## + What's an Elo?

The Elo rating system is a method to determine the relative skill of players of a game. Originally developed to rate chess players, the method has been adapted to compare NCAA football teams, video gamers and now NHLers.

The premise of Elo is that the difference between players’ ratings defines the expectation for what will happen on the ice. Specifically, the expectation of goal differential per second of ice time, since exceeding the opponents score is the objective of the game. Ratings are adjusted shift-by-shift when outcomes deviate from expectations.

To explain how ratings are updated, take for example, a 60 second shift played between a line on team-A and a line on team-B. Based on the ratings of players going into the shift, let's assume that the A line is expected to score an average of 0.05 more goals than the B line every 60 seconds. If neither team scores, players on the B line would get a slight increase in their ratings because they beat the expectation, while players on the A line would receive a slight decrease for the same reason. Similarly, if a line scores, players on that line would increase their ratings but the increase would be larger for the B team because it is more unexpected for B to outscore A. Applying these rules over hundreds of thousands of real NHL shifts since 2002 amazingly separates the wheat from the chaff. The result is a fantastically simple and accurate measure of two-way play!

Outcome | Scale of player rating change | |

A line | B line | |

No score | -0.05 | 0.05 |

A scores | 0.95 | -0.95 |

B scores | -1.05 | 1.05 |

## + Why an Elo?

At the end of the day, outscoring your opponent is the way to win a hockey game. That is why player +/- was introduced as a statistical measure. However, +/- is heavily biased by the quality of competition/teammates and is limited to even-strength play. With the Elo rating system, these biases are calibrated implicitly, and furthermore, power-play and penalty-kill performances can be included.

Elo is a simple, elegant algorithm that is self-correcting and fast to update. It provides a powerful measure to track two-way play and can be used in parallel with other statistics to identify strengths and weaknesses in players’ games. It is particularly useful at identifying defensive stalwarts who can shut down a top line, but might not find their name on the score sheet too often. These types of players help teams win and may cost only small fractions of the salary cap.

Finally, the Elo algorithm can be applied across multiple leagues (as long as play-by-play game statistics are available) using the same metric. One day, we might be able to seamlessly track a young player’s Elo rating as they move through Midget, Junior, Minor leagues and into the NHL.

## + How do I interpret Elo?

We set the starting Elo of all players to be 1.5 and run the algorithm over every shift in every game since 2002. The rating difference between two lines measures the expected goal difference per second when they play each other. It takes a player roughly 500 minutes (about 30 games) to reach a reliable Elo rating. Active players, who played at least 500 minutes in 2014/2015 have ratings as distributed in the figure below:

Elo rating distribution of active players with more than 500 minutes in 2014/2015.

The highest current Elo rating of 1.83 belongs to Pavel Datsyuk – a player known for his exceptional two-way play. Elite players (the top 5%) have ratings above 1.65, while bad players (the bottom 5%) have ratings below 1.4. The Elo careers of the exceptional players Sidney Crosby and Pavel Datsyuk are shown below.

*AVERAGE RATINGS:*

While the median rating of active players is 1.5, the average rating of players weighted by their ice time last year was 1.534. That is because, obviously, better players tend to play more minutes. This subtle distinction however, is important to consider when analyzing trade value, or making roster decisions etc.

*EXAMPLES:*

If an elite player, rated at 1.7, played 20 minutes with other players rated 1.5, the expected goal difference would be 0.25 goals.

If an entire team of elite players rated 1.7 played a team of average players rated 1.5, for 60 minutes, the elite team would be expected to win by a margin of 4.5 goals! This scenario is analogous to team Canada playing a group-stage match in the Olympics.

A power-play line of players rated 1.5, would be expected to outscore a penalty-kill line of players rated 1.5, by 0.19 goals over two minutes. It's no co-incidence this is the historical average goal difference on power-plays - variables were calibrated to ensure it.

## + What's Corsi-Elo and how do I interpret it?

Corsi-Elo is just like Elo, except instead of relating goal differential, it relates shot differential. It is a better possession measure than relative Corsi because it removes situational biases. It also tracks form over the course of multiple seasons, rather than just collecting stats for one season at a time. As with regular Elo, all players start with a rating of 1.5 and the distribution of ratings among active players is similar to the Elo distribution (see the figure below). The highest current Corsi-Elo of 1.77 is owned by possession beast Joe Thornton! Elite players (top 5%) have Corsi-Elos above 1.6, while bad players (bottom 5%) have Corsi-Elos below 1.38.

Histogram of Corsi-Elo ratings of active players with at least 500 minutes ice time in 2014/2015.

## + What information do Elo and Corsi-Elo provide?

Plotting a player’s career Elo versus career Corsi-Elo can provide insights into their game style. Take a look at P.k. Subban’s Career below.

Elo and Corsi-Elo ratings over the career of P.k. Subban

P.k. has been an elite possession player (red line greater than 1.6) since his emergence in late 2010. Interestingly, as P.k. improved his two-way play in early 2012 (blue line rising above 1.6), it coincided with a reduction in his Corsi-Elo. One possible explanation is that P.k. became more disciplined regarding when to jump into the play from the blue line. This would have resulted in his team taking fewer shots, but also reducing high percentage breakaway scoring chances for his opposition. While scouts and coaches may have had their suspicions, the Elo plot is able to quantify the result of the tactical change.

While increases in possession generally correlate with increases in scoring, they do not necessarily correlate with increases in Elo because playing an aggressive possession game can sometimes leave a team open to high percentage breakaway chances. Elo plots can be used in situations like this in two ways:

The coach or scout suspects a player of being too defensive or too aggressive and uses the Elo analysis of their recent games to confirm this suspicion

The Elo analysis may reveal an intriguing aspect of a players game, which the coach or scout can then look out for in game situations or game-tape