Introduction to Hockey Analytics Part 6.1: Luck and Random Variance: An Introduction.

Luck is a very odd concept to talk about in professional (and amateur) sports. The players in the NHL all got the opportunity to play NHL hockey mainly because they are quite simply the most skilled hockey players on Earth. They're the cream of the crop - if one of them showed up for a recreational hockey game, they'd beat the living daylights out of you (hopefully not literally). We don't speak of these players making it, of their results in the league, as the result of luck. We talk of it as being because of skill.

And yet, in every professional sports league (and amateur sports too, don't get me wrong), "luck" plays a huge part in how the games play out and how each player looks and plays in the game.

What do I mean by Luck? And why do I occasionally also use the term "Random Variance?" (See the title of this post) To answer these questions, I first need to explain that there are really two types of luck/random-variance in sports:


The first type of "luck" is really caused by the limitations of human ability: If you took a professional basketball player and had him attempt 100 free throws, he almost certainly would miss at least a few. If you took a baseball player and threw him 100 80 MPH fastballs down the middle, he'd undoubtedly miss a few. If you took a hockey player and him shoot a slap shot from the blue line at an empty net 100 times, he'd miss the net a few times.

The reason for this should be obvious: human beings are far from perfect. We can train all we want to repeat certain actions over and over again such that they become second nature, but each time we make such an action, we are inevitably going to be doing something slightly different than the time before. We're not robots of course, we're human beings.

The end result is that the best human beings can get at performing an action successfully over and over again is to do it a percentage of a time (For example: a 90% Free Throw Shooter).

This is why, for a large number of things in sports, we use statistics that are in percentages: A batter has an on base PERCENTAGE of .400 (40%), a bball player has a 3-point shooting % of 40%, a hockey player has a shooting percentage of 10%. We can't really figure out whether a given action by a human player will succeed just from the player's own talent, but we can figure out the percentage of time that player will succeed.

Yet these percentages leave open the possibility that a player will fail to perform these actions successfully -- even high percentages do this! And these failures aren't caused by a player's lack of skill, but the simple inability of the human body to repeat an action perfectly every single time.

So if a player's first four attempts at hitting the net in a game are failures, it might not mean the player is a bad shooter. It may simply mean that he has, in a sense, gotten unlucky - the player will normally get let's say 83.33% (5/6) of these shots on net, but in these few attempts, the 16.67% (1/6) chance of missing came up instead. It's the same thing as if you rolled a die 4 times and got a 6 4 straight times --> it doesn't mean that the die was bad, it just means you unluckily (or luckily depending upon the game) rolled a 6 a few times in a row.

Now I've just referred to this as luck, and it really doesn't sound like what we think of as luck. After all, the failures are - unlike the die - the result of a player's control and no one else's. So the statistical term which makes more sense here is to call this "random variance" --> Players are going to randomly fail a certain portion of the time and there's no way to prevent this from happening. The only thing players can do - and the difference between good and bad players - is try to reduce their percentages of failure and increase their percentages of success. But even then, random variance will still exist, and players will thus still have occasional cold stretches. This isn't necessarily a result of the player sucking or losing confidence or just being bad --> it's just a force of nature.


The second type of luck is different in that it's closer to what we typically think of as luck - they involve situations where the results are changed not by the player's own actions but rather by the actions/non-actions of others.

A few examples:

  • Does that baseball player's deep fly ball go out of the park for a home run or does Mike Trout rob him with an insane once in a lifetime over the fence catch?
  • Does that basketball player's risky bounce pass get intercepted by an alert opponent or does it go right to the open center for an easy Dunk?
  • Does Mark Sanchez's pass get dropped by the opposing cornerback or does the cornerback make the play for the easy typical interception?* ....*This was written after the Jets-Titans game if you couldn't tell.....but yeah...sorry fellow Jet Fans, I had to do it.
  • Does Mark Streit's slapshot hit an opposing stick and direct past the goalie or does the opponent's stick move as he takes the shot so that the puck sails wide of the net?

Each of these hypotheticals I just used shows an example of "luck" making an impact on a particular sport....the batter has no control over whether the outfielder can make the amazing play, but whether he gets a HR or an out depends not upon him, but on that fielder. The Basketball player has no control over whether he will be credited with a steal or an assist. Mark Sanchez could be credited with just an incomplete pass or he could get another pick - all based upon what the defender does. Mark Streit's shot could result in a goal or not even a SOG depending upon the stick of a guy not even on his same team (and if it does touch the stick of a guy on his own team, it's no longer counted as a goal for Streit despite Streit's own effort remaining the same).

