It’s now been a little over a month since The Athletic Philadelphia launched, and 40-plus posts later, I’m extremely proud of the Flyers coverage that we’ve been able to provide. As I noted in my “Welcome to The Athletic” article last week, our coverage promises to be a combination of in-depth analysis of each game, instant reactions to news and detailed research articles evaluating the team and players.

In order to deliver on that coverage, we’ll be regularly dipping our toes into the pool of hockey advanced stats. For anyone who has read my work in the past, this will come as no surprise, considering my regular deep dives into grading players and attempting to pinpoint the reasons why the Flyers succeed and/or fail on a nightly basis.

But with a new platform come new readers, and it’s become clear that not everyone is familiar with the concepts that make up these stats. That’s why I’ve put together an Advanced Stat Primer of sorts. The goal of this article is not only to clearly articulate the definitions of the stats that I tend to use most often, but also to explain the background of the metrics themselves.

Think of this as Hockey Stats 101 class. It won’t be exploring especially complex concepts — if you’re here to learn the difference between Rel and RelTM metrics, wait until next time — but hopefully it will provide enough of a foundation so that all of our readers with an interest in following along with future articles and conversations in the comment section can do so more easily than before. And as always, if you still have questions, I’ll be happy to answer them in the comment section of this post.

General Concepts

Corsi

Corsi is the foundational concept behind hockey advanced stats. It may be an odd name for a metric, but it’s actually a fairly straightforward stat to explain. Corsi — at its core — is just plus/minus for shot attempts instead of goals. Just as a player finishes with a plus/minus of +2 if he was on the ice for two goals by his team at even strength and zero by the other team, a player’s Corsi rating would be +2 if he was on the ice for 10 shot attempts by his team and 8 by the opposition.

A few things must be noted here. “Shot attempts” does not mean just shots on goal — it counts missed shots and blocked shots as well. In addition, no one uses raw plus/minus Corsi to judge players anymore, and the reasons for that will be explained later. Still, it helps to start at the conceptual level first to fully explain how the final, better versions of the metric are derived.

But why is Corsi such a key element of advanced stats? It’s because the goal of using stats in hockey is to better predict what will happen next, specifically which teams are likely to outscore their opponents and win more games in the future. The key finding with regards to Corsi was that shot attempt differential — both on the team and player level — does a better job of predicting future goal differential than past goal differential.

Let’s break this down. Assume that after twenty games, a team is +50 in shot attempt differential at even strength, but has been outscored by ten goals during that stretch. They’re losing the goal battle, so their record is unimpressive and pundits are already beginning to write them off. But research has shown that they’re more likely to have a positive goal differential in the next 60 games due to their ability to “drive play” rather than repeat awful goal-based results simply because they struggled in that area over a 20-game stretch.

This is why a player with a great traditional plus/minus but an awful Corsi is generally expected to “regress” in the future. A player (or team) can only survive being buried in shot differential for so long before the goal battle starts being lost.

Fenwick

Another strange name for a metric, but also fairly straightforward when you break it down. Fenwick is nearly identical in definition to Corsi, with one exception — blocked shots are not part of the equation. Only shots on goal and missed shots count when it comes to Fenwick.

Generally speaking, Corsi is more predictive of future goal differential than Fenwick, which raises the question of why the latter is still in use. There’s a few reasons for that. To start, it’s a good metric to have in the arsenal when evaluating players and teams who tend to block lots of shots as part of an intentional strategy. If a defenseman finishes a season with 200 blocks and grades out poorly in Corsi, it might be worth taking a glance at his Fenwick to see if the poor differential is solely due to blocked shots, which by nature are less dangerous than misses and shots on net.

The more important reason, however, is that Fenwick forms the basis for the most widely-used Expected Goals models. Blocked shots are not included in that stat, making xG essentially “Weighted Fenwick” by definition.

