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We're bad at seeing randomness. And that has consequences.
Before I begin, an admission: I am a Boston Bruins fan. A reader may thus conclude that this post is a long exercise in sour grapes. And I would agree. My Bruins are supposed to be playing in the Stanley Cup finals now, but they are not, and this post is, to some degree, my psychological coping mechanism. But there is also a much larger point — one that applies far beyond hockey — so let’s get to it.
This post is about luck. Randomness. All the stuff of life that happens whether we mortals wish it to or not. There is far more luck at work in our lives than we typically recognize. That’s partly because we misunderstand luck. But more, it’s because we are strongly inclined to conjure cause-and-effect explanations that replace randomness with human control. We routinely do not see the role of luck, in other word, because we delude ourselves.
Which brings me to the Florida Panthers.
If you are a hockey fan, as I am, you know two things about this NHL season.
One, the Boston Bruins were a team for the ages. The Bruins won games at an unprecedented rate from opening day and set a new all-time record for most wins — 65 — in a season.
Two, you know that the Florida Panthers barely squeaked into the playoffs. And in the first round, the Panthers eliminated the Bruins by winning game seven of a seven-game series.
Since then, the Panthers went on a tear. They beat the Toronto Maple Leafs in five games. Then they swept the Carolina Hurricanes in four, and now they’re in the Stanley Cup finals. Stated that way, these series sound like blowouts. They were anything but. Florida was badly outplayed in many games that they still hung on to win. Game after game went into overtime, meaning they were tied at the end of regulation time and the team that scored the next goal won the game. In all, Florida won six overtime matches. As Carolina coach Rod Brind’Amour said after being eliminated on a fourth straight loss, all people will remember is that his team was swept in four straight games but “this could've been four games the other way.”
At the start of the playoffs, every objective measure said the Leafs were a much better team than Florida. Carolina was even stronger. And the Bruins were widely considered one of the best hockey teams to ever lace up skates.
Florida beat them all.
Here is one expert’s analysis, complete with reams of data:
Hockey just isn’t like football where you can draw up a trick play or coverage scheme, practice over the week, and roll it out on Sunday. The next games arrive rapidly and without much practice, the run of play is unpredictable, and so your best bet is to build systems that work for the talent on your roster, execute them well, and challenge your opponents to stop you.
That to me is the Florida Panthers this year in the playoffs, who have revealed themselves to a degree that feels borderline indecent. They came into the playoffs advertised as a fast forechecking team capable of creating some turnovers, and have won 11 of their last 12 games by … being a fast forechecking team capitalizing on chances off turnovers. They’ve been nothing if not true to exactly who they told us they were.
Their only secret is that it’s really hard to defend against a team whose strength is capitalizing on quick lapses. You need to play the full 60 minutes, and in the case of playoffs, often far more.
It goes on and on like this. So do other such analyses. I myself am not a deeply learned hockey analyst so I will take it as given that these sages have correctly identified real causal factors.
But notice what’s not mentioned, not even in a secondary or tertiary role.
The idea that Florida may have benefited from an unusual number of lucky bounces at crucial moments, and this was a major factor in their success, is not given serious consideration. It is not discussed at all. That is absolutely typical of sports analysis, which always puts human agency — what one side did right or the other side failed to do — front and centre.
In fact, the word “luck” only appears once:
Along the way they’ve won a ton of close games – including six in overtime - in large part because of great goaltending, but the OT winners they’ve scored haven’t relied on the prototypical playoff screens, tips or rebound luck. In fact, four of the six winners have seen the puck go below the opposing team’s goal line within seconds of it ending up in the back of their net. It’s been that same forechecking and quick strike mentality.
That reference is telling. Everyone who has ever watched a hockey game knows that with so many players and sticks and skates moving at high speed, a puck can easily take a surprising deflection and a bounce and … goal. These sorts of flukes are unmistakeable. That’s luck. No denying it. But this sort of screamingly obvious luck wasn’t the source of the Panthers’ overtime goals, the writer notes, therefore there’s no need to reflect any further on the subject.
That’s the sort of conclusion people draw when they don’t think about luck seriously. Which people seldom do.
Consider, if you will, Jake DeBrusk’s fingertips.
In game six of the Bruins-Panthers series, the Panthers’ goalie Sergei Bobrovsky was playing with increasing brilliance but the Bruins were dominating the Panthers. Shot, shot, shot. The Bruins kept firing. Finally, they scored the crucial go-ahead goal, seemingly putting themselves on a glide path to a win in this game and advancement to the second round.
But Florida challenged the play. Extreme slow-motion review showed that, well before the goal, as Bruins’ forward deBrusk got up from the ice, he moved his hand to his stick and in the course of that motion his fingertips grazed the puck. The contact was clearly unintentional but that doesn’t matter. It also made no difference to the chain of events that led to the goal, but that also doesn’t matter. The rule says a player may not “direct” the puck to a teammate with his hand, and I see not the slightest indication DeBrusk’s fingertips changed the puck’s direction or had any effect on it whatsoever, so it doesn’t look like a violation to me — but remember, I am a Boston fan so I am the last person who should be judging this. After a painfully long delay that took the steam out of the game, the officials scrapped the goal. The Bruins were visibly stunned. The momentum of the game completely shifted. Florida won.
If Jake DeBrusk had moved his hand a few millimetres to the left, his fingertips wouldn’t have grazed the puck and the Bruins likely would have won the game and the series. But he didn’t. So they did. And they didn’t. It was, in other words, pure, unadulterated luck. (Also the horrible judgement of NHL officials, I would say, but that is disputable. And sour grapes. So I’ll leave that out.)
