On Tanking, Part I: Tanking is Bad, and Should Be Stopped

“Tanking” – or purposely losing games in order to acquire a higher draft pick – has long been a potential strategy in North American sports leagues, but I think the extent to which it’s ruining the NHL is a recent change. The difference has been the rise of people who analyze the game with statistics in mind. Thanks to those people, there is easily available statistics on whether tanking works. Here are the results. It works really well. You are more likely to be a top quartile team three years from now if you are terrible, than if you are really good. That’s not actually that straightforward – the results strongly depend on what years you start with and how you draw your window. We’ll talk about that in a subsequent post, but for now all we have to see is that tanking is at least a plausible strategy.

Whether tanking works is less important than whether it happens. Are teams doing it? In an NHL that has or had front office employees like Mike Milbury, Steve Tambellini, Randy Carlyle, Doug MacLean and Michel Therrien among others, it can be hard to differentiate tanking from just general incompetence. But looking at Buffalo’s moves at the trade deadline, for example, quickly puts to rest the notion that tanking doesn’t happen. This amusing video makes the point: it’s supposed to be hyperbole, but by now Buffalo actually has sold off all of those players. They purposely traded for an injured player this year. Of course they’re tanking. Other teams are indisputably doing so as well. And it goes beyond the general manager. Former Leafs and Capitals coach Ron Wilson recently admitted that he has previously been directed by management (he did not say where or when) to lose games. And it would be odd if general managers did their best to rearrange their team to ensure that they lost games, and then tried to get them to win games instead. When you are tanking, the management wants losses. And it gets them. Of course, some people on the team are still trying to win. But why? If it’s apparent to you that it’s better for the team if they lose, and losing is easier than winning ([citation needed]), then putting in the effort to win is a bad idea.

So teams are tanking. Do we have any objections to it other than that it’s weird that the players and management have diametrically opposing goals? We do, if we remember why the NHL exists in the first place. The problem with tanking is that hockey is supposed to be entertainment. And the product of hockey is hockey games. Therefore, the NHL should be trying to deliver entertaining hockey games. When teams that are already bad are trying to lose, then the games are not going to be entertaining. Watching the (obviously tanking) Toronto Maple Leafs face the (not really tanking, but just bad) Edmonton Oilers, James Mirtle had an existential crisis. From a good-for-the-world perspective, I hope James Mirtle goes and helps out in a soup kitchen. But from an entertaining hockey perspective, this is a huge failure. The other problem with tanking is that hockey is a violent and dangerous sport. For hockey players to put themselves and their health on the line for our entertainment and for glory is already a questionable premise. When you ask them to do it for no reason at all, in fact if the team would be better off if they didn’t play… well then asking the players to play seems like an insult. If you get injured in the Stanley Cup finals trying to bring a huge, happy celebration to your city and prove that your team is the best, that’s unfortunate. But if you get injured as a member of the Buffalo Sabres right now, what was that injury for? So that the Sabres could get a slightly worse draft pick? If the achievement actually has negative value, any price is too big a price to pay.

Finally, as Maud Flanders once said, won’t somebody think of the children? Being a sports fan is something we develop as children, and although adults make the majority of sports audiences, the importance of sports fanhood in a (reasonable) adult’s life is minor compared to that in a child or teenager’s life. I was a young teenager when the Canucks were last completely dismantled, and it was just the worst. Maybe they were trying to tank to build for the future, but I didn’t know it. All I knew was that Mike Keenan either pissed off or traded away everyone I liked, brought in players that you couldn’t get excited about because you knew he would just trade them out again in a couple months, and watching the Canucks play a game was just super depressing.

And that last part is the point. The product of the NHL is selling is entertaining hockey games, and yet tanking destroys that product. Even if, as, say, a Buffalo fan who understands tanking, I would be excited for Buffalo to lose so they have a better shot at Connor McDavid, there’s no way in hell I would actually want to watch them play. The Sabres fans who cheered when the Coyotes scored yesterday are not happy fans. They are people whose souls have been twisted by the NHL. The incentives for teams here are all wrong for what watching hockey should be.

