Did your NHL team over or under perform last season?
Estimated 12 minute read
During every season in every sport, teams have descriptors slapped onto them: clutch, lucky, unlucky, chokers, overachievers, underachievers, better than their record, etc.
How can we measure objectively which teams fit into these categories?
Did you win more or fewer games than your offense and defense said you should? Expected winning percentage is a metric that can be used in all team sports and is derived from the Pythagorean Expectation formula created by Sabermetric pioneer Bill James. Despite the name, the formula is not related to the Pythagorean Theorem you learned in geometry. There’s only two inputs: offensive output and defensive vulnerability. In baseball, you score (offensive output) and allow runs (defensive vulnerability). In hockey, you score and allow goals. Basically how well did you score and how well did you stop opponents from scoring.
Every sport has its own variant of the formula, which is designed to predict winning percentage. Each sports has a specific coefficient (n below) based on the nature of the game. For baseball, the original constant was 2. Now, the most accepted value is 1.83. Written most generally, the formula is:
If you put in baseball specific information, this is how the equation looks:
This gives us what percentage of games we expect each team to win. In order to estimate their wins, simply multiply the winning percentage by 162, the number of games in an MLB season.
Does any of this have value? Here I plotted 2023 MLB Expected Wins, using only each teams runs scored and runs allowed, against their actual record.
An R² of .86 indicates a strong correlation between expected and actual outcomes. I highlighted the Padres and Texas Rangers on the plot. The 2023 Padres are widely considered one of the most disappointing teams of all time, failing to make the postseason after an offseason spending spree and talent accumulation. Given their place on the plot, their actual wins came in way below their expected wins. What happened to the Padres? Over time, MLB teams tend to perform near .500 in extra innings games and one run games. One run games only give a +/- of one run (intuitive), and therefore have the smallest possible impact on your expected win percentage. Extra inning games have a wide degree of randomness, especially given rule changes on “ghost runners.” The Padres were historically dreadful in both of these type of games, going 9-23 in one run games and 2-12 in extra inning games. By the season end, the Padres had underperformed expected wins by 10 games. Going .500 in one run games (16-16) would improve their run +/- by 14, but eat 70% of the difference in their record. In the offseason, the Padres made wholesale changes, firing their manager and trading their star outfielder, Juan Soto.
Also highlighted are the Texas Rangers, who won the World Series. The Rangers were one of the best teams by run performance, and similar to the Padres, underperformed. The Rangers did make the playoffs, and, once there, made a run to the World Series championship. The Padres, it may be noted, went 20-7 after September 1st, scoring 148 runs while allowing 93.
So enough about baseball, which is a sport for nerds. Let’s copy and paste all this to the NHL and call it a day.
Not quite yet.
There are a few key similarities and differences. For one, there are fewer goals per game in hockey than runs in baseball. Generally, the lower scoring a sport is, the lower the constant n is in the base formula. In the NHL, there is not a universally accepted n, ranging from 2 to 2.7. Baseball has a lower constant n despite being higher scoring partially because in hockey, you can only score one goal at a time, and in baseball you can hit a grand slam, or other pile on runs quickly in a manner not seen in hockey.
Using the winning percentage formula for hockey:
NHL seasons are 82 games long. Multiplying by 82 yields expected wins:
For the New York Rangers the formula is:
Converting to wins:
The Rangers won 55 games, so this seems to be off a bit.
But let’s do a regression and plot of last season as a whole:
When evaluating the league as a whole, the R² here is even higher than baseball’s! The value of .93 is higher, despite not using a precise n.
Unlike the Padres and Texas Rangers, I highlight two teams under the line, or over achievers. The Rangers were thought to be over achievers from early in the season with their underlying metrics showing weakness. The Rangers, who won the Presidents Trophy, did win a playoff series - against the Washington Capitals, who were right with the Rangers in over performance, visually indicated by distance under the line.
This is great and all but we need to address something fundamental: unlike baseball, the NHL’s standings are determined by points, not just wins, which totally messes with the base of the formula. Fortunately there is a solution of sorts.
There are a few steps to calculate expected points:
Adjust the formula for wins to account for a point for OT losses.
Now we go back to bring out expected wins formula:
And losses:
We need the results from the expected wins to use an accepted way to estimate OT losses. Roughly 20% of teams’ losses are in overtime.
After that, we will estimate points by combining our results:
Let’s put in our New York Rangers values we calculated before:
The Rangers scored 114 points! Off again! But let’s check out the league!
The plot looks the same, with a slightly lower R²!
We could tinker with the formulas to try to improve the accuracy by modifying the n or change the estimate of OT losses league-wide. Both could improve the correlation. I’m not going to endlessly modify the formula. I personally like the level of correlation we got here with a simple n of 2 and OT loss percentage of 20%. The round numbers feel nice.
Across sports, there are certain metrics that regress to the mean over time. In football, fumble recovery rates and one score game records trend to 50% over time. Teams that recover a lot of fumbles, which bounce randomly, and win lots of close games one season are strong candidates for disappointing season the following year. The same is true the other way - surprise teams often have underlying strengths that regress to the mean season to season.
This is true in the NHL as well. Some metrics that regress over time are special teams performances, particularly variation from even strength to power play performance, “puck luck,” shooting percentage, “timely scoring” or scoring more goals in the 3rd period, and performances in overtime and shootouts.
Even teams with elite goalies and quarterbacks don’t routinely dominate from season to season. Recent exceptions in the NFL and NHL are Tom Brady and Andrei Vasilevskiy and Linus Ullmark. Not Drew Brees or Peyton Manning. Not Sergei Bobrovsky or Connor Hellebuyck.
Recent examples of teams with underlying weakness that asserted itself the following season are the 2020-2021 Montreal Canadiens and the 2017-2018 New Jersey Devils. While some of the variance in 2020-2021 is explained by COVID-19 modified seasons, the Canadiens went from Stanley Cup Finalists despite a negative plus minus to last place finishes in their division the past three seasons. The Devils earned 97 points and a playoff berth in 2017-2018, but sported only a +4 goal differential. The Pythagorean Expectation formula we used gave them a 5.6 point over-performance, posting a high team shooting percentage and a career year from Taylor Hall, who won the Hart Trophy while setting career highs in goals (39), assists (54), points (93), power play goals (13), power play assists (24), and shooting percentage in a full season (14%). His next several seasons were marred by injuries. Even in full seasons since, he has not matched the number from the 2017-2018 season. Less timely scoring, a decrease in team shooting efficiency, and a drop-off in special teams performance led to an underperformance of 4.21 points in 2018-2019.
Candidates for disappointing 2024-2025 seasons include the Washington Capitals, New York Rangers, and New York Islanders. Candidates for dramatic improvement include Columbus Blue Jackets, Utah Hockey Club, and Buffalo Sabres. Teams that over-performed in a previous season may think they are close to “getting over the hump” and try to bolster their roster through free agency and trades, only to be a disappointment.
The Capitals were buyers this offseason, despite sporting the biggest over-performance in 2023-2024. Even if they improve their goal differential, they were such dramatic over-performers that even a large bump could land them at .500. The Rangers largely stood pat. The buying and selling distinction is most apparent at the trade deadline, rather than the offseason. Utah is hard to pin down because of the bizzare nature of their offense, but behaved as buyers, shipping away prospects and draft picks while signing veterans.
If you’ve made it this far, congratulations. You’ll find the complete list of 2023-2024 Expected Win and Expected Point performances in the spreadsheet below on different tabs.