All of these examples show an impact of what is commonly referred to as "luck" in sports - things out of a player's control that affect the player and his team's results. And in each of these examples, the common statistics don't reflect the fact that there was luck ever involved - this is best illustrated by the football example, where Sanchez's throw is treated just as another incomplete pass if the opponent drops it despite the pass being far worse than the typical incompletion.


Now that we've gone over the two types of "luck" (or "random variance") that exist in sports, we come to the question: So What? Sure, Luck exists in sports, but how does that matter to us, to the players, and to the people making personnel decisions?

Let's start with a basic answer: Luck matters because if we see that certain players are getting lucky - think Mike Comrie scoring 4 goals in two games - we might be a little more wary about getting excited about those players. After all, if a player is getting good results through good luck, it stands to reason that over a longer period of time, when the player's luck evens out, the player will not be getting as good results (and may even be a negative player).

The converse is also true - if we see a player with poor results due to notoriously bad luck, then we should be cautiously optimistic about the future of that player as his luck evens out. One such example of bad luck by the way, would be Nino Niederreiter last year, whose shooting was incredibly unlucky (We'll go over this particular example in another post on this topic).

Luck also of course applies to teams - if we see a team is getting lucky to win a few games early in the season, we expect them to fall in the standings as the season goes on (see the 2011-2012 Minnesota Wild) while if we see a team that is losing a few games mainly to bad luck, we'll expect them to go up in the standings.

So that's nice, but this raises a new question:


I've seen this question asked in a variety of forms in the comments in this site before and it's a good one. The general comment that repeatedly comes up seems to be that even if we accept the impact of luck on play, it's impossible to quantify and thus it doesn't really help us to say that luck could be making an impact.

Of course, this comment isn't true. One of the things that analysts of all sports have tried to do is develop measures to evaluate how much off a player or team's performance is due to luck, rather than skill. In Baseball this area is probably the most well explored: a statistic called Batting Average on Balls In Play (BABIP) is used to determine when pitchers or hitters are getting good/bad luck on balls put into play. If a pitcher is getting good luck - due probably to his fielders being positioned perfectly and making some amazing plays - we expect him to decline and BABIP (along with a few other statistics such as HR/FB) is used to determine when pitchers are getting such good luck.

In Hockey a variety of statistics are used by analysts to determine whether or not a player has gotten lucky. Only one or two statistics really are solely used in order to determine the luckiness of a player/team (in particular, a statistic known as "PDO"), while many other statistics - which have other uses - can be used in order to determine whether or not a player has been lucky (ex. Shooting Percentage). We'll go over these in detail in a future post in the series (Post 6.3 will start this discussion).


Now we've discussed what luck or random variance is. We've discussed that there are measures that allow us to tell when a player or team is getting lucky.

But we haven't discussed, as someone analyzing these players and teams, what you do when you find out that luck is impacting some numbers. What should we expect from these players/teams? How do we adjust?

The answer is the concept of regression, which we'll talk about next post.

The Intro to Hockey Analytics/Advanced-Hockey-Statistics Primer so far:

Part 1: - What is the field of Hockey Analytics and Why Might You be Interested?
Part 2.1: - The Importance of Context Part 1 - Time on Ice
Part 2.2: - The Importance of Context Part 2 - Evaluating the Difficulty of Certain TOI through QUALCOMP and Zone-Starts
Part 2.3: - The Importance of Context Part 3 - Evaluating (and Compensating for) the Effect of Teammates via QUALTEAM and Relative Measures
Part 2.4: - The Importance of Context Part 4: The Concept of the Replacement Level Player
Part 3 - The Perils of Sample Size
Part 4.1 - Introduction to Hockey Analytics Part 4.1: Possession Metrics (Corsi/Fenwick)
Part 4.2 - Introduction to Hockey Analytics Part 4.2 - Possession Metrics: The Various Forms of Corsi Available on Hockey Sites
Part 4.3 - Introduction to Hockey Analytics Part 4.3: Possession Metrics: Fenwick a Measure of Effective Possession
Part 4.4 -
Part 5.1 - Introduction to Hockey Analytics Part 5.1: Evaluating Neutral Zone Play: Zone Entries

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