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Catch-all Statistics Part I: GVT versus Point Shares

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In past, present, and future articles, readers will note the use of catch-all statistics; statistics meant to show the total worth of a player. While some sports like baseball have a clear winner in this field (WAR statistic) others like hockey are still searching. Today we look at two possibilities, GVT and Point Shares.

USA TODAY Sports

A good chunk of the questions that come up in comments on this website in some of my past articles have been requests to explain the stats that are in use or the logic in using them. In many cases in the past, having an all-encompassing stat has proved to be very useful. When attempting to find explanations for player performance like I did in my article, Does Size Matter? or attempting to find how certain players success leads to team success like I did in my best subset analysis last week, having a stat that attempts to depict a players entire game comes in very useful. The two most commonly used catch-all statistics are GVT developed by Tom Awad and Hockey Prospectus and Point Shares developed by Justin Kubatko at Hockey Reference. Rob Vollman gives a run-down of some other published catch-all statistics here.

In this article, as a general rule, I will notate all operations (in other words, I will not place variables next to each other to imply division I will actually notate it with an asterisk), and capital letters indicate a context for a stat (T=Team, P=position, L=League).

I will first give the broad formulas and very brief explanation of terms for each statistic. If you feel confused

Point Shares

The full explanation in its original publication can be found here. It's goal is to show how many standing points a player contributes to his team. It is calculated in 3 separate portions: Offensive, Defensive, and Goalie Point Shares.

Goals Created

Before moving on here, it is important to be made aware of another stat forged at Hockey Reference calls Goals Created which has the following formula.

Goals_created

Offensive Points Shares

They use this to help create the statistic for offensive point shares whose formula is below.

Offensive_point_shares

This essentially finds the goals created by a player, subtracts the expected goals created from a player at that position who spent the same amount of time on ice. The result is the number of goals added by the player in question. That value is then converted to points by the Lpoints/Lgoals term which expresses how many standings points a goal is worth.The final result shows how many standing points a players offensive production is worth. The next statistic is defensive point shares

Defensive Point Shares

The Defensive Point Share formula is written below.

Defensive_point_shares

The DPS formula consists of 6 components. They are, in order: The proportion of team time on ice the player has, the proportion of marginal goals (goals adjusted for team scoring), positional adjustment value, marginal goals against, plus minus contributions, and the conversion to points. Marginal goals against is given by the formula 1+(7/12) * Tgames*Lgpg-Tgoalsagainst. The intended result of the numerator is goals prevented by the player in question. The denominator then converts the goals into standing points.

Total Point Shares is calculated by adding Offensive Point Shares and Defensive Point Shares together.

Goals Versus Threshold

Goals Versus Threshold also intends to judge a players total contribution to the game, but instead of judging it in standings points, it is judged in goals added. This statistic is a combination of Offensive and Defensive GVTs which we will look at, and Goalie and Shootout GVTs which you can further research at the GVTs original publication here.

Point Value

Just like we needed to learn about goals created in the Point Shares section, we need to be aware of the concept of point value when calculating GVTs. The formula is below and it attributes the value of a typical goal in a certain situation. The "x" indicates the context the statistic is being used in because we could be calculating team point value or league point value or any designation.

Point_value

Offensive GVT

The formula for Offenzive GVT is given below:

Ogvt

This essenitally takes the total value of a players points and subtracts the expected point value of a threshold player resulting in the total goals added by the player.

Defensive GVT

Dgvt

The defensive GVT formula is judged in 3 sections. They are as follows: goals prevented via shot prevention, plus/minus adjusted for team and position, and the the contribution to the goalie GVT that the player is responsible for adjusted for position. DGVT is calculated by adding the three components together. It is meant to show expected goals prevented.

As mentioned before total GVT is calculated by adding OGVT and DGVT together plus the GGVT (goalie) and SGVT (shootout) values to get an all encompassing GVT.

Comparison of GVT to Point Shares

We will compare three things between these stats: the assumptions they make, the tools they use, and the implications for the Devils.

Assumptions

There are several assumptions made in both of these statistics that make them unique. Is has to do mostly with the subjective value the stat author attributed to certain events or positions.

Point Shares

In point shares, you will see that there are a few 7s and 12s floating around. Those are explained with this excerpt from the original article cited in the Point Shares section by Kubatko:

Why 7/12? At even strengh a team has six players on the ice, five skaters and one goalie. Imagine each of these players having two chips to contribute to one of two buckets: offense and defense. Collectively the skaters will contribute five chips to the offensive bucket and five chips to the defensive bucket. However, the goalie will contribute both of his chips to the defensive bucket, giving the defensive bucket seven of the twelve chips.