Expected Goals

There’s a common critique of the concept of Corsi, and if you’re a newbie to advanced stats, it may have already crossed your mind while reading the above explanations. “Obviously outshooting your opponent is important, but what if you get outshot but the shots you do create are really good? It might be a good Corsi period if a team racks up 10 shot attempts and allows just five, but what if all five from the opposition were breakaways and all ten from the team in question were weak wrist shots from the point?”

These are the problems that Expected Goals addresses.

The models behind xG (shorthand for Expected Goals) weigh each unblocked shot for a number of factors. Shot location is the main one, but the models also recognize events like rebounds and rush chances as well. It then assigns a value to each shot, based on the likelihood of the shot resulting in a goal. A point shot may have an xG value of 0.02, while a rebound chance directly in front of the goalie might be worth 0.40. By accounting for quality, xG responds to the criticism of Corsi that “not all shots are equal.”

It’s important to note that there remains debate whether xG is actually “better” than Corsi when it comes to evaluating teams and players. The most-widely used version of the stat was developed by Emmanuel Perry for his Corsica.Hockey public website, but he has acknowledged that his version is not more predictive of future goal differential than Corsi has proven to be. A competing xG model, developed by DTMAboutHeart, does claim superiority to Corsi as a predictive tool, but it remains a proprietary metric and cannot be tested by a third party to the same degree as Corsica’s version. It is also less widely available on a game-by-game basis.

Personally, I use the two metrics — Corsi and xG — in tandem, knowing that the former describes a raw territorial advantage, while the latter describes whether the shot quality battle was won as well.

Turning the concepts into useful stats

_____ For Percentage

Fill in the above blank with Corsi, Fenwick, xG, even Goals and the concept remains the same. I noted earlier that no one uses raw plus/minus counts when presenting advanced stats anymore (when was the last time you read a stat article saying that Claude Giroux was a +4 Corsi on the night?). That’s because the hockey community has shifted to presenting advanced metrics in ratio form, and then turning it into an easy-to-read percentage.

Let’s assume Michael Raffl was on the ice for six Flyers shot attempts and four attempts by the hated Penguins. In terms of raw Corsi differential, that’s a +2 rating. Sean Couturier, on the other hand, got far more ice time and was out there for 20 Flyers attempts and 16 Pittsburgh ones. Couturier finished with a +4 Corsi rating, so he had the better game, right? Well, not exactly.

This is why it’s helpful to put these metrics in ratio form. Raffl was on the ice for 10 total attempts (6 by the Flyers, 4 by Pittsburgh). Therefore, 60 percent of the shot attempts were generated by his team. That’s what Corsi For Percentage is. Couturier, on the other hand, saw the Flyers generate 20 out of 36 total shots, good for a Corsi For Percentage of 55.56% (20 divided by 36).

A good rule of thumb for these metrics is that anything over 50% is solid performance, both on the team and player level. It means that the team in question outshot the opposition, which is obviously a positive outcome. Corsi For Percentage isn’t the only usage of this enhancer, of course. Fenwick For Percentage, xG For Percentage, Goals For Percentage — it’s all driven by the same concept.

_____ Relative to Teammates

Just like the first qualifier above, this applies to Corsi, Fenwick, xG and Goals in the same exact way.

Relative metrics answer a simple question — how did a player perform in comparison to his teammates? We already know that finishing with a Corsi For Percentage over 50% is generally speaking a good outcome, but what if the whole team finished above 50 percent? What if the whole team was below 50%? How do we judge who truly produced the most positive outcomes?

With relative metrics, it all comes down to how the team performs with a player on the ice versus when he sits on the bench. For example, let’s imagine a game in which the Flyers created 60 percent of the shot attempts with Claude Giroux on the ice, giving him a Corsi For Percentage (CF%) of 60 percent on the night. Seems good, right? The problem is, when he was on the bench, Philadelphia did even better, generating 66 percent of the attempts. Therefore, Giroux’s Corsi Relative to his Teammates (Corsi Rel) was negative-6.0 percent, since the team performed six percentage points better without the captain on the ice.

