# The curious effect of a narrative angle

## by Tyler Dellow • January 5, 2010 • Uncategorized • 21 Comments

Eric Duhatschek explains why the NHL is just so unpredictable:

Generally, what sets the NHL apart from the far more predictable (and parity-free) NBA is the curious effect that team play and chemistry, coaching and camaraderie can have on results.

On personnel alone, Phoenix shouldn’t be this good. Colorado shouldn’t be this good. And one cannot underestimate the effect of goaltending (Ilya Bryzgalov for the Coyotes, Craig Anderson for the Avalanche) on the results thus far.

I’ll give him part marks for the analysis. The goaltending, obviously, is a significant thing. Colorado’s decision to go with a duo of Peter Budaj and Andrew Raycroft last year was a bad idea and landed them 28th in the NHL in save percentage. It also resulted in Francois Giguere getting fired, AS DECISIONS ABOUT GOALTENDING THAT ARE SO OBVIOUSLY STUPID SHOULD. The Avs are currently 10th in save percentage.

I’ve been meaning to take a look at Phoenix’s turnaround – unfortunately, this won’t be it – but Duhatschek is onto something with the goaltending. The Coyotes were more of a middling group goaltending wise last year, finishing in 17th with a .904 save percentage. This year they’re in fourth. They also weren’t a completely terrible team last year, finishing with 79 points and only 4 OT/SO wins, which placed them last in the NHL. The goal differential wasn’t so hot (205 GF and 244 GA). They’re currently on pace to score 204 and allow 183 goals. That’s still a pretty bad offensive club but it’s an excellent defensive one. I guess that, just as partisan politics stops at the water’s edge, team play, chemistry, coaching and camaraderie stop at the edge of the offensive blue line.

There’s another explanation available, which could either complement Duhatschek’s theory about team play, chemistry, coaching and camaraderie or supplant it. Duhatschek is correct that there are far more surprises in the NHL than there are in the NBA. Tom Tango has made some interesting posts on the topic at his site, the always excellent Book Blog. Two points worth driving home. First, the length of a game impacts on the degree to which randomness affects it.

Suppose, for example, that a tennis match lasted only one set. That is, a set is a match. Would Federer win 88% (or whatever it is) of his matches? No, of course not. If he’s winning 88% of his matches because he’s winning 65% (or whatever it is) of his sets, then having a one-set match means he’d only win 65% of the time. Similarly, if you had 7-game or 9-game matches (spread say over two days) then he’d win 95% or 99% of his matches. He’d look unbeatable (except for when he plays Nadal).

Basketball is like that. 48-minutes is simply way too long a game compared to the 9-innings in baseball. A 9-inning game in baseball is like say a 20-minute game in basketball. If that’s all you had with basketball, then you’d probably have a similar uncertainty as with baseball. Baseball and hockey are comparable in terms of how much randomness affects the performance of teams (and presumably players).

Tom’s point about the rules having significant implications on the variance in outcomes seems to be beyond debate to me. The more opportunities you give to the better team, the more likely skill will win out.

In the other post that I’ve linked, he did some math and concluded that, to have the same reliability in terms of knowing the strength of a given team, you’d need a 32 game schedule in the NBA, a 28 game schedule in the NFL, an 82 game schedule in the NHL and a 162 game schedule in MLB. This, I think, gives rise to an alternate theory to “team play, chemistry, coaching and camaraderie” – we (or those of us who care about basketball) know a lot more about an NBA team from the preceding season’s results than we do about an NHL team. Phoenix has played 43 games this year – that’s the equivalent of about 17 NBA games.

Say that you think Phoenix is a .450 hockey team. That’s a pretty bad team in Gary’s NHL, where basically everyone is above average. The Detroit Pistons (.476) and Indiana Pacers (.439) were both about .450 basketball teams last year. The Pistons had a number of 17 game stretches in which they went 11-6. Indiana had 12 17 game stretches in which they were 9-8, .090 better than their ultimate winning percentage.

This isn’t really proof, only some anecdotal examples of the point. Tom made the following comment in one of the threads linked to above:

The NBA further compounds its problems by having so many teams in the playoffs. I don’t follow the NBA, but I would bet 1-8 (1st place team against 8th place team), and 2-7 upsets are rather rare. In the NHL, those are not uncommon.