There are more examples but I’ll spare you. I noticed them all, and can write about them at great length, because I am a Bruins fan and those incidents are burned into my memory. I could taste Stanley Cup champagne. I know how close we were. I know how easily things could have gone the other way any number of times. And — let’s be honest — the idea that luck made the difference is psychologically satisfying to me, so I’m only too happy to keep the possibility front of mind. That makes me the rare sort of observer — a highly motivated observer — not only willing but eager to consider the possibility that the outcome was in large part the product of plain old luck.
And of course my memory is horribly biased. You will notice, for example, that I have not mentioned moments when luck favoured the Bruins.
That latter point is important. I guarantee you Florida fans would respond to what I’ve written here by pointing to lucky bounces that went the other way.
That’s how it goes, they would say.
Sometimes the bounces go your way, sometimes they go against you. But overall, luck evens out. A team may score a goal it doesn’t deserve thanks to luck, or even win a period. It may, in extreme cases, win a game thanks to luck. But a whole series? Three whole series? A trip to the Stanley Cup?
Luck has nothing to do with it. It’s skill. Florida’s forechecking. Bobrovsky’s brilliance. They deserve it.
This is how hockey analysis routinely goes. Sports analysis in general. In fact, it’s how people talk about human affairs of any sort all the time.
The first thing to notice there is the false dichotomy. Luck or skill. Choose one. That’s a major mistake: Florida’s skill may be real, and an important contributing factor, but that does not preclude luck having also played a significant role. Outcomes are seldom driven exclusively by one or the other.
There’s an even more basic mistake in this reasoning: Luck does not always “even out.” We only think it does because we have little intuitive feel for randomness.
Ask people to randomly draw dots on a blank sheet of paper and they will spread the dots fairly even over the entire page, with few or no dots close to each other in clusters. That’s how we intuitively feel randomness works. And why we feel luck must “even out,” and why, if you play enough hockey — like a whole seven-game series — luck must be a wash.
This thinking is quite wrong.
In a truly random distribution of dots, it is extremely likely that clusters of dots of varying quantity will form — while an even dispersal of dots is possible but highly improbable.
This is why people find it so hard to wrap their heads around what a “once-in-a-century flood” really means. After one happens, they feel safe. It will be years — maybe decades — before there is another such flood. Luck evens out, after all. If you got very unlucky, you won’t get very unlucky again for a very long time.
But every now and then, people are shocked when a once-in-century flood is followed the next year by a once-in-a-century flood. They get angry with the scientists who provided them with calculations that must be wrong — because it’s almost impossible to intuitively grasp that randomness produces clusters and in a big, complex world it is effectively inevitable that we will occasionally encounter extreme clusters that are wildly unlikely.
You may even get a once-in-a-century flood three years in a row. Really.
So is it possible for a team to get unusually lucky and win a period of hockey it otherwise wouldn’t have? Yes.
And a game? Yes.
A series? Yes.
Multiple series and a trip to the Stanley Cup final? Absolutely.
A Panthers fan may say, fine, it’s theoretically possible. But surely it’s fantastically unlikely that the Panthers got that lucky this year. So that almost certainly did not happen — by definition. Hah! Take that!
But zeroing in this way is a classic mistake people make when they think about randomness.
Picture someone who has made sixteen stock market recommendations in a row that all paid out handsomely. How likely is it that this person simply got lucky? It is extremely unlikely. So this person must be highly skilled, you think.
But now consider a scenario in which 1,000 people all make sixteen stock market picks. How likely is it that one of those 1,000 people will get all sixteen picks right simply by dumb luck? A lot higher.
Or think about it this way: You have three ordinary dice. You roll them. How likely is it that you roll three sixes?
Unlikely in the extreme. The probability is about 0.46%.
But now imagine you and 99 other people all roll three dice. How likely is it that any one of you will roll three sixes? That is 46%.
Big difference, yes?
The Stanley Cup playoffs involve sixteen teams. They are held once a year. Over a decade, that’s 160 teams competing. Out of 160 teams, how likely is it that one will benefit from such an abundance of lucky bounces that we can fairly say luck played a major role in advancing that team to the Stanley Cup final? I would suggest that is not terribly unlikely. In fact, the probability is likely high enough that we should expect it to happen every now and then.
But here I am spitballing and saying maybe Florida is in the finals because, in part, the Panthers got lucky. People hate explanations that include the words “maybe” and “possibly.” We want statements of definite fact. “It was Florida’s forechecking. And the goalie. Period.” We want certainty.
This aversion to uncertainty is another big reason we unreasonably discount the role of luck.
Just listen to business news on any given day. You routinely hear statements like, “stocks rallied on news that…” Or, “stocks fell after companies reported slower earnings.”
What we never hear is this: “An aggregate index combining thousands of individual stocks whose prices went up or down today for a myriad of reasons we can only barely grasp — even if we did a detailed analysis of each stock, which we did not — finished down (or up) today for reasons no one fully understands.” That’s the truth most days. But a business show that said that wouldn’t be on the air long.
So we make up explanations that fit observed facts, and give a starring role to human agency, and don’t give a moment’s thought to the possibility that what we’re looking at is the product, in whole or in part, of dumb luck. Which gives us the belief that we understand what happened. Which is what we most crave.
For the record, if the Bruins win next year, luck will have had nothing to do with it. And I will immediately cancel the subscription of anyone who sends me a link to this post.
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