Hockey Analysis Player Ratings
There are a number of general philosophies behind the development of the HockeyAnalysis player ratings. These are:
1. Not all contributions to a teams success is measures by traditional statistics such as goals, assists, shots, blocked shots, etc. A player can make a positive contribution to his team through good positional play, screening the goalie, intimidating the opponent with hard physical play, etc. that are not measured by any traditional stat. For this reason the hockey analysis ratings are not a result of tabulating individual statistics (i.e. how many goals and assists someone accumulated) but rather team statistics while the player is on the ice (i.e. how many goals or shots did his team give up while a player was on the ice).
2. It matters a lot who a player plays with and who a player plays against. There is a big difference between lining up against Marleau-Thornton-Heatley and lining up against Fredrik Sjostrom, Tim Brent and Colby Armstrong. Linemates and opposition need to be take into consideration.
3. Positive contributers make their teammates better and their opposition worse when they are on the ice where as negative contributors make their teammates worse and their opposition better when they are on the ice.
With that in mind I set out to create a number of player ratings to evaluate a players offensive and defensive contribution. To do so I started out by calculating the number of goals for and goals against per 20 minutes of 5 on 5 even strength ice time when neither goalie is pulled (i.e. normal regular strength play) while each player is on the ice. We’ll call these GF20 and GA20 respectively and these are a players non-adjusted offensive and defensive ratings.
GF20(x) = Goals for per 20 minutes of 5 on 5 even strength ice time while player x is on the ice
GA20(x) = Goals against per 20 minutes of 5 on 5 even strength ice time while player x is on the ice
Next I attempt to account for a players teammates and opponents by calculating teammate and opponent weighted averages of GF20 and GA20 weighted by the time a player is on the ice with his teammates or against his opponents.
TMGF20(x) = Weighted average of all GF20(y) when players x and y are not playing together for all teammates y weighted by the time that x and y were on the ice together.
TMGF20(x) = Weighted average of all GA20(y) when players x and y are not playing together for all teammates y weighted by the time that x and y were on the ice together.
OPPGF20(x) = Weighted average of all GF20(y) when players x and y are not playing against each other for all opponents y weighted by the time that x and y were on the ice against each other.
OPPGF20(x) = Weighted average of all GA20(y) when players x and y are not playing against each other for all opponents y weighted by the time that x and y were on the ice against each other.
From here we can calculate an expected GF20 and GA20 based on his teammates and opponents production levels.
ExpGF20(x) = [TMGF20(x) + OPPGA20(x)]/2
EXPGA20(x) = [TMGA20(x) + OPPGF20(x)] /2
From here we can calculate the following ratings:
HARO(x) = Hockey Analysis Rating-Offense for player x = GF20(x) / ExpGF20(x)
HARD(x) = Hockey Analysis Rating-Defense for player x = ExpGA20(x)/GA20(x)
HART(x) = Hockey Analysis Rating-Total for player x = [HARO(x) + HARD(x)] / 2
Essentially what HARO is a measure of whether a players team scores more or fewer goals when that player is on the ice than is expected based on the offensive ability of his line mates and the defensive ability of his opponents. A number better than 1 indicates team performed better than expected and a number less than one indicates team performed worse than expected when the player was on the ice. HARD is similar except with respect to goals against and since we divided GA20 by ExpGA20 we also get anything greater than one being better than expected and anything less than one being worse than expected.
Given a large enough sample size of ice time with and against players I believe that we should have a reliable rating system in which any HARO, HARD, or HART greater than 1 indicates the player is a better than average player and anything under 1 indicates the player is a below average player. Unfortunately a full season might not be enough, especially for secondary players or players who miss a number of games due to injury, and as a result statistical anomalies crop up. One attempt to resolve this was to take the just calculated HARO and HARD statistics and feed them back into a similar calculation as above since presumably HARO and HARD give us a better indication of once offensive and defensive ability than GF20 and GA20 which was used initially. This process can be done iteratively and it is found that after several iterations the system often (but not always) becomes stable. I have called the output of this process the following:
HARO+ = Enhanced Hockey Analysis Rating – Offense
HARD+ = Enhanced Hockey Analysis Rating –Defense
HART+ = Enhanced Hockey Analysis Rating – Total
Previously I considered HARO+, HARD+ and HART+ experimental rating statistics but I now have enough confidence that they produce reliable results that I have removed the experimental label. In fact I have chosen to remove standard HARO, HARD and HART ratings from this site altogether as I prefer the HARO+, HARD+ and HART+ statistics.
A number of other sites put a lot of stock into Corsi (shots + missed shots + shots that were blocked) and Fenwick (shots + missed shots) so I created the following statistics as well:
CorHARO+, CorHARD+, CorHART+ which are the same as the above but calculated using Corsi for/against instead of goals for/against.
FenHARO+, FenHARD+, FenHART+ which are the same as the above but calculated using Fenwick for/against instead of goals for/against.
ShotHARO+, ShotHARD+, ShotHART+ which are the same as the above but calculated using shots for/against instead of goals for/against.
The advantage that many claim about Corsi, Fenwick and Shots is that there are more significantly more events taking place which means we can get more reliable results in fewer games than it would take if we just considered goals. The downside is that not all shots (or shot attempts) are created equal and some are tougher than others. Another downside is that we cannot include goalies in our analysis and they must be evaluated separately but I do include goalies in my calculation of the goal version of HARO+, HARD+, and HART+. Furthermore, given 1 year or more of data I feel that goal based ratings produce as good or better results. Less than one full season of data and corsi or fenwick analysis might produce a better indication of a players true value but even then using less than a single season of data to draw any conclusions is sketchy. My personal preference is to use HARO+, HARD+ and HART+ from 2 or 3 years of data.