Puck, Hockey, Malcolm discussed on MarketFoolery
You're losing by one goal at the end of an NHL game and you're GONNA lose any way As the time is running out so the coach might say I'm GonNa pull the goalie out in favor of an extra attacker and what that does is it puts a little bit more pressure on the opposing. HOSING team's goal. It increases the probability of you scoring by about three times but it also increases the probability of them scoring by about seven or eight times but at some point. If you don't try you'RE GONNA end up losing the game anyway. So the question is doesn't matter if you lose by one goal or to or to write In the crowd gets a little bit more more excitement too so I think we were trying to do is to say look you know. Play it safe. Maybe thirty seconds before the end of the game. Let's pull the goalie and see what happens. And the started. Apparently in the thirties But basically it's been going on for some time famously The Russians did this Tikhonov. Who is the famous coach? Said I'm never going to pull the golly. That's ridiculous so for years and they had like a twenty year winning streak so he certainly did. Yeah but not against the best Canadians. But that's different. So what we we looked at was all right. Is there a way to to figure out. What is the optimal time? Meaning when is it equivalent for you to pull the goalie really towards the end of the game Versus not politically. That's quarter the the crossover point and could figure this out using the plus model and I looked at it and said you know what this this doesn't take into account the flow of a hockey game because indeed the puck could go into the net at any time but I like to think of the flow of a hockey game as something that goes back back and forth with the Puck so there are various states to the game. And so when you turn on the TV and you're kind of late the first thing you look for is of course the PUCK. Where is it and and if it's in the neutral zone you don't think twice about it but if it's in the offensive zone you leaned forward and if the defensive zone you get a little nervous and the reason is he can't score if you're not in the offensive zone and the old Expression in Haughey's you can't score if you don't shoot so what I said was look they're seven states to the game and that's what we call a Markov chain. It's a birth and death chain and I estimated the probability of going from the neutral zone to the offensive zone to the point where you get a shot to the point where you actually Lee score and then back and forth to the other side and what that does is it basically helps you estimate what would be the optimal time to pull the goalie. Only if you're in the neutral zone but also what happens when you're in the offensive zone and when you're in the defensive zone so I wrote up this paper after I'd graduated Took a little while in two thousand and one and the magazine was called chance. And I WANNA shout out to all the people a chance for basically following up and chances the one that's has been publishing this paper for other authors for quite some time so I forgot about that was two thousand and one Chris and then so one day as their rebuttal. I'm ought to go back. Yes or no. Interestingly I moved to Asia didn't watch as much NHL. As I'd like Hobson do as well as well but I ended up getting a call from one of my friends who went to mit with me and he was really angry. I said why are you so angry. And he said I was just listening to the Malcolm. Glad glad well revisionist history podcast. And he says that one of his rules for life is pull the goalie and he didn't give credits. I said what do you mean. And he said look this guy no cliff assis wrote a paper in two thousand sixteen and Malcolm did an entire episode on it. You gotTA listen to it. But I'm furious. I didn't think much I sat down. Whatever right it's been many years so I finally get to my My favorite podcast APP Download Malcolm in a start listening to it. And it's a brilliant brilliant podcast because it takes the problem and goes a lot further than what us in math geeks would do and it talks about two people cliff. Fastness and Aaron Brown and cliff runs a multi billion dollar Hedge Fund which is a quote fund and he and Erin are apparently apparently disagreeable people according to Malcolm. And it's kind of the core to this problem the pull the goalie problems and the Brown model which I call the ABC model title basically uses some new techniques. Some new data dynamic programming to calculate the optimal time to pull the goalie and what they find is basically basically the same thing that I found in two thousand one that it should be about six minutes before the end of the game. What's also interesting? Is that in the paper. They they cite my paper twice in a very favorable way. They said you should look at this. I'm on paper to figure out the state and it would be great to be able to see how are data corroborates. 'cause we almost got the exact same result and when I really thought about it they were using the same assumption. That is a state nonspecific. They didn't really care where the puck was in calculating their model as it brilliant model and it works really well and and the the the rules have changed a little bit. They optimize for points because there's an overtime loss cost now but for all intents and purposes They just refresh the model and got a lot of airplay with Malcolm which is of course something. That's really interesting and and So I looked at it and I said well. What am I going to do? Dan and I looked at it. Some more and I realized something of course I could do. I could update the ABC. Be Model using the same Markov idea and I love the fact. That Markov is a wonderful hockey name. Right it is I mean. He used to be a defenseman for the the penguins and obviously further Russian national team. So Markov fits very well for hockey and for math so I basically do. What Agnes Brown suggest? Which would be nice to see what happens if you made the state dependent but I realized one thing and I admit it which is my math was rusty and you take a little time off so that the interesting thing was? Maybe math wasn't rusty but the best way to do this was Coating it in Python and I needed a thought partner so I went to the national the University of Singapore and this guy named Hongming loves doing sports stuff and I went to mit with one of his professors. And we got together. And we we coded I did and he was the lead programmer and I was thinking about the math and effectively. What we were able to do is to modify that Ashton's Brown model to fit with The idea that the PUCK can flow from the offensive state to the defensive. Have you reached out to play ball with the new paper so partly this is is an attempt to say. Let's let's talk about this so effectively. What we found which