This is where the School of Stats gets interesting. The best website that I have found for quantitative analysis in hockey is Puck Prospectus.
Puck Prospectus is more or less a spin-off of the very popular Baseball Prospectus. The contributors to Puck Prospectus are very bright and are constantly developing new ways to quantify the on-ice contributions of players. Tom Awad has developed the “Goals Versus Threshold” (GVT) stat as a way to factor every aspect of on-ice performance into one, easy stat which includes; offense, defense, goaltending and shootout performance.
Compiling all of those factors into one stat makes it possible to compare the respective values of players at different positions. Wouldn’t it be useful to have a single value to compare a defenseman to a forward or a forward with a goaltender? That’s what GVT attempts to do.
Here’s an excerpt from the website, http://www.puckprospectus.com/article.php?articleid=233, that helps to define the parameters used to determine the GVT stat:
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.
GVT attempts to break down an individual player’s responsibilities into four separate functions and values: offensive, defensive, goaltending and shootout performance. The GVT stat blends each of those functions into one, easy to use number. Here are the specific functions and the information that goes into determining the values of each:
Offense – this may be the easiest value in the GVT stat to quantify in that it incorporates several existing stats such as games played, estimated ice time, goals and assists.
Defense – Basically this stat centers on preventing shots on goal. The fewer the shots allowed while on the ice, the higher the defensive GVT rating.
Goaltending – The key to goaltending is stopping shots on net. Thus the higher the percentage of shots on net that a player stops, the higher their goaltending GVT rating will be.
Shootout performance – This is the newest of the GVT factors since the shootout didn’t become part of the NHL until the 2005-06 season. Quite simply it is the comparison of goals scored (or allowed if a goaltender) versus the number of shootout shots for (or against).
Another critical aspect of determining GVT is to assign some values to the “type” of ice time players get. For instance, players that receive more power play ice time than their teammates will theoretically be able to contribute more to his offensive GVT score. Conversely, a player who kills penalties will have a greater likelihood of scoring higher on his defensive GVT value. That could skew the statistic unless of course those possibilities are accounted for.
What Puck Prospectus does is determine what situations a player’s ice time comes in and accounts for it in the GVT rating. As an example, here is how Puck Prospectus accounts for a players PP ice time:
PP Ice Time = PP Time Team * PGF Player / PGF Team
Short-handed ice time is figured by inserting the short-handed data in place of the PP data in the above formula. Even strength ice time is calculated by using this formula:
ES Ice Time = ES Time Team * ES Goals Player/ Es Goals Team.
Now we sum up the ice time based on Offensive and Defensive Ice Time.
Here’s an excerpt on how Puck Prospectus does this:
Offensive Ice Time is the total time spent on the ice weighted by the opportunity to score for each minute spent. Power-Play Ice Time is more valuable offensively than even-strength ice time but less valuable defensively, while Short-Handed Ice Time is less valuable offensively but more valuable defensively. Historically, Power-Play Minutes have been worth about 3 minutes of even-strength time offensively and about 0.5 minutes of even-strength time defensively.
Finally, because there is a bias in the ice time numbers, we smooth out the ice time estimates by adding a constant factor which is proportionate to the number of games played. 25% of the team’s ice time is distributed evenly according to games played by position, so if defensemen got 40% of the total ice time and a team had 6 defensemen who each played all 82 games, then the estimate of ice time for each of them is:
60 minutes-per-game * 5 players on the ice * 40% / 6 = 20 minutes per game.
*Now I do have questions about the specific, positional ice time determined in the formula above. However, I will save that argument for another post.
Obviously there are some holes in this equation; notably in its use of shots allowed as a variable. As I’ve argued in a previous post, shots on goal are not necessarily all created equally. Of course Mr. Awad takes that possibility into account when discussing the merits of the GVT stat. Here’s what he has to say about defensive GVT:
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 might argue that shots which result in “scoring chances” would be a better measure than just shots on goal but that isn’t a common NHL stat currently. As its currently defined, “scoring chances” might constitute a better alternative than shots on goal but again, I will leave that for a future post.
I leave you now to digest the complexities of the information introduced previously before I really get into the mathematics. Please don’t feel overwhelmed; I promise you that I can explain this if you give me a chance. It really is interesting stuff and has a tremendous potential to help assign values to individual players. A quick sneak peek into a future post once I satisfactorily explain GVT: GVS – Goals Versus Salary which utilizes the GVT rating in comparison to an individual player’s actual salary.