If we have encouraged a bad outcome through misaligned incentives, it should be in our power to remedy the situation by changing the incentives. In other words, if the structure of the NHL is what encourages tanking, we can change the structure to discourage tanking. But before we do that, we need to understand the reasoning behind the current structure, because that was originally dictated by entertainment considerations, too. If some teams are always bad, and other teams always good, then the contests between these teams are not very interesting (see the Scottish Premier League). Therefore, there needs to be a mechanism that continually corrects team quality imbalance. Making it hard for good teams to stay good forever, and making it easy for bad teams to get better. Thus the original method of the draft: worst team gets first pick of player, second-worst gets second pick, and so on.

As with most things, this logic stopped working with extreme NHL expansion. Top NHL talent falls off relatively quickly in the draft (see this article), so that having a high draft position is a lot more of an advantage in a large league than a small one. A 1st overall pick is only going to be 2.5 times as likely to be a good player as a 10th overall pick, but is something more like 5 times as likely as a 30th overall. Rather than keeping the draft as a weak check on extreme lack of parity, having a large league makes the draft a very strong check to the point where it overcorrects. And thus, the graph we referred to in the first paragraph, and thus also the tank. (Among other things, this suggests that, without further changes, NHL expansion will make tanking worse, which is one more reason to avoid it).

There have been minor efforts to discourage tanking since the original institution of the draft. A lottery system, where the first overall pick isn’t guaranteed to the worst team made tanking less of a sure thing. However, the proof of the pudding is in the eating, and the proof of NHL team strategy is in the tanking. Remember that we care about entertainment. And so we should worry less about theoretical considerations than whether teams are actually tanking. Which, as mentioned, they are. And we should stop that from happening. In Part II, I will look at ways to change the draft system to discourage tanking, and what effects such changes might have.

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Carnet de chansons de tous les jours: Journée de la Francophonie

Comme le Radio Canada m’a avisé, le 20ème était la Journée Internationale de la Francophonie. Même si c’est quelques jours en retard, fêtons-la en écoutant chansons qui vient de la Francophonie. Offrez-nous des suggestions supplementaires!

Miossec – Chanson pour Nathalie
Jacques Brel – Knokke-Le-Zoute tango
Françoise Hardy – Tous les garçons et les filles
Tiken Jah Fakoly – Il faut se lever
Alain Peters – Caloubadia
Difficiles de Pétion Ville – Ce la vie
Enrico Macias – Je n’ai pas oublié
Jane Birkin – Comment te dire adieu
Coeur de Pirate – Ensemble
Richard Desjardins – Tu m’aimes-tu?
Bérurier Noir – Descendons dans la rue

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Start Your Own Terrible Business, Part II

Here are two more bad ideas in the spirit of this post. Note that I think these ones are less bad than the previous ones. At this rate, by part XLIX, we should be onto good business ideas.

Promote synergy!

Front view mirrors: this will become obsolete once the self-driving cars take over, but for now I don’t see why cars don’t come with front view mirrors. By this I mean mirrors mounted high up on the beam between the front right-side window and the back right-side window in most cars driven on the right side of the road. The point would be that if you have a car in front of you in your lane, it would not totally prevent you from seeing what was ahead of you in the lane to the right of you. So, for instance, if you wanted to get around traffic in the middle lane, but wanted to know whether there was a parked car in the right lane, rather than switching lanes back and forth, you could just look in this mirror. It would also allow you to see bicyclists in the right lane in a similar situation. And it would let you see traffic lights when your direct view is blocked by a large truck in front of you in your lane. The mirror would have to be placed in a way not to interfere with the right-side rear-view mirror. But this is easy: it just needs to be placed higher than the right-side rear-vew mirror and then there should be no problem. I think. Is there a good reason why this isn’t done? Is it just too much of a hassle for too little benefit? And if so, how come there are windshield wipers for headlights?

