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March 4, 2010
Howe and Why
Ten Ways to Measure Defensive Contributions

by Robert Vollman

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A common criticism of statistical hockey analysis is the perception that there are no ways to measure a player's defensive contributions as reliably as a player's offensive contributions. In today's article I would like to blow that myth out of the water by presenting ten ways you can use statistics to evaluate a player's defensive contributions in ways that rival offensive statistics of comparable complexity.

Real-Time Scoring Statistics

For years the NHL has made a variety of defensive-minded statistics available to the general public, including hits, blocked shots, takeaways and faceoffs won. These statistics can be used to evaluate certain aspects of a player's defensive game, but not their overall defensive abilities. Even taken together, these statistics only present part of the picture, because there are a number of non-recordable ways that a great defensive player can prevent goals without throwing hits, blocking shots, winning faceoffs or taking the puck away.

Beyond that, there are still other limitations to this approach. For instance, there is currently no quantifiable relationship between these statistics and the actual prevention of goals. How many goals does 100 block shots prevent? How many wins does 100 hits or takeaways contribute?

While a goal is a goal, the definition of a hit, blocked shot, takeaways and a won faceoff are all subjective, and can vary from scorekeeper to scorekeeper. You can look at road-only statistics to eliminate (some of) this bias, and get some value out of the NHL's real-time scoring statistics.

Defensive Zone Faceoffs

Speaking of faceoffs, Gabe Desjardins of Behind the Net studied the correlation between faceoff location and results, goals scored in the precious 7-12 seconds that follow, and wins/losses. He concluded that teams should (and generally do) use their best faceoff men when in their own or opposing ends, especially in certain situations.

My Puck Prospectus colleague revealed some very interesting insight by showing which centers are favored by each team in those situations. The major limitations are that defensive zone faceoffs won't tell you anything about wingers or defensemen, and also doesn't take game context into account, such as the time of game, whether you're protecting a lead or down by a goal.

Adjusted Plus/Minus

For years the only statistics with even the slightest ability to measure a player's defensive contributions was the plus/minus statistic, the limitations of which are very well known, and the study of which almost becomes a rite of passage for budding hockey statistic analysts. In fact, my first foray into this world was getting to make my own modest contribution in working with Iain Fyffe, who was already one of the most established names in hockey analysis even back in 2002. For a more contemporary analysis, including a discussion on the limitations of plus/minus and how they can be addressed, take a look at what our colleague Tom Awad wrote as one of his earliest articles on Puck Prospectus.

Goals-Against Average

Adjusted Plus-Minus looks at a player's offense-relative-to-defense contributions, so the natural evolution would be to remove the offensive component (the "plus") and look only at the defensive component (the "minus"). Goals-Against Average is perhaps the most convenient way of extracting that defensive component, and presents that information in a fashion to which we've already become accustomed in our evaluation of goaltenders.

Often a player's GAA will even be broken down by situation (even-strength, short-handed), but it still remains a highly contextual statistic since a player's individual GAA is so heavily influenced by his goalie, his linemates, his opponents, the game situation, and the role he's asked to play.

To address the team bias, some people look at a player's GAA when he's on the ice and when he's not on the ice. And studying shots allowed per 60 minutes instead of goals is an attempt to remove the small bias caused by goalies with exceptional save percentages. However, not all shots are created equally, so I suppose the ultimate metric would incorporate shot quality into the mix as well.

Relative Corsi

It doesn't seem fair to reward players playing in front of extremely talented goaltenders, nor to penalize anyone playing in front of shaky netminders, but by looking at goals instead of shots, that's exactly what we're doing. Buffalo Sabres goaltending coach Jim Corsi popularized the movement to replace the plus/minus statistic with the Corsi number, which looks at the attempted shot differential while a player is on the ice, instead of the goal differential.

A player's Corsi number will include not just shots that the goalie had to stop, but any defensive pressure that resulted in blocked shots, or shots that hit the post or missed the net entirely. Despite the attempt to remove the goaltending factor, Corsi remains a very contextual statistic, and players on teams with systems that allow a lot of shots from the outside will be shown in a very favorable light with Corsi.

To address some of these limitations, Gabe Desjardins introduced Relative Corsi to measure territorial dominance. Given the correlation between shots taken and in which zone the action is primarily taking place, he felt that the best application of Corsi is to study it relative to a player's teammates, a concept he explored a little further in one of his earliest Puck Prospectus articles.

Quality of Competition

One of the most significant remaining limitations of Adjusted Plus/Minus, Goals-Against Average and Relative Corsi is that a player can get a huge boost from playing with certain linemates, against certain opponents, and being asked to play certain roles in certain game situations. That was the primary motivation when Gabe Desjardins introduced the Quality of Competition measurement.