This assumes that goalies contribute the same amount to the game on the whole but exclusively in the defensive end.

The other assumption is that defenders are twice as involved in defensive play as forwards. The "Padj" statistic is 10/7 for defenders and 5/7 for forwards. The logic here being that there are 5 players worth of value on the ice but defenders are twice as important. The 2 defenders contribute 20/7 combined units and the 3 forwards contribute 15/7 for a total of 35/7 (otherwize known as 5) units.

GVT

There are 3 big assumptions in this statistic. The first comes in the Point Value statistic where we assume that an assist is worth 2/3 of a goal. This is based in the idea that in a given NHL season there are roughly 1.5 assists for every goal. The second assumption is that defenders are twice as responsible for defense as forwards which translates to being 1.5 times as responsible per minute played (defenders play more). The third assumption is that skaters are approximately 25% responsible for GGVT, the goals versus threshold determined chiefly by SV%.

Since both of these statistics attempt to merely approximate player value as opposed to being the decisive unit, we can stop here. There are several other assumptions, but I consider them trivial.

What is Used

Offensive Stats

The only player-produced stats that both OGVT and OPS use are goals and assists. They then subsequently adjust based on position and time on ice and position. OPS also adjusts for Team and League output.

Defensive Stats

The only real substantive statistic in the DPS is the plus/minus. They subsequently make a lot of adjustments using time on ice, team, league, and position expectations. DGVT uses plus minus, shots against, and to some degree indicates that a player is at least partially responsible for goalie SV%.

What the Devils Look Like

This is an excel sheet depicting the GVT and Point Shares for all Devil Skaters: Devils GVT and Point Shares with Rankings

Offensive Stats

Dainus Zubrus finished 25th out of 31 eligible Devils in OGVT but 14th in OPS. I expect this to be mostly due to the facts that OPS weights value of points more towards goals and OGVT has a stronger positional adjustment, expecting more from forwards. This is realistic since the only other player who played more than 21 games who had a radically different position was Volchenkov who had no goals as a defender and he did better in GVT. Our top 5 players are in the same order in both statistics and they are 1. Jagr, 2. Elias, 3. Zidlicky, 4. Hendrique, 5. Gelinas.

Defensive Stats

There is more variation here which makes sense since the stats are compiled differently. Henrique, Zubrus, Gio, Elias, and Zajac all enjoyed appreciable increases in the team rankings when looking at GVT. However, defensemen and Steve Bernier come off better when looking at point shares. Obviously, the GVT values forwards defensive contribution more than point shares do. What's interesting is the Bernier did better in point shares despite having the worst plus/minus on the team. It's nothing to be too worried about though because he had 0.7 DPS and 0.9 DGVT. Some of it is probably just the way the stats fell. Andy Greene is the best defensive player on the team in both statistics. Volchenkov is the only other player who was in the top 5 in both. They also agree, however that our top 4 defensive players were Zajac, Henrique, Zurbrus, and Jagr but in different orders.

My Opinion

I think that Point Shares works better when comparing through the years because they convert everything based on how frequently goals were scored that year. I think GVT is more elegant in its construction particularly with regards to the defensive statistics. The DPS is one statistic with an absurd amount of adjustments. That being said, I do not thing one is significantly more accurate. The elegance of the DGVT stat is somewhat undermined by the crudely accounted for GGVT. Attributing 25% of the SV%-driven statistic to skaters may be realistic, but is almost completely arbitrary.

My apologies for the intense amount of numbers in this article. It will pave the way for many lighter articles in the future. My next article will be about the Devils Point Shares, GVTs and where they rank in the NHL. It will be more interesting and less dense.

Your Opinion

Which method of assigning value to a player do you like more? Which one would you like to see used here at ILWT? Are there situations where you think one may be more applicable than another? What amendments would you make to these statistics?

This is not a battle that has been won already. WAR has run away with the title in Baseball but hockey's defining statistic is still up for grabs. These are two popular ones, but the one with the most statistical merit is THoR by Michael Schucker which is proposed here. On the one hand, it has more predictive power than its counterparts, but on the other hand, there were some startling omissions from the top 150 THoR players. Our opinions will help push hockey analytics in a new direction. So don't be shy: Reply!

Formulas Used Referenced in this Article