Strength of Opponents.
How is the 'Strength of Opponents' or 'Quality of Competition' statistic calculated?
It is the average On/Off-Ice +/- of the opposing players a player faces. For example, if you lined up against Anaheim's top line, you'd get:
| Name | Pos | Team | # | On/Off +/- |
| KUNITZ | F | ANA | 14 | +1.97 |
| SELANNE | F | ANA | 8 | +1.65 |
| PRONGER | D | ANA | 25 | +1.61 |
| MCDONALD | F | ANA | 19 | +0.94 |
| NIEDERMAYER | D | ANA | 27 | -0.31 |
The strength of opponent would be the average of 1.97, 1.65, 1.61, 0.94 and -0.31, which is 5.86/5 = +1.17. In general,
if a player matches up against the other team's first line, he'll face a high strength of competition.
How do you know who's on the ice together? Are you just estimating this somehow?
The NHL has published graphical shift charts for years, and mid-season 2005-06, they finally started publishing a
text version of those shift charts. Here's an example:
Shift Chart||
Text Version
All of the ice-time data comes from these shift charts, and the two teams are cross-referenced to determine who's
on the ice together.
How accurate is this data? How can anyone keep track of who's on the ice?
There are numerous NHL statisticians assigned to every game and they keep track of who's on the ice. Do they do this
perfectly? No, but they have been doing it for years and nobody questions the overall icetime figures they produce. Nor does
anyone question their decisions in awarding +/-.
From looking at the data in detail, a good rule of thumb is that they get changes at a whistle right, while changes on-the-fly
have about five seconds of uncertainty on them. This might add 10% of variability to these ratings, which while not unsubstantial,
does not make them so inaccurate as to be of no use.
Why isn't my favorite player listed?
Every regular NHL player should be listed here somewhere. Short-term call-ups who share numbers might be missing, and
players who switched jersey numbers screwed up the system just in 2006-07.
What about defensive forwards like John Madden and Jay Pandolfo who line up against the other team's top line? Do they
qualify as 'strong opponents'?
Overall, Madden and Pandolfo have negative On/Off-Ice +/- ratings. A player who faced them would appear to have not
faced strong competition. But keep in mind what it means to be a 'defensive forward' - it implies skill on only one side
of the equation: goal-prevention. There is very little risk of allowing a goal when you're facing a defensive line, as opposed
to lining up across from Sidney Crosby. If Madden and Pandolfo also had among the best offensive skills in the NHL, they'd
be superstars, as opposed to candidates for Defensive Forward of the Year.
According to your 'Quality of Competition' stats, the Canadiens' Radek Bonk and Mike Johnson were at the top of the
list in 2006-07. How is this possible?
Bonk and Johnson are used in very well-defined roles. Canadiens' coach Guy Carbonneau almost always matches them up
against the other team's top line. They haven't necessarily been used in this role in the past, so they have yet to
acquire the 'Good Defensive Forward' label.
'Quality of Competition' is a flawed statistic because it penalizes good players who play against other good players.
This is definitely a flaw in a "first-order" Quality of Competition calculation. When people calculate Power Rankings
in football (or Chess ratings) they run a recursive algorithm so that good players or teams aren't penalized when they
play against others with the same skill level. We could calculate a recursive version of Quality of Competition that
would solve this problem, but it's computationally cumbersome. Quality of Competition still gives us a lot of insight,
particularly into the NHL's few checking lines.
Why are power-plays and penalty-killing separate from even-strength play?
Plus/Minus only includes even-strength play, so we retained that convention here. Even a casual observer can see that
man-advantage situations completely change the way offense and defense are played, so it makes little sense to lump
them all together.
Why aren't 5-on-3 man-advantages included in the power-play?
Because 5-on-3 situations typically only happen when two penalties overlap, players typically don't get much 5-on-3 play.
So those five-second errors that official scorers make in recording icetime are no longer insignificant.
Why isn't 4-on-4 play included in even-strength play?
In addition to being a much more wide-open game, most 4-on-4 situations occur in overtime, when the value of a goal is completely
different than it is during regulation time. There's also no 4-on-4 play in the playoffs, so it's not really a situation that would
come about were it not for the need to settle every regulation season game. The vast majority of hockey games are played at 5-on-5.
Why are all these statistics separate? Why isn't there one statistic that combines every aspect of a player's game?
Baby steps. After thirty years of baseball analysis, there still isn't agreement on how to evaluate player performance. For example,
every MLB team uses its own proprietary fielding metrics, and on many players, they don't agree. Hockey is decades behind, and for now,
we're still trying to figure out what we even want to know about hockey players.
It's not that I haven't thought about it, but the risk of generating meaningless statistics is very high.
So for now I'm leaving it up to hockey fans to decide how they want to weigh the relative importance of teammates,
opponents, drawing penalties and man-advantage play.
Is your methodology secret?
Not at all! I think what I'm doing is pretty straightforward (see 82 Games for similar
analysis in basketball) and I think I've explained it fairly well here. If you have any questions, please feel free to contact me.
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