In order to get more drama in the NBA, you need to cut down the season to 32 games, or cut the game down to something like 12 minutes.

I’m sure that Tom’s right. I read a story many years ago about a guy with a gambling problem who was in debt to bookies. He put a pile of money on the Seattle SuperSonics who were the one seed in a series with the Denver Nuggets, the eighth seed. This series, which took place in 1994, became famous as the first time in which an eighth seed beat a one seed – it’s happened twice since then. It’s worth noting that the series was a best of five series as well, as all NBA first round series were at the time, which increases the chances of an upset – a lesser team is more likely to win if there are fewer trials. The NHL, by comparison, has seen eight number one seeds fall in the first round during that time.

If Duhatschek’s theory that “…what sets the NHL apart from the far more predictable (and parity-free) NBA is the curious effect that team play and chemistry, coaching and camaraderie can have on results” were correct, it seems to me that we shouldn’t see eighth seeds falling to one seeds with such numbing regularity in the NHL compared to the NBA (particularly when first seed NHL teams have enjoyed the advantage of seven game series for most of the period in question). This could be looked at further – I’d bet that, for example, .600 teams playing .500 teams in a seven game NBA playoff series have better records than .600 teams playing .500 teams in the NHL – but I’m inclined to think that “team play and chemistry, coaching and camaraderie” is a euphemism for variance.

It feels like you’re hinting at something here.

Considering there’s something like 100 baskets in an NBA game, versus 5-6 goals per NHL game, I can see why NBA games are inherently more predicatable at their current length: much larger sample size to work with. Even looking at scoring chances, Dennis’s tallies typically add up to what? 30-40? And he’s apparently a lot more giving than when the Oilers track their own chances. (He has their scoring rate as 1/7, while they have 1/4.)

I think fundamental differences in the two games is a better explanation than “team play” or variance.

First of all, if you are an elite player in the NBA you pretty much play the whole game. So you get a whole game’s worth of an elite player in basketball, whereas you only get half the game at most in hockey.

Secondly, elite players in the NBA can dominate a game, whereas a similar level of domination cannot be achieved in hockey. In hockey, offensive advantages in skill are mitigated significantly by sticks (which would be like giving a defender in basketball an extra 70 inch reach), the fact that you can only score from about 5 spots on the ice (which means teams have to resort to tipping in point shots), and the fact that players on skates can’t make the kind of cuts that a basketball player on a court can (which diminishes the value of skill discrepancies).

So differences in absolute skill are far more pronounced in basketball than they are in hockey, and that’s why teams with better players almost always win.

So, essentially, variance.

I guess. But variance doesn’t explain why an 8 seed is more likely to beat a 1 seed in hockey versus basketball. The difference in mean outcome does, and that difference results from differences in absolute skill advantages.

A good basketball team is better than a good hockey team relative to their peers because of fundamental differences in the sports, not variance.

true enough, but the fundamental difference in the sport is that as a result of the way the game is played, single-game variance is far smaller in the NBA. i guess we’re just saying 6 of one, a half-dozen of the other.

I think fundamental differences in the two games is a better explanation than “team play” or variance.First of all, if you are an elite player in the NBA you pretty much play the whole game. So you get a whole game’s worth of an elite player in basketball, whereas you only get half the game at most in hockey.

Secondly, elite players in the NBA can dominate a game, whereas a similar level of domination cannot be achieved in hockey. In hockey, offensive advantages in skill are mitigated significantly by sticks (which would be like giving a defender in basketball an extra 70 inch reach), the fact that you can only score from about 5 spots on the ice (which means teams have to resort to tipping in point shots), and the fact that players on skates can’t make the kind of cuts that a basketball player on a court can (which diminishes the value of skill discrepancies).

So differences in absolute skill are far more pronounced in basketball than they are in hockey, and that’s why teams with better players almost always win.—

I guess. But variance doesn’t explain why an 8 seed is more likely to beat a 1 seed in hockey versus basketball. The difference in mean outcome does, and that difference results from differences in absolute skill advantages.A good basketball team is better than a good hockey team relative to their peers because of fundamental differences in the sports, not variance.—

mclea: You are talking yourself into some crazy shit here, and making the game more complicated than it is.

Or if you prefer a counterpoint: why does football have a crazy high variance??? Plays go through the same player!!!

