Random Thoughts – Poker and Lottery Tickets
By Kent Wilson
9 years ago
It’s been a pendulum season for the Flames. At first, the club enjoyed some of the league’s best goaltending. When that cooled off, they start winning with the league’s best even strength shooting percentage. After a couple months of exceeding everyone’s expectations, they’ve finally run head first into a five game losing streak, despite the fact the team has been playing fundamentally better hockey in December.
Which is why I feel like this is a good time to talk about luck a bit more in depth.
– The role of luck and natural variance continues to be a sticking point for those congenitally allergic to “new stats”. Which is fair, because it’s grossly counter-intuitive for most people given it’s at odds with how our brains are wired.
Here’s an analogy I hope will clarify things:
Imagine watching a game of heads up Texas Hold’em poker, that is, a game between two opponents. Your friend is one of the players and you can see the cards of both people at the table. You naturally cheer for your buddy, but you notice he practices impractical, undisciplined poker – he chases flushes and straights, he telegraphs his hands and his bluffs are obvious.
Nevertheless, your buddy starts off the night winning a lot because he’s getting the cards – pocket face cards, beneficial flops (first three cards on the table) and hand saving river cards (final card on the table). His bad bets are paying off because sometimes the cards just the right way. Anyone who has spent time at a poker table has spent time in either role – as the player who can’t lose as well as the player who suffers bad beat after bad beat for awhile.
Nevertheless, it’s obvious that your friend will eventually go bust if he continually tests fate by playing low percentage hands. You can’t dance with lady luck all night.
The competing roles of skill and luck in poker is clearer than in hockey, but this is the primary insight new analytics has brought to the game – that, over the long run, teams who have good puck possession are playing good poker; they’re consistently tilting the odds in their favour. Which doesn’t mean they won’t lose a few hands, because sometimes the other guy makes his straight on the river, even if it was a long shot.
– To further understand the role of randomness in hockey, it helps to think of every shot at the net as a lottery ticket and each ticket has a varying degree of probability of “winning” (ie; being a goal), depending on factors like position on the ice, if it was a rebound, etc. After counting scoring chances for several years, I’ve found that about 15% of them average out to goals over large enough samples. That is, even the best looks only end up in the net just three times out of every 20 shots or so.
– The issue is, sometimes those winning lottery tickets will cluster together in strange, unpredictable patterns. Some clusters might feature 20 winners in 50 tickets (40%). In other clusters, it might be 3 out of 50 (6%). This is natural when it comes to probabilistic processes and small samples – though the average probability of an event may be X, it’s possible that it will occur to much greater or lesser degrees randomly in short bursts.
– Here’s the thing about that sort of randomness – the human mind doesn’t believe it. Even when we observe processes which we know intellectually to be completely random (like flipping a coin), we will start to create explanations and narratives to explain seemingly unexplainable patterns in these processes. This is one of the reasons why gambling is so seductive and debilitating an addiction.
In fact, human brains are so bad at understanding randomness that we can’t even fake it.
Here’s a party trick. Get two friends. One will flip a coin 30 times and write down the sequence of heads and tails. The other will imagine flipping a coin 30 times and also write the sequence of results. They do this in secret, so you don’t know who has flipped the real coin and who has flipped the imaginary one. The ‘wow’ moment comes when you’re presented with the two lists of heads and tails and it’s usually instantly obvious which is which.…You can tell the difference because humans are very, very bad at faking randomness. We just can’t do it.There are different ways to tell the fake and real randomness apart, but the most obvious is to look for runs of straight heads, or straight tails. If one of the lists has a run of five heads or tails in a row, you can be pretty sure that’s the real coin. In a list of 30 coin flips you’re reasonably likely to get a run of five.…As humans, when we come across random clusters we naturally superimpose a pattern. We instinctively project an order on the chaos. It’s part of our psychological make-up.
– I go to great pains to point all of this out because I’ve heard more than once recently that the appeal to “luck” in new stats is a cheat or “fudge factor” that analytics people use to make their projections “never wrong”. This is inaccurate. The talk of luck is a recognition of the influence of randomness in the proceedings. We have begun to understand the influence of chance in the NHL (it’s much greater than what we thought previously and what is intuitive) and we have created measures that help understand the bounds of variance in the league.
– Which doesn’t mean anyone can reliably and precisely predict the future. It just means we know what is more likely over time. The work that is being done at the bleeding edge now is either discovering what skills and strategies influence puck possession and the degree to which we can truly tease apart skill from randomness.
– Let’s get back to hockey talk. As mentioned, the Flames have actually been better recently in terms of controlling play. Here’s a graph from war-on-ice charting their corsi according to a 5-game rolling average this year:
Since December 1, Calgary has been pushing the play north more reliably than earlier in the year. This is reminiscent of last season, when the Flames improved after New Years en route to a much better second half of the season.
We can likely expect further improvement, assuming the club ever gets fully healthy. Calgary’s best two-way forward was Mikael Backlund last year and the Flames puck possession looked like the Kings or Bruins when he was on the ice with Brodie and Giordano. He’s the club’s best tough match-ups forward option and his loss is a huge one for the club’s 5on5 play, so it’s encouraging to see an uptick before he even gets back on the ice.
– Related – the recent game against the Blackhawks is an exception to the Flames recent improvement. Calgary hung tough on the scoreboard, but got run over to the tune of 34.3% corsi on the night. That’s not an indictment of Flames, it’s just something that can happen when you play an elite team on home ice at the peak of their powers.
Still, clashing with the big boys can be an instructive pressure test – it can show you some of the more non-obvious leaks. It’s games like that shows Sean Monahan’s current assignment isn’t entirely fair to the kid. Going head-to-head with the likes of Jonathan Toews and Marian Hossa with Curtis Glencross and David Jones on your flanks is a tall order for anyone, nevermind a 20-year old sophomore.
Recently I’ve noticed the kid sinking under the weight of his circumstances, not in terms of quality of play, more just in the fact that he’s speeding a lot more time in the defensive end than he was previously in the year. As a result. his relative fen wick rate has fallen to from top three on the team to 12th amongst skaters with over 100 minutes of ice this year.
– While Monahan is begin buried, Johnny Gaudreau is getting slightly better circumstances and he’s taking full advantage. He’s now second on the team in relative possession and by eye is probably the club’s most persistently dangerous forward on any given night. It’s clear already Gaudreau is a special talent and it won’t be long before he’s facing the other team’s best players every shift, if only because opposition coaches will start targeting him.
– To that end, I’ve begun to wonder when and if Hartley will move Monahan onto a line with Hudler and Gaudreau. While that feels very much like putting all of the Flames eggs in a single basket, it may be the only way Monahan can reasonably be expected to survive his current match-ups given the make up of this roster. Glencross and Jones are capable enough NHLers, but they are far better suited to a third line role.
Hartley’s options will change when Backlund comes back, but for now it would be interesting to see a Sean and Johnny combo at even strength for a few games.
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