This context is key to truly understanding which forwards and defensemen qualify as “play-drivers.” Not only do you want your best players to be consistently finishing with Corsi For Percentages over 50%, you also want them possessing positive Corsi Rel rates as well. Patrice Bergeron is a classic example of a forward who excels in both — over the past five seasons, Bergeron owns a 59.32% Corsi For Percentage, and is +8.78% relative to his teammates, meaning that when he has been on the bench, the Bruins have managed a merely decent 50.54% Corsi For percentage. That’s the resume of a true play-driver.

“Score-Adjusted”



You may have taken note that I often qualify a player or team’s Corsi For Percentage in my articles with the caveat that it is “score-adjusted.” This is actually a relatively new development in the analytics community — Eric Tulsky (now employed by the Carolina Hurricanes) identified a way to account for the impact of the score of the game on Corsi/Fenwick results back in 2012, and Micah Blake McCurdy expanded upon Tulsky’s findings in 2014. They both concluded that such an adjustment serves to improve the existing metrics.

But what does it mean to “score-adjust” metrics like Corsi, Fenwick and Expected Goals? The answer goes back to an aspect of hockey that most fans intuitively understand — score effects. Generally speaking, teams treat games differently depending upon the score. When down by one goal, a trailing team tends to unleash the hounds, taking more risks to move the puck up ice and attempt to pepper its opponent with shots and tie things up. By the same token, when up by five goals, a team would be forgiven if it let a foot off the gas, resulting in the trailing team gaining the territorial edge on the ice even though its chances of a comeback are minimal at best.

Score-adjustment of metrics like Corsi and xG accounts for these factors, and in turn gives a more accurate measurement of how well play was actually driven. Essentially, it notes league-average shot results in each score situation, and uses that as a baseline (rather than 50 percent) to judge performance. Generally speaking, score-adjustment favors a team that leads in a contest — a club that jumped out to an early 3-0 edge and held it throughout may have finished with an raw 45% Corsi For Percentage, but after score-adjustment, that rate may jump to over 50 percent. Score adjustment also improves the predictivity of future goal differential for metrics like Corsi, confirming its importance.

“Per 60” Metrics

Time to briefly move away from “play-driving” stats like Corsi and xG, and turn to the most frequent adjustment made to basic metrics like goals and assists. Obviously, when evaluating point totals by individual players, the easiest way to do so is simply by counting them up. If an NHL forward scores 20 points in an 82-game season, he’s probably a fourth-line talent; 50 points and now we’re in second line territory; anything over 60 and it’s a player fans should be comfortable seeing on the top line.

But this simplistic way of evaluating point totals misses a key element of context — ice time. To truly measure scoring efficiency, the amount of time a player spent on the ice needs to be taken into account. Let’s assume that Taylor Leier has two points in 40 minutes of 5-on-5 ice time, while Valtteri Filppula has five points in 200 minutes. Filppula has more points, yes. But he would be averaging a point scored every 40 minutes, while Leier was on a point-every-twenty-minutes pace. Who truly was the more efficient scorer?

This is why we use “Per 60” metrics to evaluate scoring efficiency. Essentially, a player’s Points Per 60 (Points/60) rate is how many points were produced on average every sixty minutes a player was on the ice. In the above scenario, Filppula would have a 5v5 Points/60 of 1.50, while Leier would hold a 3.0 Points/60 mark, clearly ranking him superior from a scoring efficiency standpoint at 5-on-5.

Per 60 stats aren’t limited to goals and assists, of course. There’s Shots on Goal/60, Individual Expected Goals Generated/60, Penalties Drawn/60 — anything that would benefit from accounting for ice time can be turned into a “Per 60” stat and made superior to raw counts.