A bargaining alarm clock: actually, this might already exist, I haven’t checked. But if Leibniz and Newton could both be said to come up with calculus, then I say I came up with  the bargaining alarm clock. So here’s the pitch – what’s the problem with alarm clocks? They are either impossible to turn off, or, alternatively, possible to turn off. And neither is a good system. Alarm clocks which you can just turn off are not sufficiently useful. I have one of those, and when I set it, half the time I just turn it off and go back to sleep. Alarm clocks which you cannot turn off are also bad because they are cruel and hurt your quality of life, not to mention the potential poor souls who are not you, but still have to listen to your alarm clock. So the solution has to be somewhere in between. The snooze worked for some time, but we have come to know the snooze, and the snooze-able alarm clock is now just a version of the turn-off-able alarm clock. New alarm clock inventions are all about solving complicated puzzles to turn off. That seems to me misguided – either the puzzles are hard, in which case you have an unturnoffable clock, or you learn them, and then it’s turnoffable. An ideal alarm clock is bargainable – that is, it turns off if you really want it to, but doesn’t if you just slightly don’t. Thus an alarm clock that takes small amounts of your money is the solution. An additional possibility is to have the alarm clock actually bargain – say bargain snooze duration, where the relative leniency of the clock can be set in advance (but cannot be reset at the time).

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The Experimentalist’s Apprentice

William of Occam, who is not impressed by this post. Or by anything.

There is a rule in science that says you should assume the simplest explanation that fits with what you observe. This is named Occam’s Razor after the medieval monk William of Ockham, who, it is generally agreed, didn’t come up with it, and was probably talking about something different altogether. It’s central to how we know anything at all about the world, whether in science or in everyday life.

For instance, I just looked outside my window and saw the street. I assume that that’s because the street is actually there. It could be, instead, that my window was replaced with a huge realistic flat screen TV. Or maybe my visual cortex was replaced with elaborate street-rendering software. But using Occam’s Razor, I chose to go with the simplest explanation.

When we look at the track record of Occam’s Razor in science, though, it seems pretty bad. After all, everything is really complicated! If you assumed everything had the simplest possible explanation consistent with the data available at the time, you’d be proven wrong very quickly.

Say you came up with this idea for the tiniest indivisible particles that make up both protons and neutrons and you decided to call them quarks. The simplest theory you can make is that there are two kinds of quarks and you need them in different proportions for protons and neutrons. That is enough to explain why protons and neutrons weigh the same, but are otherwise quite different.

And yet here is what we currently believe about quarks: there are (at least!) six flavours of them, each of which comes in three colours, and all are available in the antimatter variety as well. And even this is not necessarily the whole story – it’s just the simplest thing consistent with what we know *now*. So why do we stick with this method in science, just to be proven wrong?

To me, one convincing explanation is that it is so commonly effective in our daily life that we are conditioned to use it. Anthropologist Mark Collard calls it the flying carpet test: you take the plane to get somewhere because you have experienced it working to get from place to place. You could choose to believe that the flying carpet is more effective, but try to act upon that belief and actually get to your destination!

Occam’s Razor, in daily life if not always in science, often means trusting your experience and your senses. And we go through with it, because though it may not be absolutely foolproof, if you *don’t* trust your experience and your senses, it’s very difficult to come up with anything on which to base your beliefs at all.

Very difficult, but not impossible. For example, you could organize all incoming information to fit with some theory you really like. People who do this are called conspiracy theorists. Their theories are often considered silly precisely because they are never the simplest, clearest available explanation. But in another way, conspiracy theorists are actually radical Occamists – the belief that everything is connected to one big explanation is a simplifying tool of its own.

The aphorist Igor Yuganov had a joke theory during Soviet times: the United States didn’t really exist, it was just invented by the KGB to root out dissidents. The KGB is a notoriously shady organization, so if you have to believe in something strange to stick with the idea that the US is a KGB plot, it might well actually be worth believing. On one hand, it’s not simple: you have to explain away lots of things, like mail from the US, the moon landing, and hamburgers. On the other hand, what could be simpler than having one explanation – the KGB – for absolutely everything. A lot of conspiracy theories work like that.

