The topic of "luck" in hockey comes up fairly frequently when we discuss that sport, and any time it does it is subject to various forms of criticism. I've also personally used the term "natural variation" to describe this concept, while the term "probabilities" is probably the most accurate from a technical standpoint. Gabe Desjardins has used the term luck to describe what I call natural variation, as he did in this piece called What Exactly Is Luck? That piece explains natural variation or luck in a purely mathematical way, and I think it does so quite well, but it doesn't really explain how that works in terms of hockey, which is what I'm going to try to do.

People criticise luck for a number of reasons. Some people simply dislike the concept of luck and dismiss it out of hand, while others try to come up with reasoned explanations for why they believe the concept is not applicable to hockey players and teams. One of the common criticisms of the concept of luck is that hockey is a physical game, played in a physical universe, and that therefore everything that happens on the ice must have a clear physical reason. I'm going to explain why that might not necessarily be so, but more importantly, why luck both can and does exist within systems that we would typically define as deterministic (and, relatedly, what this means for hockey).

There are two ways in which I'll respond to the idea that hockey must be bound by physical determinism. The first, simpler response is that the physical universe may actually be probabilistic rather than deterministic. For example, the widely accepted explanation of quantum physics describes the behaviour of matter as probabilistic, while the genetic mutations underlying evolution are held in some theories to be probabilistic as well. Most scientists believe that at least some aspects of the universe are not deterministic.

But let's put complex scientific fields of inquiry like quantum physics and gene mutations aside for now, because there is a far simpler way of thinking about this. I find analogies to be a useful way of trying to explain controversial concepts because they can help to pull people back from their preconceptions about a topic they feel strongly about in order to try to demonstrate the logic of a proposition while avoiding areas that people respond to reflexively. So before I get to hockey, I'm going to start with Texas Hold 'Em poker.

In Texas Hold 'Em poker each player is dealt two cards which only they are able to see. A round of betting takes place, followed by three cards which all of the players share that are dealt face-up in the middle of the table, followed by another round of betting, then one more face-up card, then another round of better, followed by one last card and one final round of betting. Players can exit a hand at any time, forfeiting any money they have bet up to that point. After the final round of betting, all remaining players reveal their two cards and whoever can make the best 5-card combination using their two cards and the five cards in the middle of the table wins the money that was bet on that hand.

Now, here's the thing about Texas Hold 'Em that's interesting for our purposes – it is a game that is deterministic and probabilistic at the same time. The cards, being physical objects in the physical world, are all deterministic. There is nothing "random" about a deck of cards being shuffled; the cards end up where they do as a result of very specific physical actions, either on the part of a dealer or of a card shuffling machine. And yet, when poker players play the game, the results are still probabilistic.

Let's look at it this way – all of the cards have been dealt, and there are two players remaining, Player A and Player X. Player A knows what the quality of her hand is, she knows how many cards are left in the deck, and she knows which cards on on the table. Because of this, Player A can determine her odds of winning. Let's say she knows that, given the cards in play, there is only one card in the deck that could beat her. There are 5 face-up cards on the table, plus the two in her hand, so she knows her opponent's odds of winning are just 1 in 45, or 2.2%. There are to some degree ways that players can effectively stack their odds through betting behaviour, but to keep this simple we'll just stick to the cards and their 2.2% odds. Because of that, Player A calls the bet that Player X has made. The cards are turned over, and it turns out that Player X has that one card and wins the hand. What has happenned here?

What has happenned is that Player A has just been hit by "bad luck" or, more realistically, they've run into the wrong end of natural variation. While the order that the cards were going to come out in was pre-determined by the physical, deterministic act of shuffling, because Player A does not know what that order is, she is still playing a game of probabilities even though the actual physical result is already decided. If the same hand were to be replayed over and over again, with Player A holding the same two cards, the same 5 cards out on the table, and the rest of the deck re-shuffled, over time her winning percentage would approach the 98% that the odds predict. We can prove that this is the case by writing a computer program using a random number generator and re-running the hand over and over again. Random number generators in computers, like card shuffling, are probabilistic despite the fact that their results are determined by physical forces that are well understood. In fact, generating a deck of cards that shuffles and produces "random" results is often the task given to beginner computer science students to demonstrate how computerised randomness works.

So I have established, I think, that a physical process can be both deterministic and probabilistic at the same time within a game; but what does this mean for hockey? Well, hockey is deterministic and probabilistic in much the same way that poker is. Much like in poker, what happens on the ice in hockey is the result of discrete, well understood physical effects like friction, momentum, inertia and so on. But because players can not, ahead of time, know and understand how all of those things will play out, they are dealing with probabilities just like a poker player is.

There are all sorts of ways that can actually play out over the course of a game. Many of these occur largely in a player's brain, such as a goalie's reflexes; sometimes a goalie won't stop a virtually identical shot to one he stopped earlier in a game for reasons that, while physical, we can't actually comprehend because they take place in firing synapses which we don't know how to measure.

But there are other ways in which probabilities play out that we actually can describe. Here's an example of one such play – Wayne Gretzky is skating down the left wing with the puck on his stick. The other two forwards on his team are both skating towards the net, and each of them is guarded by one defender. Wayne doesn't have a clear shot, but he figures something good might happen if he just throws the puck into the mess of players all moving toward the front of the net, so he does. As this is happenning, one of the defenders is knocked off balance in a battle with a forward trying to get to the net. His skate moves backwards out of its previous path slightly, and the puck deflects off of it and goes under the goalie's blocker arm. The Great One has just picked up a goal; and yet, the fact that the puck went in has little to do with what Wayne did.

And this is what it means when we talk about probabilities. That exact same play is performed all the time in hockey, and yet sometimes it works and sometimes it doesn't. The reasons it works or doesn't work (bad balance, bad ice, a forward going hard to the net, etc.) are generally clear, but because Wayne himself has no control over them, whether or not he actually picks up a goal on the play is a matter of probabilities or "luck"; he's simply taking advantage of a situation with a certain rate of success, and benefitting when the odds turn in his favour. There are elements of skill involved (for example, Gretzky getting clear of the player guarding him to get the shot off in the first place, or the other forwards on his team going hard to the net) but the fact that Gretzky actually ends up with a goal is largely out of his hands.

I hope I've given a clear description here of how a physical system like hockey can still produce probabilistic or "lucky" results. If there's anything that isn't clear or if you have any corrections you'd like to make, please leave them in the comments and I'll do my best to respond to them.

[A glove tap goes out to a physicist friend of mine who read this over to make sure I hadn't butchered my explanations of quantum or classical mechanics.]