When we last left off, we took a look at some of the characteristics to GVT, as well as the foundational building blocks. Before we proceed further, let's take a look at three main things to keep in mind as to what GVT does and does not do:
 GVT works best for regular season statistics. During the regular season, you can assume that the average of all the opponents you face will approximate the average of the league. During the playoffs, that is far from being the case: you may play only seven games, all against the best defensive team in the league. Another problem is that, given the large number of games in the regular season, goal differential is a good proxy for overall success. In the playoffs, this is not as true: a team could muscle through three rounds and get to the finals, only to get trounced, and could finish with an even or negative goal differential, even though they managed to make it to the finals. One of the main corrections that needs to be made is compensating for the increasing strength of teams in each round, since performing at a certain level in the Stanley Cup Finals, against a team that is the best of its conference, is not the same as playing at that level in an opening round, which itself is tougher than the regular season (remember, almost half the teams don’t get into the playoffs). Still, the method does apply well to the playoffs. It is especially useful in figuring out which players were critical on a given team.
 GVT does not measure a player's talent. The statistic measures a player's contribution to his team's goal differential. A goaltender that faces zero shots will have a value of zero, regardless of whether he is Patrick Roy or Andrew Raycroft. Likewise, a player that is injured or gets little ice time will see his GVT reduced accordingly. It also does not take into account environment: a player will score more with better linemates, and I make no attempt to adjust for that. Other metrics used at Puck Prospectus, especially QUALTEAM and QUALCOMP, do a good job of that.
 GVT does not measure intangibles. Things like leadership do exist in hockey, and they do help to make your teammates better. However, there is no way to measure this through statistics, and any attempt to quantify it is futile. In effect, we are not trying to see what information is “hidden” in the statistics; we are simply trying to better characterize the information that is at hand. Once the goal differential for a single season is established, to compare players’ performances across different seasons, it is necessary to normalize their performances. In this case, I have normalized for 2 things: schedule length and the average number of goals per game. Obviously, in order to correctly compare performances, a player playing a 70game season must be given more credit per goal than one playing an 80game season. Luckily, over the last 35 years, the schedule has only varied from 74 to 84 games, with the exception of the 48game season in 199495. We have normalized to the current length, an 82game schedule. The other normalization factor is goals per game. Obviously, over the last 60 years, the level of openness of the game has varied, and players deserve credit for playing within the level of their era. A 40goal scorer is much more impressive in 2002 than it was in 1982. GVT has been normalized to 3 goals per game, close to the historical average.
THE METHOD
A player's GVT value is the sum of three things: his Offensive Goals Versus Average (OGVT), his Defensive Goals Versus Threshold (DGVT), and his Goaltending Goals Versus Threshold (GGVT). In recent years, with the introduction of the shootout in the NHL, a fourth component, Shootout Goals Versus Threshold (SGVT), has been added. Each of these factors is calculated independently. However, before calculating any GVT values, we must first estimate ice time.
Ice Time
Different players don’t spend the same amount of time on the ice, and consequently don’t get the same level of opportunity to contribute. To estimate a player’s contribution, it is important that we have a rough idea of his ice time. Sadly, the NHL only started tracking official ice time in 1999. Since GVT was meant to work well historically, I took inspiration from my colleague Iain Fyffe and estimated ice time indirectly using the raw data from the plusminus calculation. The NHL has tracked goals for and goals against while a player was on the ice since 1967, and this data can give us a good idea of the amount of time a player actually spent on the ice, even if there will be a bias (defensive players will seem to have spent less time on the ice and viceversa).
We first begin by estimating how much time each player spent on the ice in powerplay, shorthanded and evenstrength situations. We estimate that the time a player spent on the powerplay is the fraction of his team’s powerplay minutes equal to the number of powerplay goals he was on the ice for divided by his team’s total powerplay goals:
PPicetime = Pptimeteam * PGFplayer / PGFteam
We do the same for shorthanded situations and evenstrength. For evenstrength, the fraction is the average of ESGF and ESGA.
We then sum up all ice time into Offensive Ice Time and Defensive Ice Time. Offensive Ice Time is the total time spent on the ice weighted by the opportunity to score for each minute spent. PowerPlay Ice Time is more valuable offensively than evenstrength ice time but less valuable defensively, while ShortHanded Ice Time is less valuable offensively but more valuable defensively. Historically, PowerPlay Minutes have been worth about 3 minutes of evenstrength time offensively and about 0.5 minutes of evenstrength 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 minutespergame * 5 players on the ice * 40% / 6 = 20 minutes per game.
Armed with our ice time numbers, we can now start calculating GVT.
Tom Awad is an author of Hockey Prospectus.
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