Apr 9, 2020
Apr 9, 2020

What is it like to be a bookmaker in disguise? - Pinnacle Betting Podcast

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What is it like to be a bookmaker in disguise? - Pinnacle Betting Podcast

There are many similarities to be drawn between actuarial science and a successful approach to betting. In this episode, Ben Cronin speaks to an actuary (PlusEVAnalytics) to find out how using math and statistics to solve problems as a job can help with betting. Read and listen now.

Ben:

Hello and welcome to the Pinnacle Betting Podcast brought to you by Pinnacle.com. The online bookmaker that bring you the best odds, highest limits, and unique winners welcome policy. Today I'm joined by Matt. Matt is an actuary who applies his risk assessment skills to sports betting and often shares his insight under the wonderful Twitter handle, @PlusEVAnalytics. Welcome to the Pinnacle Podcast, Matt.

Matt:

Hi, Ben, thanks for having me on.

Ben:

No, thank you for joining us. This podcast is going to be about your job and betting and everything from there. Before we discuss your job in any great detail, can you tell us briefly about what you do now, and perhaps a little bit of what came before that?

Matt:

Great. Sure. So I'm an actuary, and I guess nothing really came before that. I went to school for actuarial science, and came right into the profession right out of university. And in my job, what I do is I come up with pricing for insurance, which is kind of a cool little niche, because it combines the technical mathematics of probability with a deep understanding of the dynamics of markets. Because you're not pricing in a vacuum, you're pricing in competition with other insurance companies in the marketplace.

I always get a kick out of when you retweet that article from a couple years ago from Pinnacle, The Top Professions That Are Best Suited For A Career In Betting, and actuary is at the top of the list. You can see from my brief description how these skills are transferable and how they come in handy. So I'm sure we'll get more into that as the discussion proceeds.

Ben:

You mentioned there about universities. So for anyone that's interested in following the career path and becoming an actuary, apart from actuarial science and stuff like that, what kind of skills or fields of study are required?

Matt:

So, there are a lot of schools that offer a degree in actuarial science, but that is not the only way to get into the profession. I've worked with actuaries who have degrees in business, in mathematics, even in hard sciences like physics. Really the qualification to get into the profession is a series of exams that are maybe a little bit tougher than they need to be, but if someone has the aptitude and the motivation and the study skills to get through the exams, it's actually quite an interesting and rewarding career.

Ben:

So, the other thing we'll talk about today is betting. Where did your interest in betting stem from, then?

Matt:

I think it's always been a part of me. Even when I was a little kid, occasionally my parents would buy me a $2 scratch-off at the convenience store, and I love those things. I've always been a sports fan as well, and a Toronto sports fan. That's where I grew up, that's where I live, and at the risk of dating myself, I was at Game Six of the 1993 World Series when Joe Carter hit that walk-off home run against the Phillies. That was one of the greater moments of my childhood. Obviously, it's a great summer in Toronto to be a sports fan, with the Raptors celebrating their recent NBA championship. But I've always been into gambling. I've always been into sports. So it's a bit of a good match.

Your listeners may not know this, but in Canada where I live, sports betting is legal and has been legal since the early '90s, with a caveat, and that is there's a weird quirk in the law that says parlays are allowed but single game bets are not. So you have these quasi-sports books run by the provincial governments here in Canada that only offer parlays, and the vig on these things is outrageously high to the point where a lot of serious betters don't even bother with them. But they do offer some bets, especially some prop bets, that were challenging to model, but were right in my wheelhouse of what I can do.

There are not as many opportunities out there in these types of games as there used to be. There are people who came around 10 years before I got started and they actually made millions at this. The opportunities are fewer and farther between right now. But it certainly got me started into gambling, into sports betting and into sports betting analytics.

Ben:

And I guess whether it's betting comes from being a sports fan, or trying to make money, or just doing it for fun, a lot of people also say there's an enjoyment of trying to predict the unknown, or the challenge of making more accurate predictions than the market. Is that part of the allure of what you do for a job and maybe why you bet as well?

Matt:

Absolutely is. And like you say, being able to say I can predict the future is putting it tritely, but to be able to come up with probabilities of things that might happen in the future more accurately than the competition, the market, the books, whomever, is something that really appeals to me, both in my career and in my hobby.

Ben:

Okay. So let's move on to your job in a little bit more detail. And I mean, the similarities between actuarial science and betting, it's very clear. You talked earlier about a lot to do with risk and stuff like that. I mean, as you said, the profession is very difficult to get into. It requires a lot of intelligence and a lot of hard work. And I mean, hopefully your little intro at the beginning there gave people insight into what it is that you actually do. But can you tell us more, a bit maybe about the day-to-day life of an actuary?

