NHL PLUS/MINUS vs. SITUATIONAL PLUS/MINUS

The traditional National Hockey League measure of plus/minus is much maligned. In an effort to measure a player’s impact on goal scoring (either for or against), the NHL sought to exclude goals deemed “easier” to obtain or give up.

Here is the official NHL definition of plus/minus, which only applies to skaters, not goalies:

Plus/Minus: A player is awarded a “plus” each time he is on the ice when his Club scores an even-strength or shorthanded goal. He receives a “minus” if he is on the ice for an even-strength or shorthanded goal scored by the opposing Club. The difference in these numbers is considered the player’s “plus/minus” statistic.

What is glaring is the exclusion of power-play goals. For a more complete picture a player should be credited positively or negatively with being on the ice when any kind of “team-based” goal is scored (excluding penalty shots and shootout goals, which are not team-based goals). Also, the definition above assumes all goals are counted equally. Thus, the weighted value of goal scored in a five-on-three situation is the treated the same as one scored at even strength.

I have often thought of how to improve the plus/minus stat to make it at least serviceable. It will never be the holy grail of statistics (but it can still be useful as a supplemental stat). The flaws in the current calculation boil down to two questions. Number one: Why not include all team-based goals for a truer representation of plus/minus? Number two: How to devise a method to factor the difference in the number of skaters on the ice when a goal is scored?

In order to solve the second question, I just looked at the relationship of the number of skaters on the offense vs. defense and made the following calculations:

Goals For:

• Even strength (6v6, 5v5, 4v4, 3v3) – 6 divided by 6 = +1.00, 5 divided by 5 = +1.00, 4 divided by 4 = +1.00, 3 divided by 3 = +1.00
• Advantage (5v4, 5v3, 4v3) – 4 divided by 5 = +0.80, 3 divided by 5 = +0.60, 3 divided by 4 = +0.75
• These are less than +1 since it is theoretically easier to score in these situations
• Short-handed (4v5, 3v5, 3v4) – 5 divided by 4 = +1.25, 5 divided by 3 = +1.67, 4 divided by 3 = +1.33
• These are greater than +1 since it is theoretically harder to score in these situations
• Extra attacker up (6v5, 6v4, 6v3) – 5 divided by 6 = +0.83, 4 divided by 6 = +0.67, 3 divided by 6 = +0.50
• Extra attacker down (5v6, 4v6, 3v6) – 6 divided by 5 = +1.20, 6 divided by 4 = +1.50, 6 divided by 3 = +2.00

Goals Against:

• Even strength (6v6, 5v5, 4v4, 3v3) – 6 divided by 6 = -1.00, 5 divided by 5 = -1.00, 4 divided by 4 = -1.00, 3 divided by 3 = -1.00
• Advantage (5v4, 5v3, 4v3) – 5 divided by 4 = -1.25, 5 divided by 3 = -1.67, 4 divided by 3 = -1.33
• These are worse than -1 since it is theoretically harder to be scored on in these situations
• Short-handed (4v5, 3v5, 3v4) – 4 divided by 5 = -0.80, 3 divided by 5 = -0.60, 3 divided by 4 = -0.75
• These are better than -1 since it is theoretically easier to be scored on in these situations
• Extra attacker up (6v5, 6v4, 6v3) – 6 divided by 5 = -1.20, 6 divided by 4 = -1.50, 6 divided by 3 = -2.00
• Extra attacker down (5v6, 4v6, 3v6) – 5 divided by 6 = -0.83, 4 divided by 6 = -0.67, 3 divided by 6 = -0.50

Now, the weighted value or difficulty of a goal changes depending on how many skaters are on the ice when a goal is scored. It is presumably harder to score short-handed (4v5, +1.25) than even strength (5v5, +1.00), which is subsequently harder than on the power play (5v4, +0.80). Conversely, it is easier to be scored upon short-handed (4v5, -0.80) than even strength (5v5, -1.00) than while on the power-play (5v4, -1.25).  Also, in the same way Goals Against Average is presented to two decimals, so too is the Situational Plus/Minus.

PlusMinusLine.com presents in-season data for all players who dressed for a game in the NHL.  See the Legend for abbreviations used on this website.

GOAL DIFFERENTIAL

It is also useful to compare the player’s Situational Plus/Minus (or “Sit +/-“) to the player’s Goal Differential (or “GDiff”).  The GDiff is simply the net difference between team goals for and team goals against for which a player is on the ice.  It does not take into account the weighted value of a goal, as noted above.  If the Sit +/- is higher than the GDiff, it typically indicates a stronger correlation to short-handed goals either given up and/or scored.  A Sit +/- that is the same or very close to the GDiff typically indicates the majority of goals are even strength.  Lastly, a Sit +/- that is worse than the GDiff indicates a preponderance of goals scored on the power-play.

GOALIES & SITUATIONAL PLUS/MINUS

The NHL does not track plus/minus for goaltenders.  However, these days the goalie can be just as much a part of the action as a skater – clearing the zone, getting assists, scoring the occasional goal.  Sit +/- and GDiff is also available for goalies. Normally there should be a strong correlation between a goalie’s win total and Sit +/-. And from the detailed Sit +/- stats we can see how goalies fared in different scoring situations, whether even strength, short-handed, etc.

The success among goalies is often measured in Goals Against Average (or “GAA”). What is interesting, though, is looking into “goal support” (similar to run support in baseball).  By calculating the Goal Support per 60 Minutes (or “GS/60”) we can directly compare how often a team scored against the opposition by goalie.  Extrapolating the difference in GS/60 and netting it with a goalie’s Sit +/- may be a way to level the playing field when comparing goalies (especially those on the same team).  What this does for a goalie’s psyche is a matter of debate. Still, one still needs to stop the puck in any event.

More stats are available on nhl.com.