Who is the most valuable player?

When I look for the best players I ask one basic question. What percent of the team’s offence was this player on the ice for? A great player will be on the ice for almost every goal, a horrible player will be on the ice for every goal against. In reality a star forward will see around 50% of a team’s offense (240GF*(1 IGF¹/2 GF)*(3 Goals or Assists/4 IGF¹) = 90 Points. Do they contribute to that 1 goal out of four in which they don’t get a goal or an assist I would say most certainly they do, is it maybe as large a contribution as the assists? Maybe, maybe not it would depend on the player. In contrast these star players are often on the ice for very few goals against. Now to make things “fair” I’ve excluded goals against when short handed as some star players play short handed and others don’t (their percentage of goals against would be much larger if you play short handed). The difference between the two gives some sort of value of a given player. If for example a player is on the ice for 75% of the goals for and 80% of the goals against, I wouldn’t consider that player as amazing as the one on the ice for 50% of goals for and 40% of goals against. So the difference between the two values equals a sort of “star power” ranking.

Equations

The basic equation is quite simple I look at how many goals the player scored on the power play, penalty kill and at even strength and divide by how many goals the team scored in those same situations. For goals against I look at how many goals the player has against at even strength and when their on the power play and compare that to how the team did as well. This can be expressed in an equation as:

GF% = (GF.pp + GF.sh + GF.ev)/ (TGF.pp + TGF.sh + TGF.ev)
GA% = (GA.pp + GA.ev)/ (TGA.pp + TGA.ev)
GF = Goals for, TGF = Team goals for
GA = Goals against, TGA = Team goals against
pp = power play, sh = short-handed, ev = even strength.
GF.pp = Goals for on the power play
GA.pp = Goals against while on the power play
Score = GF%-GA%

Summary

TGF and TGA can either be used as the total number of goals over the course of the season or only calculated using games in which the given player has played in. For example, Forsberg has played 40 games I could use Philadelphia’s total goals for and against in the 74 games they have played or I could use just the goals for and against in those 40 games. I prefer to work on a per game basis so that’s what I’ve chosen. There is a number of ways to present this data; I could make a long list of players and their scores (which are unit less percentages), however I have decided to graph them as a scatter plot, where the individual score is on the Y-axis and ice time per game is on the X-axis. This will help analyze players who don’t play as much and make them comparable to players who player more, which makes it easier to compare defenseman to forwards. In order to present these graphs and have 300 names visible I needed a large graph (4000x3000 – 500kb), which some people may find annoying. I decided to compile two different seasons in graphs so people can see how well they correlate.

Problems

This statistic has the opposite problem to the plus minus statistic in the fact that it will make players on bad teams (teams without depth) look better then they maybe are and players on good teams (teams with depth) look average as when the player is off the ice the team is still producing goals. Therefore, this should be a good balance to a plus minus statistic. This effect does not prevent top players from getting to the top, be they on a bad team or a good team. This statistic, like almost all hockey statistics, suffers from line quality factors, which should be kept in mind. Since I’m looking at total goals for on the power play and even strength I excluded players without power play time, to be specific: power play time/even strength time > 13%. For most players this works out to about 2 minutes of power play time per game.

Results

• 2005
  
• 2006
• Time (S) should be Time (min/game)
  

Last season Joe Thornton won the Hart Trophy and rightly so, with a +25% difference between percentage of offence and percent of defense Joe Thornton ranked number one in his ice time category (Nagy was #1 over all, 1.1 points/game on a bad team). Smyth last season scored +10% and +20% this season (+25% so far in NYI). Bergeron was 5% in 2005-2006 and 2006-2007, and sitting at amazing 30% (in 13 games). So anyone dying to look at these huge tables in person, here they are:

Hart

Should Crosby get the Hart Trophy? I would argue no, there are too many good candidates above him: Pronger (90²), Visnovsky (99²), Lidstrom (102²), Thornton (#2³), Brind’Amour (#19³), Selanne (#10³). But since it normally goes to the forward with the most points (in recent years) or a goalie with an insane save percentage (1 defenseman as won it in 32 years) I would expect Crosby to get it.

1. IGF = individual goals for, IGA = individual goals against (plus or minus statistics including power play and penalty kills)
2. A comparable number of points for defenseman to compare to forwards (1.7*Points)
3. Point ranking out of all forwards.