# The Puck Stops Here

## Calculating Offensive Point Shares

by PuckStopsHere on 08/26/11 at 05:32 PM ET

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I started discussing point shares as developed by Justin Kubatko. It is time to dive in and discuss the details of this calculation. There are three parts to the point shares calculation: offensive, defensive and goaltending. Goaltenders get point shares only from the goaltending portion and position players get them from the sum of the offensive and defensive portions. I will start today by detailing the offensive portion of the system.

There are two ways to calculate the offensive portion. From the year 1998/99 onward, there are easily available ice time numbers so ice time numbers are used. Before that time, reliable ice time numbers are not easily available, so games played numbers are used as a proxy for ice time. This is an approximation. It would be ideal to have ice time numbers because we know that ice time does not scale perfectly with games played.

The first thing to do is calculate the “goals created” for the player in question. There are multiple different formulations of goals created. Here is one I once discussed. In this case, a slightly different formulation is used but it is similar in concept. The idea is to determine how many goals an individual player produced with the goals and assists of that player. It is at best an approximate calculation and it can be done using slightly differing assumptions and calculation methods. In the point shares method, the calculation is described in this glossary (GC is goals created). This calculation is goals plus half the assists and it is multiplied by their team`s goals divided by its goals plus half its assists. As a formula this is GC = (G + 0.5 A) * TG / (TG + 0.5 TA), where GC is goals created, G is an individual player`s goals, A is an individual player`s assists, TG is the team`s goals total, TA is the team`s assists total. The total goals created for all players on a team is the total number of goals the team scored in this formulation. This is a strength of this method, but the weighting of goals relative to assists is somewhat arbitrary.

We next want to calculate the marginal goals for each skater. This is essentially the number of goals they produced in excess of a theoretical replacement player. This is calculated using ice time when it is available and games played before 1998/99, when it isn`t available. When ice time is used the formula is marginal goals = GC - 7/12 * ice time * goals created by forwards/defencemen in the league / ice time by forwards/ defencemen in the league. If ice time is not available, it is replaced in this formula by games played. The factor of 7/12 comes from the consideration that each player contributes offensively and defensively. Each position player contributes both offensively and defensively, while the goaltender contributes only defensively. This makes 5/12 of a team`s effort offensive and 7/12 a defensive effort. Forwards and defencemen are treated separately here because they score at different rates. This number may be negative for a lower scoring player. That means that this player scores less frequently than a theoretical replacement player.

The main assumption here is that all position players contribute equally to offensive and defensive efforts. This is false. Some players are more involved offensively and others are more involved defensively. This system also treats all ice time (or games played) equally. If a player spends his time on the penalty kill, he is far less likely to score than a player who plays on the power play.

Next we calculate marginal goals per point. This is done by dividing the number of goals scored in the league by the number of points teams got in a season. I think this is problematic because of the NHL point system. In the NHL some games are worth three points and others are worth two points. The total point value of a game depends upon whether it is tied at the end of regulation or not. This is not particularly logical when it comes to assigning points to players. If three points are available in a game, it doesn`t mean that individual players played better than they did in a game where only two points are available. Also, the point for winning a shootout is too arbitrary and it is given for results not included in this calculation (nowhere does a shootout result get included in marginal goals yet shootout points are included in their valuation). I think it is more useful to value games as two points if they are won before a shootout, one point for both teams if they go to a shootout and zero points for teams that lose in regulation or in overtime.

The final step is to calculate a player`s marginal points. This is marginal goals divided by marginal goals per point.

I will look at offensive point share numbers for individual players both on a single season level and on a career level in the future. This will help to get a better idea which players are seen as the best offensive players in this system and see if it fits with what we believe to be reality.

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