GVT in hockey most closely resembles VORP in baseball. Basically, GVT measures the amount of goals above a "threshold player" (13th forward or seventh defensemen) that any player creates. However, for people who know anything about GVT, they know that they're are a lot of problems with the statistic, including the arbitrary assigning of certain percentages and not including the value of many other plays in hockey, including faceoffs and penalties drawn/taken.
To my knowledge penalties have not been incorporated into GVT.
I would like to focus on penalties taken/drawn. Anyone who watches the game knows that certain players have a knack for drawing penalties. Sometimes we see this in great players who draw penalties just because they are so much better than everyone else. We also see this in pests (think Sean Avery) who goat other players into taking stupid penalties. Regardless of who is drawing the penalty, we all know that penalties can decide the outcome of a game.
Penalties taken and Penalties drawn should be included in the GVT of a player. I apologize if I make some mistakes in the math, but I hope my over-arching point is received that penalties can be incorporated into GVT.
Calculating the value that should be assigned to a player based on his penalties drawn/taken should be relatively simple. First we should start with drawing penalties. This can be incorporated into OGVT (offensive goal value threshold).
First, we need to calculate the league wide power play percentage rate:
PPPCT = sum(PPG)/ sum(PPO)
Where PPPCT is league wide power play percentage, sum (PPG) is the sum of all the power play goals scored by each team in the NHL, and sum (PPO) is the sum of all the power play opportunities by each team in the NHL.
Because GVT compares players to a threshold value, we must establish the threshold value for drawn penalties, keeping in mind that according to the already established value set by the creator of GVT, a threshold player has 75% of the offensive contribution of an average player
TPDV= sum (PD)/ sum (mP) * PPPCT/100 * OTV
where TPDV is threshold penalties drawn value (per minute), sum(PD) is the total number of non-coincidental penalties drawn in the NHL, sum (mP) is the sum of all minutes played in the NHL, and OTV is offensive threshold value, here set to .75
we can then calculate the penalties drawn goal value:
PDGVT= PD * PPPCT/ 100 - (TPDV * mP)
where PDGVT is penalties drawn goal value threshold, mP is minutes played by that individual player, and PD is number of non-coincidental penalties drawn.
Now we can calculate the penalties drawn goal value threshold. This can be included in the defensive goal value threshold.
Again we must establish the threshold value
TPTV= sum (PT)/ sum (mP) * PPPCT/100 * DTV
where TPTV is threshold penalties taken value (per minute), sum(PD) is the total number of non-coincidental penalties taken in the NHL, sum (mP) is the sum of all minutes played in the NHL, and DTV is defensive threshold value ( I will give it a value of .75 to remain consistent with the OTV)
we can calculate the penalties taken goal value:
PTGVT= PT * PPPCT/ 100 - (TPTV * mP)
where PTGVT is penalties taken goal value threshold, mP is minutes played by that individual player, and PT is number of non-coincidental penalties taken.
Both PDGVT and PTGVT would be added onto OGVT and DGVT respectively to make a new and more accurate GVT.