I think Dellow is arguing that the mean outcomes for the NBA and NHL are the same, and the observed differences are because of variances.

I don’t think that’s true. I think the mean outcomes are different, and that explains the differences, not variance. For a crude example, it’s a weighted coin flip of 70-30 in the NBA, versus 60-40 in the NHL because of fundamental differences in the two sports.

Tyler, great work as usual. This is a concept I think that helps explain why Tiger is considered to be ‘bad’ at matchplay while his tournament play is so consistent. In tournament play you get an average of 4 scores (essentially) while randomness can affect a single match with a much greater effect.

It gets even more interesting when you start talking about the number of games required by two closely skilled teams (maybe a 10% of so difference in skill) to say with statistical certainty which team is actually better. A book called ‘Drunkard’s Walk’ discusses this and off the top of my head I don’t remember the number but it’s something in the thousands of games.

This information of course makes it infinitely annoying to talk sports with people that don’t understand the concept, which is just about everybody.

Nice post, MC. Bill James wrote on the subject as well, many years ago. His conclusions are much the same as Tom’s, though his proposed changes are more practical. If my memory is working today, he suggested extending shot clock times, this to reduce the event-rate of the game and increase the influence of luck on game results.

The other, less important issue is team skill parity. Of course that’s not so easily done in a game where a single player can have such a large impact on results.

Funny you mention that Vic. I had an exchange with Cosh about this point, who pointed out that basketball introduced the shot clock precisely to increase the impact of skill in the game and I responded by suggesting that they could increase the time on the clock. I wonder if I’ve read that piece before.

Yeah, from a very uninformed point of view, it seems like there are more upsets in NCAA basketball. Of course, you don’t have seven game series, but even if you did, there would be some upsets. No?

The shorter games (40 min.) and longer shot clock (35 s.) in NCAA ball suggests that Bill James and Vic are on to something.

Moreover, the NBA has really encouraged a set of rules that allow the best offensive players to dominate, and has tried to ban solid defensive play which could help teams without a Kobe or Lebron compete. (Sort of the opposite problem the NHL had in the pre-lockout era.)

Kyle M

I think Bill James does this really well. He loves to run simulations. He would sound smarter if he called them Monte Carlo Simulations using multiplicative binomial chance models … but then he would come across as a bit of a tit. When he shuffles the cards (like when he randomly shuffles Wade Bogg’s at bats for 1978 and checks to see if he was any less streaky in the imaginary season) … that’s a hypergeometric model.

The point is that it is straightforward and his reasoning and methodology are easy to follow at one read through. And the real advantage is that when you run simulations that work in the long run … you can look at individual imaginary seasons and see how capricious the Baseball Gods can be.

The guys looking at the big picture (Birnbaum and Dolphin seem to be the heavyweights in this regard, in James’ field) assume Normal (more correctly, large n binomial) distributions for talent, and the same for luck.

The former prefers multiplicative models, or at least that’s implied with his fondness for linear regressions and pearson correlations. (Covariance and variance describe the talent distribution, which will be Normal (i.e Guassian) also, this is predetermined by their models).

The latter prefers cumulative models (And Tom does as well), but makes the precisely the same assumptions about nature in baseball.

If these assumptions are correct, then they will reach precisely the same conclusion. Hitter BABIP would probably be the best example, though plain old batting average ability would appear to be fairly close to a normal distribution also. Batting average is the easier beast to kill, what with luck being resonsible for about 50% of the variance.

Of course if Dolphin’s and Birnbaum’s work the chance variation will always be binomial, they make it so. That’s why both methods show 50% luck in BA (going by memory) over a season.

Over a small chunk of the season the results from the two methods can vary significantly, even though talent doesn’t change. That’s because luck isn’t always distributed fairly either. The gods aren’t beholding to us. I mean if you rolled a pair of dice 108 times you’d expect to get snakeyes exactly 3 times, THREE exactly 6 times, FOUR exactly 9 times, … etc. But I think we can all agree that it would be a fuck of a coincidence if you actually did.

Even Jim Albert doesn’t cross that bridge. In fairness just letting go of the notion that talent is always distributed in Guassian fashion … that makes the math ungodly, and creates a scenario where there are countless possible answers to the same question (that being, how is ability distributed).