A player's Quality of Competition is measured by looking at the relative plus/minus of the opponents he faced -- the opposing players' plus/minus when they're on the ice relative to when they're not. Unsurprisingly there's also a variation that uses Relative Corsi instead of the relative plus/minus.

Desjardins goes into a little bit more detail at Behind the Net, but not only is Quality of Competition our best way to address the influence a player's opponents have on his plus/minus, goals-against average or Corsi numbers, but it also tells us to whom coaches are turning to shut down the best lines.

Ice-Time

Generally speaking nobody knows someone's defensive abilities better than their own coach, so the players to whom he turns when killing a penalty or protecting a one-goal lead late in the game are probably his team's best defensively.

Unfortunately there's no easy way to use this to compare players on different teams. A player being consistently used in defensive situations might just be an average defensive player on a lousy defensive team, and a player being used sparingly in such situations could actually be a far superior defensive player, but just happening to find himself surrounded by the elite.

Point Allocation

Speaking of ice-time, many of the more sophisticated and all-encompassing attempts to measure a player's defensive contributions were inspired by Iain Fyffe's Point Allocation approach. Based on the ability to estimate how much ice-time a player should get based on his offensive contributions, any difference between a player's actual ice-time and his expected ice-time is most likely a consequence of that player's defensive contributions. Consequently, Point Allocation is measured in the proportion of ice-time that is explained by a player's defensive contributions. Unfortunately Point Allocation slowly faded out of the mainstream, but this common sense approach to measuring defense still exists as the cornerstone of other statistics.

Goals Versus Threshold (GVT)

Inspired by Bill James' VORP statistic in baseball, Tom Awad developed GVT in 2005, and has quickly become one of the more popular ways of measuring a player's overall contributions versus the threshold of a replacement-level player. The calculation is based on statistics readily available for generally any era or league, and it's very straightforward. Awad published a full explanation on Puck Prospectus in a three part series in 2009 (part 1, part 2 and part 3).

For ValD, the defensive component of GVT, team defense is measured by looking not at how many goals are allowed by a team, but rather how many shots were allowed (currently without regard to shot quality). The team defense is then assigned to players based on how many goals were allowed when they were on the ice. Position is taken into account, as defensemen are considered twice as responsible for preventing goals as forwards.

Player Contribution Defense (PCD)

Released shortly after GVT and belonging to the same family, Player Contribution was introduced by Alan Ryder of Hockey Analytics as a more detailed attempt to evaluate a player's contributions. For those familiar with Bill James' contributions in baseball, PC is based on the methodology behind Win Shares. Like GVT, PC not only relies on the statistical link between wins and goals, but also evaluates those goals based on comparison to a threshold of replacement-level players (or "Marginal" players, in PC lingo).

PC looks at how many goals were prevented at a team level, then subtracts the goaltending contribution. Since shot quality is factored into the goaltending contribution, PC has the advantage of measuring more accurately how many goals were prevented by the skaters. The resulting marginal goals prevented by team defense is then allocated to individuals, which is based on goals scored against and whether they're a defenseman or a forward (albeit to a slightly different ratio than GVT).

Bonus: Delta and DeltaSOT

The newest measurement is courtesy of my Puck Prospectus colleague Tom Awad, who introduced it recently in a two part series (part 1, part 2). Awad melded the best of the defensive statistics already discussed above into a single offense-relative-to-defense measurement named DeltaSOT. In a nutshell, here's how it's built:

  1. Awad introduces shot quality to a Corsi-based plus-minus statistic to remove the goaltender's influence, thus creating the Delta statistic.
  2. Next, situational information based on defensive zone faceoff research is introduced to remove the effect of being used in certain roles and playing primarily in certain zones, creating DeltaS (S for Situation).
  3. For the benefit of those players whose numbers have been significantly affected by playing against particularly weak or strong competition, QualComp is used to create DeltaSO (O for Opponent).
  4. Finally, to address the concern that the numbers are still being significantly influenced by the quality of ones linemates, Awad makes a simple adjustment to create the end product: DeltaSOT (T for Teammate).

Brilliant! Personally I would have named it GOST (Goalie, Opponent, Situation, Teammates) because it rolls off the tongue a little easier than DeltaSOT, don't you think?

Wrap Up

By improving our understanding of the many defensive statistics that are out there and how they work, we can learn how to correctly interpret and apply them. I think that will correct the misperception that defensive statistics are somehow flawed in ways that offensive statistics are not.

There are many different ways to measure a player's defensive contributions, and each one has its application. Thanks to the many methods developed by hockey statisticians like Iain Fyffe, Alan Ryder, Jim Corsi, Gabe Desjardins and Tom Awad, I believe a picture of a player's defensive contributions can be painted as accurately as their offensive contributions.

Robert Vollman is an author of Hockey Prospectus. You can contact Robert by clicking here or click here to see Robert's other articles.

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