So are conspiracy theorists using Occam’s Razor, or not? Upon looking at it closely, it turns out what simple means is not a simple question at all. The thing I cannot understand is not whether to use the simplest explanation, but what the simplest explanation actually means.

Posted in Apprenticeships, science | 5 Comments

Sushi Name Game

UBC Village has (or at least had, when I went there) a restaurant called One More Sushi. Although the name is clearly English, the name could be interpreted as Japanese written in romaji as well (おねもれ). Only a very small fraction of English words do this. I wonder what’s the best sushi restaurant name that you can make using these rules: it has to make sense in English, and be writeable using standard romaji in a way that could possibly scan as Japanese. I have language-nerd sniped myself with this question for long enough, so now it’s time to ask other people. Best (realistically, any!) suggestion wins a prize! I think using words that are clear super-recent borrowings in English (e.g. opera, mandarin) is not very interesting, although when you get to esoteric names like memento mori (めめんともり), or place names like Sochi Sushi (そち), it can still be pretty cool. But the highest points are reserved for long, relatively common English words. Degenerate Sushi (でげねらて), Sushi Nineteen (にねてえん), Sushi Massage (まっさげ), etc. Although it’d be pretty easy to write a script to play this game for me, I prefer to play by hand. In addition to the word length, extra points are awarded for the pronunciation of the string being entirely different depending on the language chosen. An if the Japanese also scans as a (totally unrelated) real word, that would be ideal. Unfortunately I don’t have the Japanese knowledge for that. Other than Aware Sushi (あわれ), I suppose.

PS: Zuuko (ずうこ) Sushi totally works.

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In Praise of the Fair Weather Fan

It’s no surprise that sports is a field where we encounter moralistic scolding, because sports are a part of life, and moralistic scolds are a fact of life. Examples from the media are well-known. Tut-tutting about professionalism and respect for the game, the concept of amateurism, the Winnipeg Jets dress code. Or, you know, grandstanding about streets filling with blood. It takes all kinds. But moralistic sport-scolds are not just in the media. They’re also all around us, in the fanbases themselves (fact of life, remember?). Fanbases police what it means to be a “real fan” in a highly moralistic fashion. And so bandwagoning, (or glory hunting for the Europeans) has got a bad reputation.

There is some restraint, because bandwagoners might just be newly initiated fans that will stick with their team. And No less an authority than Bill Simmons “only watches hockey in the playoffs.” If THE Sports Guy is okay with being a bandwagon fan, that should, in theory, immediately quiet the moralizers. You’re not gonna out-sports the Sports Guy. And yet, a niggling doubt remains. We wonder whether fair weather fans are like fair weather friends. Well, we should stop doing that, because bandwagoning is not immoral, and, also, it’s actually fantastic. That’s part of the reason it’s disliked, of course. You can say it’s the Puritan heritage of hating any appearance of hedonism. Or you can say it comes from the Catholic belief in the nobility of suffering. Take your pick. In either case, the mechanism is the same, and it’s plain to see that it shouldn’t apply to sports. But though disliking bandwagoners for religious reasons is misguided in itself, it’s doubly unfortunate because bandwagoning makes the team you cheer for better, as well.

Sea! Who? Sea! Hawks!

I believe this to be true, because I have compared the real fan experience with the bandwagon experience personally. I am a “real” fan of the Vancouver Canucks, and a “bandwagon” fan of the Seattle Seahawks. Last year, I started caring about the Seahawks right about the time of their game with the 49ers, and followed that up with joining around 80 extremely drunk, high, loud and happy people (with all four qualities increasing as the night wore on) watching the Seahawks demolish Denver in the rec room of some kind of modern condo complex. I then went to downtown Seattle and yelled “whoo!” and high-fived people. I got very hoarse and developed a sore throat, but it’s okay, because later I had some delicious throat-soothing soup. Also, that was over a year ago, and the expiration date for whining about being slightly physically uncomfortable is definitely under a year. The point is, I watched two games, and they were both filled with positive emotions because the Seahawks won. Maybe I was on my way to becoming a fan.

