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Luck is Random Variance

June 12, 2014, 1:00 PM ET [61 Comments]
Travis Yost
Ottawa Senators Blogger • RSSArchiveCONTACT
Luck seems to be the big topic of this year's Stanley Cup Final. Stat guys have been screaming about the topic since the dawn of the quantitative analysis invasion into sport. For whatever reason, June '14 seems to be the point where a lot of people realize that "shit happens" can explain quite a bit about the past.

A lot of bad stuff has, predictably, been written about this topic in recent days. There are a lot of media types who can't rationalize that hockey is, at it's purest form, a game of bounces. There's also an inability to comprehend the position of a lot of the numbers guys here. Most sensible types would agree that, while luck plays a fairly large role in the sport, it's not too difficult to combat long-term. It's one of the big reasons why we have an 82-game regular season to curb noise, it's one of the big reasons why the vast majority of the teams who reach the post-season are significantly better than the rest of the league, and it's one of the big reasons why teams who consistently create more opportunities to benefit from luck (and mitigate opportunities to be punished from luck) win in the playoffs.

The position of most sensible numbers guys is as follows: luck is massive on a per-game basis, luck is an apparent but not unilaterally deciding factor in determining single-game or long-term outcomes, and that luck tells us a lot about the past, but very little about the future.

Barry Petchesky at Deadspin wrote an interesting piece on this particular topic. Barry, who from my experience is an extremely sensible guy, put together a few paragraphs at the end that I found somewhat objectionable.

"Luck" is hockey's bullshit dump. It's the taxonomy of our inadequacies. Luck is really just a word for causal determinism on a level too micro for us to measure. A puck bounces a certain way or a player loses an edge in a crucial moment because of high-level collision physics, not because of true randomness. But we can't see it, we can't count it, we can't even philosophically come to terms with the fact that something so weird and unexpected as a puck coming to rest in "a little miniature snow fort" is simple cause and effect, and quite literally had to happen.

So, luck. The necessary waste product of quantifying the sport, the statistical remainder once you've balanced everything else. In its own way, luck has become just as much a narrative crutch as its largely discarded predecessors like momentum, intangibles, and the hockey gods. It's a stronger narrative tool, because it implicitly acknowledges our current limits of understanding, but it's overused nonetheless and doesn't actually explain anything.


Barry isn't arguing on the grounds that luck doesn't exist in the sport, but rather that we are taking a lot of what we see and can't understand and placing it into the luck box. Which, to some degree, is defensible. For one example, I think that team shot quality -- while heavily, massively overstated by most media types -- does exist. Even if it's to a small degree, and even if it's only exclusive to a few teams on both ends of the spectrum, it's still there. Betting on PDO to regress is always the right play, but it's not entirely unreasonable to expect a team like Boston to mildly inflate their even-strength save percentages through something in the systems where data isn't being mined.

The problem with Barry's argument is that he's sort of misrepresenting how, I would argue, the vast majority of stat guys position themselves on this topic. If you're paying attention to the numbers, you can see collapses like Minnesota or Toronto in the past coming from miles away -- their territorial play, far more important than an extremely unlikely finding of the magical shot quality formula, was an abomination. What Minnesota and Toronto were doing can simply be described as riding random chance: their shots were going in, the opposition's weren't, and the opposition was consistently creating opportunities where random chance should have been more favorable to them (i.e., winning territorial play decisively).

When stat guys say a team was lucky in winning Past Game X or Past Series Y, they're really saying that had the game (or series) been played a thousand times over, the outcomes would be much more favorable to the opposition. Take, for one example, this legendary game between Edmonton and San Jose. Ben Scrivens, quite literally against all odds, earned the Oilers the victory a night despite the team posting a -53 Corsi. The San Jose shots found him. Over 1,000 games of simulations, such a decisive territorial advantage would lead to more goals for, and consequently, more wins.

This brings us full circle: stat guys will say that Edmonton was lucky that night, because future outcomes will likely not jive with the specific past outcome here.

There's one other thing that I think is really at the heart of hockey fan base's acceptance of luck and its role in the game. Luck, as a word, is off-putting. Barry's probably the perfect example for how I'm sure many react when they see it. Luck, colloquially anyway, is off-putting. It tries to strip the win from the column of the victors. And, in sport, what we care about are wins and losses.

If I referred to 'luck' as 'random chance' or 'random variance' -- which is something I have tried to do in most of my writing -- would it appear more appropriate? Probably. And yet, for as long as I've been writing about the sport, I've used luck and random chance or random variance interchangeably. I think most have. It's entirely semantical, and yet I think attempts at delineating between them has caused a lot of confusion and, in some cases, resistance.

I don't object to Barry's point that things are probably being dumped into random variance that, ten years from now and with the assistance of something like SportVU, may not be. But, something like PDO -- which Barry referenced earlier in his piece -- is more of a great explainer of things to come than a bullshit dump that fails to regress to the league average.

Which, of course, we know from watching PDO regression play out for seven years (and counting). PDO measures what's happened in the past -- a combination of shooting percentage and save percentage that, on average, sits at 1000. Teams comfortably ahead of 1000 have managed to accomplish so by either shooting at unsustainable rates, stopping shots at unsustainable rates, or a combination of both. Teams comfortably behind 1000, the opposite.

What PDO measures is luck. Or random chance. Or random variance. And it tells us what has happened in every minute of hockey action in the past, on the percentages. Teams at the poles are obvious targets of discussion because we know that random chance has been extremely kind or extremely unkind. We don't care how or why it happened, because we want to know what's going to happen from today forward.

If a mound of snow stops a shot in yesterday's Stanley Cup game, Henrik Lundqvist gets a save. That's random chance. Extremely unfavorable random chance, +1 in the stopped shot column. In the event that another shot trickles by Henrik Lundqvist, it is unlikely that shot will again be stopped by a snow-bank.

In summary: Know that luck, or whatever you want to call it, is omnipresent. Know that better teams can stick the knife in luck more often than not, and that's why they win. And know that if you're going to call your 44% possession team that's winning a ton of games anything other than lucky, you're going to have to fight on a better turf than what's been tried in the past.

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