Oddly enough, when the world is not perfectly Guassian (almost always) Dolphin’s method may yield “60% luck” and Birnbaum’s “40% luck” and a Bayesian solution (of which there are many) often lies very nearly in the middle. Not always, but often. So it’s a bit of a shortcut to a first guess at a Bayesian prior.

Back to point, building models from simple bricks, as James’ does. If you do that you really get a sense for how this shit is working, though admittedly his methods seems less impressive at first glance.

Sorry for the rambling stream of consciousness above.

I heard a more general non-math explanation for the frustration that you feel coming off of RO and quain above. On CBC Radio One the other day a guest was explaining the fundamentals of evolutionary psychology. He used the example of ancient man walking under a tree and having a coconut fall and nearly strike him.

Caveman 1 thinks that it was just shit happening. Coconuts fall from trees all the time, that’s what they’re designed to do, after all. And I walk under a lot of trees, it was bound to happen sooner or later.

Caveman 2 thinks that there is some fucker up in the tree trying to murder him with a coconut.

So, even though it is overwhelmingly likely that Caveman 1 is right, and that Caveman 2 is paranoid … every once in a while someone really is trying to murder you with a coconut. So Caveman 2 types outsurvived Caveman 1 types in the long run.

So it’s the human condition to wildly underestimate the number of coconuts falling at random in the forest, and to wildly overestimate the number of cocunut murderers lurking in the treetops. And let’s face it, the latter makes for the better narrative. Which documentary would you rather see, “The Biology of Coconut Trees” or “The Search for the Legendary Coconut Murderering Tribe of Borneo”?

kris

I think that the NHL has done a terrific job of aking the results random. Over any one game it’s huge, even over a season. Standing points gained over and randomly selected 41 games is a truly poor predictor of points in the other 41 games in the same season.

The OT and shootout are terrific for this, especially with the third point in play. The increase in penalties, esp 5v3s are levellers as well. The automatic penalty for the puck over the glass … damn, that’s some inspired random shit right there.

I’m not so sure it was necessary. There is a lot of parity since the lockout. Hell, even the thought of a new CBA created more parity for a coulpe of years prior to the lockout.

Vic: If you found that interesting on CBC, you should pick up Dan Gardner’s book “Risk”. Fantastic stuff.

MC:

The link to the James article on the NBA

http://www.boston.com/news/globe/magazine/articles/2007/10/07/where_numbers_go_next/

It is only a couple of years old. The vast majority of James’ work that I have read has occurred in the last eight months or so. I often fail to remember the publishing dates.

His other principle recommendations are shortening the games and moving in the three point line.

Kris: The NCAA is a much different animal with how much bigger it is, but I don’t think upsets happen at a higher rate, even with the shorter games and shot clocks. The best teams have much higher winning percentages, even when you remove all the games played against bottom feeders.

To test out my hunch, I did a quick perusal of the 24 first round series in the NBA over the last 3 years. The higher seeded team won 19 of the 24 matchups in reality. However if you just look at who won the first game of the series as if it were a knockout tourney like the NCAA, the higher seed only wins 13 of the 24 times. That would be a much higher upset rate than you would see in the NCAA tournament in either the first or second round.

There’s a nice way to answer this question – look at playoff games (or all games); assume the line accurately reflects the odds (obviously it may not); and look at the outcomes of games that are tied starting from a given point. You’ll be able to see the percentage of upsets for what are essentially different lengths of games.

We’d have to assume that a tied game has no memory; basketball analysis suggests there is a small memory component.

Well, that was a dead end, playoffs-wise (since the lockout). The favorite’s expectation of winning in regulation is virtually unchanged with time. This is true for all favorites and for favorites over 150.

I’ll have to run it for the entire season and see if it looks any different.

Variance in results in any sport, or “unpredictability, comes about from two things: differences in skill per scoring play, and number of effective scoring plays. In basketball, the best teams can typically outscore their opponents by 10% or so, but since there are about 50 scoring plays per team per game, that makes them 0.800 teams. In hockey, the best teams can outscore their opponents by 30%, but each team has 3 scoring plays per game, so they’re 0.650 teams. Defining “fundamental” skill differences, irrespectively of the structure of the game, is almost impossible.

I don’t agree that the best players in basketball can dominate a game more than the best players in hockey. Kobe Bryant scores so much because he takes all the shots for his team, but his teams don’t demolish the opposition 100-20.