we first thing you do is to replicate the essence Brahmana which we did and then we said let's start to Do Two things first is of course figure out how it changes if the PUCK is in the offensive zone in the defensive zone and then the second thing I started to think about was the coach himself or herself their mentality changes because of the crowd and because the fact that. This isn't just something where you can press a button. And the golden gets pulled view ever seen an ice hockey goalie. TRY TO SKATE Forty meters to the bench. It's Kinda painful because they've got a bunch a little awkward right. It's a little awkward so effectively. What we figured out is even if you pull the goalie because you have an offensive cajon faceoff you can reverse that decision and the way you reverse? That decision is that you take that goalie and you put him back into the goal. Perhaps ops if you lose possession of the PUCK in the offensive zone make sense right someone for main so the problem is you can't do that when the puck in play. You GotTa wait for the next face off so what we did was we figured out. We'll just how frequently to face offs occur and luckily it was very very consistent. It's every sixty seconds so this idea of penalty or Timing of which. The coach has to live with his or her decision so the two bits of information that we found is that first of all little bits of of insight are incredibly valuable and the reason is it de risks a risky situation because what is pull the goalie. It's a situation where you're making a desperate move that increases the volatility of the whole situation and for the investment people out there. I think you've you've heard it Described as follows if you could increase the volatility of a call option as it nears the end of its term. Because you're so far out of the money it's a good idea because the chances are higher that will go in the money. That's exactly the pull the goalie problems so effectively. What we we're learning is it's you have a little bit of information about how risky the situation is? It gives the coach a little bit of air cover to say hey. The PUCK is in the offensive zone. It makes sense to the crowd that I can pull the goalie. Because it increases the chances of me score being scoring Against that goal well and if we lose control the puck over the boards up with the goalie back in the crowd can accept that so the first adage that we came up with was that we can dear risk risky situations with the particular bits of information. And that makes sense intuitively the second point. Is that the PUCK. tuck transfers between these zones very very quickly right it will stay in the offensive zone for about ten seconds and therefore this little bit of insight site is fleeting right. You really don't know after ten seconds. What zone the PUCK will be in? And you gotta live with your decision for sixty seconds so that balances things things out so when the coach can justify that because he has that advantage he has permission to be bolder but he has to basically live with this decision and you know pull. The goalie to me is about courage right and I think the question that Malcolm puts forward in which is really insightful. Chris is what happens if you have a violent robber in your home with you and your family like what do you do. Because it's socially unacceptable for you to run to get help because in case your your your kids get Get hurt so what I'm basically saying being is if you can lock your kids in a panic room for some period of time and keep them safe it gives you the air cover to go out and get help. I'll give you a couple of other examples. Apple's pretend like you're a studio executive at a pretty small label And you need to improve your results or else you're gonNA get fire right. You have one last shot so you take a risk to do an indie movie with a first time screenwriter director and you think this is the only chance I have left to actually have a low budget A high box office yield movie. And what you're basically doing. You're pulling the goal you take your saying. I'm going to throw a caution to the wind. If I could tell you you can get de risk. The situation by saying Meryl Streep's GonNa play the lead. Well it makes it a lot more palatable to say I'm going to take that risk and then the studio executives say okay if you got Maryland. That's fine the same goes with an investment manager towards the end of the year. You're not having a great year and you know that either you're not GonNa get a bonus or you're gonNA get fired. You might want to increase the volatility of the basket of assets that you hold because effectively you're gonNA lose your job anyway And therefore you might as well take a disagreeable disagreeable position. Because it's the right thing to do and it's the same ideas coach you're going to lose anyway and The last thing would be a CEO if from a management perspective affective either near the end of his tenure or. She feels like she needs something blockbuster to pull her out of the doldrums. The analyst will do something incredibly risky like acquirer appear Excetera and I think that that basically repeats itself over and over again. I just like the way that the pull the goalie problem for all intents and purposes sometimes you need courage but maybe more importantly if you can find little ways that what your courage can be justified. That's a good thing It's better than basically just making a blind bet that makes sense absolutely and it it goes goes to a couple of couple of things. One is the old adage from the mutual fund industry and this this example doesn't doesn't really hold much water certainly over the last five years or so but for a good couple of decades it was absolutely true that the old adage that no mutual fund manager ever got fired for buying shares. VM because it was the stable blue-chip Reno was a tech business in. And and no one's GONNA no one's Gonna a knock you for buying. IBM even if that stock doesn't do well the other thing you just reminded me of is An article I read recently about the economics of the film industry and in particular the economics economics of horror and how the part of the reason there are so many horror movies made one is the economics of horror. Movies are fantastic. They're low budgeted. That don't require large scripts. They don't require stars. It's also also away for first time directors to cut their teeth because they get the freedom to do whatever they want in a way but really it's it's a big part of it is just the economics are so good 'cause horror translates into every language. That's exactly the point back to the coach. which is it is easy for them to say I pull the goalie? The minute left the PUCK didn't bounce our way and and everyone's going to give him a pass right. He'll say oh. We gave it one hundred ten percent..