To become a respectable sports fan, I would have then had to learn about the team. Follow its ups and downs. Learn about the Percy Harvin controversy, agonize about the game against Dallas.

I didn’t do any of that.

In fact, I didn’t watch a single Seahawks game until the Superbowl. And then, conveniently, I jumped right back on the bandwagon. I dressed in blue and green. I filled out a Superbowl bingo card (Car ad which you can’t tell is a car ad until the last five seconds? Check! Announcers saying “unbelievable” for something that was highly believable? Check!) I bet money. I cheered when the Seahawks scored. I cheered every televised instance of Marshawn Lynch or Richard Sherman. I whooped and hollered when Jermaine Kearse made that ridiculous catch. And then, when a short slant to Ricardo Lockette was intercepted, well, I was pretty disappointed. But then, I saw people staring into walls, going for long nighttime walks, throwing things, drinking away the pain with shitty vodka, or worse. Some dude destroyed his TV to just to make a viral youtube video. And me? I was fine. Whereas, if the Canucks had a 2 minute five on three in overtime and then unexpectedly gave up a shorthanded Stanley Cup winning goal… well, then I would not be fine. Hell, when the Canucks lost to the Sharks in the first round of a series they were never gonna win, I wasn’t fine.

Part of the disdain of bandwagoners might have to do with this. You get to partake in all the good, and shake off all the bad. But such a good deal can’t come for free, so the price of admission might be some ribbing. And to this component of anti-bandwagoning, I say fair enough.

Bandwagoning and Character

The additional disdain for the fair weather fan, though, the one that comes from valuing loyalty, is not reasonable. Those that say bandwagoners are being like those terrible people who stopped loving and cherishing as soon as their partners got sick, poor or … uhh, bad, I guess? I mean, now we have to be reminded every time someone gets married, so it must be pretty important. Abandoning a team every time it’s not the best, the theory goes, is like being one of those shitty friends in “Nobody wants you when you’re down and out.”

Except it’s not. A team is not a person – you’re not hurting its feelings being venal. Maybe sports teams had that connection with the community at some point in history, but nowadays it seems quaint. You’re not going to meet your team on the sidewalk begging for change with a reproachful eye. But the bigger issue is that by sticking with a team through thick and thin, you’re not helping the team get better. By corporate logic, the absolutely reverse is true. Of course, the players are probably going to be trying to win regardless, but to a large extent it’s up to the owners to invest in making the team good, and up to the general managers to fulfill that mission. There are only two possible motivations for a team’s front office to do everything for possible for team success. The owner’s hubris, and the bottom line. How else, then, than by rewarding the team when they’re good and punishing them when they’re bad, can you, as a fan, make the team better? Maple Leafs fans throw jerseys – trying to play to the hubris of… Rogers and Bell, I guess? But throwing jerseys is weak. A corporation like Rogers isn’t going to mind that you threw a jersey – to the contrary. It’s great for jersey sales: you’re probably just going to go and buy another one. On the other hand, not buying a jersey in the first place, not buying merchandise and not going to watch the team – all that – does affect the bottom line. In other words, being a fair weather fan motivates your team to be good to try to keep you. So if you love something, let it go.

The Trials and Tribulations of the True Fan

But the true fans who suffer through the disappointments and the rebuilds, won’t their patience be rewarded when their team triumphs? Maybe, but maybe not. This is another place where convention has failed to catch up with modernity, at least in North American professional sports. In a 30+ team league, there are bound to be lifelong fans who never see their team win anything. And given the inherent advantages some teams have, it might be even worse for fans of some teams – generations without winning. Being a true fan may mean you become the sad-sack spectacle that is the fanbase of the Chicago Cubs. And when, a century or so later, that victory does happen? The pitiable misery of a Cubs fan immediately turns into aggrieved douchiness that is the hallmark of the worst kind of sports fan: those Red Sox people.