Matt:

I can. Now, there are different types of actuaries working in a whole bunch of different fields of work. Some work in the insurance industry, some work in the consulting space, some do life insurance, some do property liability insurance, some do pricing of insurance, some do more on the financial reporting side. So it's a really broad spectrum of different jobs within the actuarial space. But really the common thread is that they are using data to make decisions, usually in the insurance space, in the face of uncertain outcomes.

So an insurance policy is really just a bet in disguise, where you're taking money and you're paying out an amount if some uncertain outcome happens. That's really the key source of all commonalities between insurance and gambling, between being an actuary and being a bookmaker. I mean, the real-world context is very different in terms of the social need for insurance versus sports betting is more of a recreational pastime. But in terms of the fundamental mechanics and mathematics of how they work, they are very, very similar.

Ben:

So, when was the crossover between you getting those scratch cards and betting for fun, before it got to the point where you realized that what I'm actually doing for a job, I could use this to benefit myself in the betting market as well?

Matt:

Yeah. There's actually a specific point in my life where that turned for me in my head, and this was, I want to say, about 10 years ago, where, like I said, there is this Canada sports lottery and they take parlays. And I had been playing it really just for fun. I would throw down $10 here, $20 there. Until one day, there was a bet that I tried to make, and what you do is you go to either a gas station or a convenience store and you fill out your little parlay card, and you hand it to the cashier and they run it through their terminal. And when I gave it to that cashier, and he ran it through his terminal, he looked at me like something was happening that he didn't really understand. And he turned the terminal screen to me, and it said that the bet had been rejected because the liability limit on that particular combination had been exceeded.

That was really a light bulb that went off in my head, because here you have, in this case, the government of Ontario, which is just a massive economic entity, saying that they wouldn't take my action on a $20 parlay that was probably paying out something like $80 or $90, because they couldn't stomach the liability. To me, the only way they would do that is if that was a +EV proposition.

This particular bet was a hockey parlay on a prop that's no longer offered, around which player on which team would score more goals and assists than a player on the other team. I went home that day and I started doing some research, and I started building my own model for how to model these things out using a theory called Poisson process, or Poisson distribution, that is a standard part of the actuarial curriculum and I think you guys may have actually even had some articles about it in your betting resources archives. It's a pretty common tool for modelling sports outcomes, and it's something that I was familiar with from my education. I said, "Hey, I can apply this." And that was really the genesis of the first sports betting model that I ever built, and the rest is history.

Ben:

So you've established that model, the Poisson, and your attacking strength and defence strength and stuff like that, to distribute the probable outcomes. Are you then going with that back to the gas station that couldn't take your bet originally? Or are you looking at other avenues to bet?

Matt:

In this particular product, there is only one avenue. It's the gas stations. They're all networked together, so whether I go to one gas station or the convenience store down the street, I'm betting into the same pool. If my bet gets rejected at one place, it would get rejected at all of them. But what this model allowed me to do was to wake up at 7 a.m., run the numbers for that day's combinations, and the ones that ended up being a positive expected value, I could hit the gas station in the morning and I could play them before anybody else was.

Because I'm assuming that the reason my bet got rejected is because there were other sharp players in the market who knew the same things that I did, because this model I built, it was fairly complex, but it wasn't something that other people couldn't realize. And there are other people out there doing this, whether they had the same level of mathematical rigor as I did or whether they were just doing it off the top of their head, either way there was competition in this space for who could get money down before they shut off that combination, and I now had the ability to price this thing as soon as the lines came out, which was first thing in the morning. So I could get to these things more quickly.

Ben:

That's interesting, there, because there's some similarities and also some differences to some of the struggles people have with online betting, in the sense of as soon as a bookmaker realizes that you know what you're doing, you'll struggle to get a bet down. But in your case, it was first person to the punch gets the reward.

Matt:

For sure. And these things are built on systems. They're built on lottery systems. The same system you use to play a 6/49 ticket or a weekly lottery draw ticket, it's the same systems that are handling these. So these systems don't come with the ability to change odds in real-time during the day, like Pinnacle would, for example. So, if something gets bet too much, they have no recourse other than to take it off the board, or to shut down betting on either one game or one combination. And when they decide to do that, it's game over until the next day.

So it is similar in that you have a pool of sharp betters who are all competing to be the first in. I guess the only difference is the bookmaker's response to that. You guys can just move the lines and take more action, but in these systems, I'm assuming due to limitations of the technology, they can't do that so they'll just pull it off the board.

Ben:

There's one example of something you said was actually on your curriculum in Poisson distribution, and how you applied that to betting. I'd be interested to know, is there a flip side to that? And does betting almost have an impact on what you do for work?

