# The Puck Stops Here

## Offensive Goals Versus Threshold

One goal in hockey sabermetrics is to have one number to show the value of a player above a replacement player.  The idea is that any team should be able to find players of a low enough level either by call-ups from the minors or by waivers or some other method.  The idea is to find the production level of a replacement player and then show how many more (or less) goals a player produced than that level.  The idea comes from the baseball idea of value over replacement player or VORP.

Tom Awad has done a significant amount of work to devise a system to try to approximate this.  Bear in mind that it is an approximation and cannot be used to get more than an approximate value for a player.  Tom Awad has written three articles on it here, here and here.

Tom Awad’s system is called goals versus threshold or GVT.  The best place to find results on the net is at behind the net.

Today, I want to discuss the offensive portion of the GVT method.  The first step is to find the value of an assist and the value of a goal for a given team.  Tom makes the relatively arbitrary assumption that a goal is worth 1.5 times an assist.  This is roughly the longterm average of assists per goal; however in the modern NHL there are about 1.7 assists per goal.  Thus this makes assists slightly less valuable than goals - which may be accurate - but it is an arbitrary assumption.

For each team the team goal value and team assist value are calculated using the formulas:

GvT = (Gt *1.5) / (At + Gt *1.5)
AvT = GvT/1.5

here GvT and AvT are the team values for goals and assists respectively.  Gt and At are the total numbers of goals and assists for a given team.  Assuming 1.7 assists per goal this gives values of 0.47 for GvT and 0.31 for AvT.  Notice that one goal with 1.7 assists gives one goal created in this system.

Given the uncertainty in the approximate values this system produces, I think it is probably an unnecessary step to calculate different numbers for each team.  There does not seem to be a meaningful difference from one team to another in the value of a goal or an assist.

To calculate threshold values, it is assumed that a threshold (replacement player) will be 75% the level of the average NHL player.  This value is arbitrarily chosen, but is probably a reasonable choice.  Threshold values are calculated with ice time in mind using these formulas:

TOCf = [ sum (Gf * GVf + Af * AVf) ] / [ sum (MPf) ]  * 0.75
TOCd = [ sum (Gd * GVd + Ad * AVd) ] / [ sum (MPd) ]  * 0.75

The 0.75 reflects the 75% value of the assumed threshold player.  TOCf and TOCd are the total offensive contributions for forwards and defencemen respectively.  Gf and Af are the goals and assists for forwards on a given team (Gd and Ad are the same for defensemen).  MPf and MPd are the minutes played by forwards and defencemen respectively.  GVf and AVf are the goal and assist values for forwards on a given team and GVd and AVd are the same for defencemen.

A player’s offensive goals versus threshold is then calculated by calculating the number of goals produced by a given player and subtracting the number that a threshold player would get with the same ice time.  In his OVGT offensive goals versus threshold is:

OVGT = (G * GV) + (A * AV) - (MP * TOC)

where G, A and MP are goals, assists and minutes played respectively.

The problems with this method that make it approximate are that it values all goals, assists and minutes played the same regardless of the situation where they come up in the game.  It also assumes that contributions to goals such as screening the goalie. a turnover to gain possession of the puck, bringing the puck up the ice to start the offensive chance etc. have no value unless it results in a goal or assist.  It also gives no value whatsoever to setting up a scoring chance that is not finished by a teammate or a great scoring chance which is stopped by an extraordinary save, while giving value to a routine play that becomes a goal due to a mistake by an opponent.

In the future, I will look at the other parts of the GVT method and look at the players who did well last year according to it and analyze some of the more interesting players in more detail and then try to apply this method to historical data to draw some conclusions about the history of hockey.

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## About The Puck Stops Here

The Puck Stops Here was founded during the 2004/05 lockout as a place to rant about hockey. The original site contains over 1000 posts, some of which were also published on FoxSports.com.

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