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July 30, 2009

**Numbers On Ice**

Understanding GVT, Part 1

**by Tom Awad**

Hockey statisticians have been known to complain about how the treatment of statistics in hockey lags behind that of other sports, especially baseball. There are several problems with hockey's statistics: one is that, while offensive production is relatively easy to measure, the defensive contributions of a player are less so. In addition, it is almost impossible to compare players of different positions, especially goaltenders, due to the very different nature of their functions, and the different nature of their stats: forwards are rated mostly by counting stats (goals and assists), while goaltenders are evaluated using rate stats (GAA and save percentage). GVT (Goals Versus Threshold) was my personal attempt to address these problems.

To explain in terms already familiar to sports statisticians, GVT is very similar to VORP in baseball: it is the value of a player, in goals, above what a replacement player would have contributed. The fact that GVT is measured in goals is crucial: statistics that divide up “Win Shares”, so that the ratings of a team’s players sum to that team’s number of wins, are very erratic and non-linear, since wins don’t increase or decrease linearly with team caliber. While hockey is ultimately about winning or losing, players’ contributions always come down to scoring goals and preventing them. A player cannot “win” a game, even though he may be put in a situation where scoring a goal or making a key save would create or conserve a win. Each player's role, no matter his position, is to try and increase the goal differential in favor of his team. An offensive player who scores a hat trick only to see his teammates allow 4 goals against has nevertheless done his job; a goaltender who stops 39 of 40 shots only to lose 1-0 has likewise performed well. Using this standard, all players can be compared by the same yardstick: how much did they help (or harm) their team's goal differential?

Here are the five fundamental characteristics of GVT that would also be needed as the building blocks for any other sort of VORP-like statistic in hockey:

- GVT is measured in goals. This makes it a convenient unit that hockey fans are already comfortable with.
- GVT compares hockey players of all positions and over any period of time.
- GVT only uses statistics that lead directly to goals. You cannot incorporate goaltender wins into GVT, because they are not a measurement of goals prevented. However, if you can rationally explain what are the odds of a faceoff win (or loss) leading to a goal or goal against, it would be possible to incorporate faceoff wins and losses into GVT, though I have not done so.
- GVT has built-in accounting. The sum of player GVTs on a team equals that team’s GVT plus the replacement level. This is essential, as player statistics often come with caveats. “Kovalchuk scored 43 goals, but he doesn’t play defense and his team isn’t good”. This makes it much easier to measure "how good would this team be replacing player A with player B?" It is also essential in that player success is correlated with team success, which after all is the entire point of the sport.
- GVT automatically normalizes for the strength of the league. When looking at player statistics from different eras or different leagues, it is often difficult to know if a player was good or not. For example, for the last few years in the Czech Extraliga, a save percentage of 0.920 has been average or below average, while in the NHL today a save percentage of 0.920 is pretty good, and in the NHL 20 years ago it was unheard of. Similarly, a 50-goal season in 1982 was less impressive than a 40-goal season today. GVT takes all of this into account, giving you a single number that doesn’t need any further interpretation.

__The Fundamental Building Blocks: Offense, Defense and Goaltending__

To calculate GVT, I have split hockey players' responsibilities up into 3 functions: offense, defense, and goaltending. In recent years, the introduction of the shootout has added a fourth category. The offensive function shows the contributions to goals scored against the opposition. This function has historically been the best measured statistically, since it consists of measuring games played, estimated ice time, goals and assists. In fact, it would be rather easy to perform a rough comparative analysis of offensive contributions back to the NHL's beginnings. I have attempted to follow conventional hockey wisdom and assigned to goals a value of 1.5 assists. Obviously, opinions vary on this point, but I have assumed that this is an uncontroversial average. The upshot of this is that both goals and assists have less value each on teams that record more assists. As an example, on a team that scores no assists, a goal would have an offensive value of 1.0, whereas on a team that records exactly 1 assist per goal, each goal would be worth 0.6 and each assist worth 0.4. Note that this is different from what some other analytical methods do, which is assign a fixed value to goals of half a team’s offense and split the rest among the assists. If a team scored 100 unassisted goals and 1 assisted one, it wouldn’t make sense to assign half the team’s offense to that lone playmaker.

The second function is defensive: I have defined the defensive responsibility as preventing shots on goal. I am aware of the fact that this measure is not perfect and that not all shots are of equivalent quality; however, unless an objective and widespread measure of shot quality becomes available, this is the best information available. I am aware of the work that has been performed in analyzing shot quality, but this information is often difficult to obtain for recent seasons and impossible for older years.

The extremes work: a perfect defensive team would allow 0 shots on goal, while a horrible team would allow as many as the opposition will take. A player’s defensive value can be measured by two statistics: the number of shots on goal that his team allows, and his plus-minus compared to his team’s even-strength goal differential. Also, as an attempt at mirroring conventional hockey wisdom, I have assumed that each defenseman has twice the defensive responsibilities that a forward has. One of the components of this extra value is that defensemen play an average of 20 minutes a game while forwards play an average of 15 minutes a game, so they have 1.33 times more ice time. I also assume that, for each minute of ice time, they have 1.5 times the defensive responsibilities of forwards, so 1.33 * 1.5 = 2. This value could also be debated indefinitely without answer, so I will leave it at that for now.

The third function is goaltending: blocking the shots that do get taken on goal. Ultimately, that is a goaltender's only responsibility. All other goaltending statistics like wins, shutouts, goals-against average, and others are just by-products of blocking shots; a goaltender never gets the choice of how many shots he faces. I have incorporated a small adjustment (which I informally call the “Brodeur factor”) that gives a goaltender a small amount of the credit for the number of shots he faces, on the logic that good puckhandling goaltenders can contribute to reducing their shots against.

The last function, the shootout, is only applicable since the 2005-2006 season. As shootout goals do count in the standings, it is important that we factor in players’ shootout contributions in the total value. Most statistical databases simply choose to ignore the shootout, and many fans are happy with this since the shootout is not “real” hockey. Anything that affects the score affects GVT. The shootout value simply compares the total number of shootout goals a player scored (or prevented, if he was a goaltender) compared to his total number of shootout shots.

In the next installment, I will cover more of the benefits and limitations of GVT, as well as begin the detailed analysis of how GVT is calculated. Stay tuned!

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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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