# One-Goal Games: Puck Luck, Variance & Regression?

June 30, 2012

Hockey fans, tell me if this sounds familiar:

Your team fought until their knuckles bled. They scraped, clawed, and mauled over their opponents in the dying minutes. Deep in your heart you thought they could come back, that they were still in the game, but when the final horn went off they simply could not put that extra goal across the line. In the dying minutes of a likely disheartening loss, your team might have hit the post, been the victim of a tantalizing save, or worse, watched a goal become disallowed. And as your heart breaks, you wonder how this tilt got away.

Was it a sloppy defensive breakdown that led to an opposing goal? How about the puck that squeaked through the goalie’s legs or deflected off a defenseman near the crease?

It could be an infinite amount of sequences that took place during your latest moment of torment, until the next time it happens to your preferred group of guys.

No matter the circumstances, the verdict remains the same– your team lost. No matter how many times you try to get that vision of the opposing team in an exuberant embrace, either saluting their fans or taunting the masses, the end result is what drives us, as fans, nuts.

Down the stretch, as your team enters the final 15-20 games you wonder about those matches that got away. How would your team have fared had they come back from a 2-1 deficit and knocked a disk past a sprawling netminder? Could they have surmounted a comeback, won the game, and furthermore, grabbed some momentum during such a crucial stretch?

As much skill that is involved in every single stride in hockey, the game is still very much prone to bounces. Pucks often go off defensemen, hit weird ricochets off dump-ins, and find anomalies that your high school physics teacher likely would have trouble explaining.

* * *

In short, there’s luck in every sport, but in hockey it can mean so much more. And while we aren’t quite in the dog days of summer where the very mention of a depth defenseman signing an extension makes our ears erect like a canine who first caught a glimpse of a nearby squirrel, I though it might be fun to have a little fun with numbers now that the sample size of the regular season is completed.

Below, behold a table which breaks down the frequency of both one-goal wins and one-goal losses. In an attempt to find patterns, and essentially assess both luck and variance, this chart was compiled in what should be a somewhat interesting study.

Feel free to take a moment and toggle the various scenarios:

Team1GW1GLOTLOTWSOLSOW
Anaheim Ducks1275273
Boston Bruins8121239
Buffalo Sabres984577
Calgary Flames1557293
Carolina Hurricanes101110361
Chicago Blackhawks1164477
Columbus Blue Jackets5122254
Dallas Stars971447
Detroit Red Wings7133339
Edmonton Oilers5103275
Florida Panthers10570116
Los Angeles Kings8146396
Minnesota Wild10822911
Nashville Predators12103355
New Jersey Devils8724412
New York Islanders977347
New York Rangers952854
Ottawa Senators1456546
Phoenix Coyotes81133106
Pittsburgh Penguins693239
San Jose Sharks10135359
St. Louis Blues13713104
Tampa Bay Lightning12351033
Toronto Maple Leafs6125554
Vancouver Canucks1292778
Washington Capitals894744
Winnipeg Jets8116644

Shootout wins and losses are included to further examine how your team could have fared with an extra bounce. However, the real nuts and bolts of this exercise lies in the one-goal regulation wins and losses, written here as 1GW and 1GL.

The Calgary Flames, surprisingly, tied the Philadelphia Flyers for the lead in one-goal regulation wins which could be unexpected to some people. Last season, under head coach Brent Sutter, the Flames maintained the image of a hard-working team that was tough to beat despite their dearth of consistent scoring talent. Sutter’s squad narrowly missed the playoffs in a transition year, finishing 9th in the Western Conference with 95 points. Perhaps they were a bit lucky, but their style allowed them to stay in the game as long as possible.

What is somewhat surprising is the Flyers, and to a lesser extent the Ottawa Senators, winning so many games by such a small margin. The franchises were ranked 3rd and 4th, respectively, in scoring, but simply did not have the right combination of netminding and defense to put them over the top. Needless to say, with all parts being equal, and an upgrade at these positions, both clubs could have done more with their wealth of goal scoring.

Other clubs you would expect to see near the top, like the St. Louis Blues and Nashville Predators, each played a hard-nosed game which explains the one-goal victories. Another anomaly that is odd to say the least is the Anaheim Ducks, a team that finished near the bottom of the standings, finding themselves among the leaders. They very well could have lost a few more games.

On the flip side, we are left to look at the various teams that narrowly lost games. Two Pacific Division rivals — the Stanley Cup Champion Los Angeles Kings and suddenly mortal San Jose Sharks — found themselves quite frequently on the losing end of games. However, the Kings found a way to win those games in the postseason while the Sharks were no match for the blue-collar Hitchcockians of Missouri.

The Detroit Red Wings and Boston Bruins losing so many games by such a narrow margin explains that both clubs could have finished even higher than their April 7th standing. On the other hand, teams like the Toronto Maple Leafs, Carolina Hurricanes, and Columbus Blue Jackets were, perhaps, not as bad as their bottom-third finish.

* * *

If these teams were to play without a break, from here to eternity, the outcomes should eventually flat-line. The variation of these team’s outcomes is what statisticians, or people smarter than myself, would refer to as variance. Simply put, it’s the difference between teams finishing with 15 one-goal regulation wins, or finishing with the average (or mean) of nine.

Statisticians would have you believe that everything above the mean is luck and everything below that line is, well, poor luck. And with a sport as speedy, dynamic, and downright fickle as hockey this explanation begins to make sense. Back in March, Ellen Etchingham of Backhand Shelf wrote a beautiful piece that delves into both regression, luck, and transience between hockey players and their eventual outcomes.

If the two sentences written about variance don’t properly describe the intricate nature of advanced statistics, which they don’t, then please, please take a second to check out her piece. Or just check out her piece.

The beauty of variance is it always relates to that mean, and will always regress to it. In this case, the mean for regulation wins/losses is 9, for OT wins/losses is four, and SO wins/losses is six, or 50 percent. We know that in this exercise it does not necessarily apply, since all things are NOT equal and the regular season is broken down into 82 games, not an infinite array of contests; but, in the offseason, it will always be fun to play around with numbers in an attempt to find these correlations.

Still, an exercise of this nature has somewhat of a failure to regress to the mean. While we’ve found the mean, teams have not necessarily played enough of each scenarios to fulfill the adjustment without adding on games. Moreover, since every team plays against each other, regression essentially would mean a movement back to 50 percent, or in terms of winning percentage .500. And the nature of the sport dictates that teams are either better or worse than average.

Daniel Kahneman, a physiologist and Nobel Peace winner, describes the phenomenon of regression as strange to the human mind. Trying to quantify it with such a short sample size, and in a correlation to specific hockey scenarios may simply not apply without intricately weighing them separately, which might make my mind explode (I chose journalism over statistics for a reason).

However, the research above, does have a tiny bit of value in looking towards the future. As Kahneman explains in a very apt example, “A golfer who did well on day 1 is likely to be successful on day 2 as well, but less than on the first, because the unusual luck he probably enjoyed on day 1 is unlikely to hold.” Teams that hovered above the mean in important scenarios this season are somewhat unlikely to enjoy that same success next season simply due to the bounce of the puck.

Yet there is still hope for those who believe in the incomprehensible. Hockey is still the sport where history is made and those with superior, god-given talent have a knack for scoring the timely goal or making the spectacular sprawling save. And for that, we should all wish that the sport ran on a loop for 365 days– at least then there could possibly be regression to the mean in every possible scenario.

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