Another reason bandwagoners are looked down upon is that they act like they know what they’re talking about. To fans who actually know what they’re talking about when they talk about sports, this is highly annoying. But looked at from a broader perspective, it’s fantastic, because there is suddenly this shared feeling of community. What happened in Seattle was that nearly everyone started talking Seahawks to random people they met. Black, white, old, young. Sitting on the bus, and going through the aisles in the grocery store, Seahawks conversations spontaneously sprang into being. The Seattle Times devoted its front page to a Super Bowl related topic for two straight weeks. Is that myopic, and a colossal journalistic failure? Of course it is! But it was also part of this brief glimpse of a small community that has come together for a common purpose – something that big cities generally lack and are always trying to create. It was an exciting time. And it was bandwagon fans that made it happen. I couldn’t tell, because I don’t actually know anything about football, but it sure sounded like they didn’t know what they were talking about. But when asked why sports should matter in a world where there is so much more going on that is so much more consequential, one answer I can give is that sports are about building a community. And if we really care about using sports to build community, the fellow feeling that comes from a town full of bandwagoners is huge and wonderful.

And Yet And Yet

So does that mean that I should stop being a fan of the Vancouver Canucks until there’s a bandwagon I can hop on? For me, as I suspect is the case for most fans, “should” doesn’t enter into it – if you’re actually a fan of a team, it’s hard to turn off. And, of course, though I’ve been minimizing it in this post, real fans gain something, too. I watched the highlights of the Seattle-Green Bay game, but that’s nothing like seeing the game itself would have been. The greatest feeling I ever felt as a sports fan was watching the Burrows “dragon-slaying” goal. In a bar in Seattle. By myself. Surrounded by Hawks fans. I remember the tension, the goosebumps, and the feeling of every part of my body seemingly disconnected and even kind of numb. I remember the drunk phone conversation with Zuuko afterwards. If I was a bandwagon fan, I wouldn’t have even tuned in until the Stanley Cup final.  Is that goal worth slogging through 5-1 regular season losses to San Jose with Luca Sbisa playing top-4 minutes and his performance being referred to gently in the Smylosphere as “surprisingly unterrible”? I don’t know. Maybe. It’s not totally up to me. But what I do know is that I’m not going to get on a high horse if someone decides it isn’t. And you shouldn’t either.

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Pull the goalie!

“I can’t hear your statistical analysis with these Stanley Cup rings in my ears”

Yesterday, Patrick Roy pulled the goalie with 11 minutes left in the game between the Avalanche and the Predators. The Avs were down by 3 and on the power play, so there was probably good justification for it, even though it didn’t work out. But when is pulling your goalie justified statistically? With the plethora of new stats available on NHL.com, and my physicist’s ability to make plausible assumptions that actually don’t correspond to reality at all, I decided to investigate.

Comparing Goals For and Shots Against

When your goalie’s pulled, every shot against is a goal, so to compare the likelihood of scoring versus getting scored against with an empty net, you can start with goals for and shots against statistics. Let’s take the Canucks as an example. According to NHL.com’s stats on 5-on-4 power play time (285 min) and goals (32), the Canucks have a PPGF rate of 6.74 goals/60 minutes. It’s harder to get a PPSA rate, but looking at Lack and Miller’s stats, they have together faced 36 shorthanded shots, while only giving up one shorthanded goal. The Canucks in total have given up two, from which I conclude that the second goal was an empty netter, and also (obviously) the only empty net shorthanded shot on goal the Canucks have given up. Thus, a total of 37 shots against in those same 285 minutes (assuming no shots against in 5-on-3 seems reasonable), for a rate of 7.79 shots against/60 minutes. These numbers are surprisingly close – pulling the goalie as a general strategy should clearly not be as tempting as it seems. They are, however, highly skewed in favour of going for an empty net. The difference in the real world is that (a) the man advantage you get is 6-on-5, which is considerably less of an advantage than 5-on-4, and (b) the opposing team is probably more likely to try to shoot at your net if it is empty.