Even on-ice metrics like Corsi and Fenwick can benefit from being turned into Per 60 rates. For example, let’s say you’re trying to determine how well the best shot-producing power plays perform. It would be helpful to know that last season, no team averaged more Shot Attempts (Corsi) per 60 during 5-on-4 situations than the Anaheim Ducks, who posted a 110.52 rate. Armed with that knowledge, we can evaluate when the Flyers have a “good” shot generation day on the power play by using on-ice Corsi Generated (Corsi For) Per 60 at 5v4.

Over one-game sample sizes, raw point totals are still the best way to go. But when evaluating efficiency over longer periods of time, Per 60 stats reign supreme.

Performance by Situation

It doesn’t take a hockey expert to know that there are different situations in a game. Even strength, power plays, penalty kills — all come with distinct strategies and goals for teams. Yet all too often, performance across situations is smushed together when evaluating the performance of a player or even a team.

That’s a trap that the advanced stat community attempts to avoid. In order to provide proper context to performance, I’ll often distinguish between production at 5v5, 5v4, 4v5, and all other situations in my articles. Why? Some advanced metrics are only useful in evaluating play during certain situations.

Take Corsi, for example. Generally speaking, when it’s referenced as a stat, it’s only describing results at 5-on-5. There are a couple of reasons for that. To start, 5v5 is the most frequent situation in all of hockey. Last season, about 78% of the total minutes in the NHL were played at 5v5. Second, by nature, the two teams are on equal footing when they are playing five-aside hockey. Therefore, both teams (in theory) have an equal chance to “drive play” in their direction and win the shot and goals battles. This obviously isn’t the case when one team is a player up.

Also, limiting Corsi evaluation to 5-on-5 play removes the complication of power play and penalty kill roles. Not every player on a team has the benefit of skating on the top power play unit. If we looked at every player’s “all-situations” Corsi For Percentage, obviously the ones who receive power play time (and no penalty kill minutes to drag down his metrics) will look the most impressive. But it’s not an apples-to-apples comparison. That’s why 5v5 Corsi For Percentage is the most widely used, because every skater receives ice time in that situation, allowing for fair comparisons.

That’s not to say there isn’t any value in looking at “all-situations” metrics. I’ll often check overall Expected Goals totals after a game because a team should be given credit for drawing penalties or avoiding them when understanding if they “should have” won the game. But for the most part — on both the team and player level — it’s more precise to separate out performance by each individual situation.

Key Statistic Definitions for Review

5v5 Corsi For Percentage (CF%): A ratio that shows the percentage of shot attempts created by a team versus the total shot attempts in a game during 5-on-5 situations.

5v5 Score-Adjusted Corsi For Percentage: The above metric but adjusted for score effects.

5v5 Corsi Relative (Corsi Rel): The percentage point difference between a player’s CF% and the team’s CF% with that player on the bench.

5v5 Score-Adjusted Corsi Rel: The above metric but adjusted for score effects.

5v5 Expected Goals For Percentage (xG%): A ratio that shows the percentage of weighted unblocked shots created by a team versus the total weighted unblocked shots in game during 5-on-5 situations.

5v5 Points Per 60 (Points/60): The amount of points averaged by a player per sixty minutes of 5v5 ice time. This metric can also be presented for all other situations (5v4, 4v4, etc).

Individual Expected Goals Created (ixG): The amount of Expected Goals generated by an individual player. This metric can be filtered by situation and can also be presented in “Per 60” form.

5v4 Corsi For Per 60 (CF60): The amount of shots generated by a team during 5-on-4 situations per 60 minutes of play. A good way to evaluate the shot creation efficiency of a power play. This can be presented as a team-metric, or for individual players (how many shots did the team average when an individual was on the ice).

4v5 Corsi Against Per 60 (CA60): The amount of shots allowed by a team during 4-on-5 situations per 60 minutes of play. A good way to evaluate the shot-prevention efficiency of a penalty kill. This can be presented as a team-metric, or for individual players (how many shots did the team allow when an individual was on the ice).