We can also just count the number of goals for and goals against with the net pulled. It’s harder to get statistics on this, but from reading this kind of analysis, it seems that the ratio of empty net goals to goals with the goalie pulled for an extra attacker are anywhere from 2 : 1 to 3 : 1.

The Likelihood of Scoring at Even Strength

No matter the exact ratio, we know it will not be favourable, and so ideally, every team would like to score without pulling the goalie. But how likely are they to do that? To figure that out, we calculate the even strength goal scoring rate. For the Canucks, again using NHL.com stats and excluding power play and shorthanded time, I get around 2.41 goals/60 minutes (this is a slight overestimate because I didn’t factor in overtime).

So how likely are the Canucks to score in a given amount of time? To figure that out, we use the Poisson distribution

\!f(k; \lambda)= \Pr(X{=}k)= \frac{\lambda^k e^{-\lambda}}{k!},

where k is the number of goals for in a certain period of time, and λ the expected number of goals for. We have assumed that goals in hockey are approximately Poisson distributed because they are random, rare and (sort of) memoryless (this paper by Alan Ryder verifies that assumption). Thus, for example, the likelihood of the Canucks scoring exactly one goal in a period played entirely at even strength would be the above expression with k = 1 and λ = (2.41/3) = 0.80 (the amount of even strength goals the Canucks score in an average period) – about 36  %.

Comparing Likelihoods

Likelihood of the Canucks scoring the goals necessary to come back at even strength x: game time (seconds); y: probability. The black dashed line indicates a guess at the probability of scoring the first goal in an empty net situation

Figure 1: Likelihood of the Canucks scoring the goals necessary to come back at even strength x: game time (seconds); y: probability. The black dashed line indicates a guess at the probability of scoring the first goal in an empty net situation

In order to decide whether to pull the goalie, a coach must decide what is more likely – that the team can score at even strength, or that they’ll have the first goal in an empty net situation. To figure out the latter, we simply treat “goals in an empty net situation” as balls in a hat, and ask which is more likely to be picked out. So, if the ratio of empty netters to extra attacker goals is 3 : 1, then that (25 %) is also the probability that the team with the extra attacker scores first. (Is this reasonable? It sounds too simple, but I can’t see a problem with it at first glance. Someone with some knowledge of stats would be useful here). To figure out the former, we simply use the Poisson distribution (well, actually the Poisson distribution’s cumulative distribution function because in actuality we’d be fine with the Nucks scoring 2, or, say, 7 (if last year’s Islanders could do it in one period…), goals in whatever period of time we pick). Figure 1 shows the likelihood of scoring n goals in the remaining time for the Canucks at even strength. Whenever the Canucks are down by that amount of goals and that likelihood dips below the 25% mark we have set for likelihood of scoring first with an empty net, our analysis says that they should consider pulling the goalie. That means that if they are down by 1 goal, according to Fig. 1, they should consider pulling goalie with 7 minutes left. If down by 2, they should do so late in the 2nd, and if down by 3, late in the 1st. If they’re down by 4 or more, they should pull the goalie immediately regardless of the situation.

Problematic Assumptions

Do I actually think that this calculation is correct? No. There are some very obvious problems. The most clearly problematic assumption is that in calculating the Canucks ESGF/60 we neglected to consider the other team. After all, they’ll be trying to score, too.  So even if the Canucks are down by a goal, don’t pull the goalie, and proceed to score, this doesn’t guarantee that they will have tied the game. And what’s more, the quality of the other team clearly matters. A subtler problem is that the probability of extra attacker goals is inflated by the fact that if you only have the net empty for a short time, you can keep your best offensive forwards on the ice for that time. You may have a 25% chance of scoring first if you have the Sedins on all the time against the other team’s penalty killers. But when your four forwards are Higgins-Vey-Dorsett-McMillan or whatever, that probability reduces to something more like 2.5%. So of course this is not what a coach should actually do. But I wanted to point out that there is probably a way to figure out when to pull the goalie that’s an alternative to “let’s look at when we pulled the goalie before at this time in the game and whether we scored then,” and to point in the direction of what such a way could be.

Posted in hockey | 2 Comments