Matt:

Absolutely. There's no doubt that my career has helped me in my hobby. The Poisson distribution in that hockey model is just one example. But what I would say even more strongly is that my hobby has helped me in my career. So to most people in my field of work, things like risk, probabilities, markets, these are abstract concepts. They're abstract objects that they read about in a textbook. Where I interact with these things intimately on a daily basis. You can learn anything you want from a textbook, but there's no substitute for real-world experience, in any domain, especially in this one.

So, I have a natural advantage over other actuaries working in my space. This thing called risk, I really know it and work with it more closely than they do. So I would encourage anyone who's coming up in the actuarial field, or really any of the applied mathematical fields, to take up gambling. And I'm not saying become a professional bettor and bet for high stakes. Even if you're betting for pennies, doesn't really matter. The stakes aren't the point. The point is to interact with this thing called risk in a bit of a different context that then you would in your career, and that will give you a much deeper understanding of what risk is, what probabilities are, what markets are.

Ben:

Yeah. Pinnacle's training director has spoken a lot about the ability to think probabilistically, and how Pinnacle trade is they often come from a gaming background, because they have that ability to assess situations, and calculate probability in an instant. Is that part of your skillset, that very quick thinking to translate data or figures into probability? Or is it more you have to take time to ensure those calculations are as accurate as they have to be?

Matt:

I'd say it's a little of both. There is some quick thinking to it, in that if you do something over and over again, it's the Malcolm Gladwell 10,000 hours theory, if you do something over and over again, enough times, it becomes second nature to you. There is coming up with a quick, back-of-the-envelope estimate, and there is sitting down and working out the numbers, and getting something accurate to the fifth decimal place, and there's a time and a place for each. And I think they're both important.

Ben:

I guess with Pinnacle, the benefit of that perhaps leaning more towards the back-of-the-envelope approach is you've got the market to instantly guide you on your decision, just how right or wrong it might have been. Is that the same in the insurance market?

Matt:

It is the same in the insurance market, but it's opposite. So, my favourite author is a guy named Nassim Taleb. I think your authors have written about some of his stuff in the past. One of his books, called Antifragile, he really goes deep into the concept of fragility, and adverse selection. And my job I find extremely stressful sometimes, because it's fragile. Because I'm vulnerable to this phenomenon known as adverse selection.

And what I mean by that is if I'm coming up with a price for 100 different types of insurance based on a probabilistic assessment of the likelihood and amount of claims that we might pay out in the future on those 100 different types of insurance, and I nail it on 99 of them, and I get it wrong on one of them, the market will find the one and it will exploit it. So 99% accuracy rate is not going to be good enough. You have to be near perfect, and that's something that really I find stressful about my job, is that constant pressure to be perfect, or near perfect.

Now, the flip side of that is my hobby, my betting hobby, is what Taleb would call antifragile, where I can actually benefit from the fragility of others. So Pinnacle as a bookmaker can set lines on 100 different sporting events, and I can look at 99 of them and say, "Yep, those lines are bang on," and I can choose not to bet those lines, but I can see one out of 100 where I think the line is wrong. And if I'm correct in that assessment, I can exploit the one and pass on the 99. So really the conclusion of all this is that the fragility that I have to endure in my job is offset by the antifragility that I enjoy at the expense of bookmakers, unfortunately, in my hobby. Because I am the selected-against in my career, and I am the selector-against, if you will, when I'm in the betting space.

Ben:

Yes. There's clearly a lot of similarities between the two, and the job that you do can quite obviously help you find an edge in the market and take advantage of that. I'd like to know, do you think that the work that you do can almost limit what you want to do with betting, in a way? Is there enough time in the day to develop the models? Can you bet where you want because of work?

Matt:

Yes and no. Of course, there's only so many hours in the day, and between my work and my family, I'm fortunate to have two young children, which is fantastic, but they're a lot of time and energy to go into that as well. So there's only so many hours left in the day for betting. And you really do the best you can with those hours that you have.

Would I have more opportunities if I did this full-time? Of course I would. In my past, I have done some modelling for a horse racing syndicate, and I would just build the models in my spare time and it did well for a few years. But after about three or so years of doing this, what I found was that I just couldn't keep up with the competition. The other people who were doing horse racing modelling were improving their models at a faster rate than I could improve mine, because they had teams of analysts who were working full-time on this, and I was just one person working on it one or two hours a day.

The natural question would be, why don't I just quit my job and bet full-time? And believe me there are days when I consider it, especially when I'm not having the greatest day at work, with company politics, or inability to get things done, or the other normal things that plague typical office life. And there are times when I say, "Hey, I should just give it up and go bet full-time." But at the end of the day, I do enjoy my job 99 days out of 100. It does pay fairly well. So the opportunity cost for me of leaving my job to become a full-time better is much higher than, let's say, if I was a cashier at Walmart faced with the same decision.

Another criteria that I ask myself sometimes is, if I was to take a year off and bet full-time and then either not do well, or not enjoy it, and want to come back into the traditional workforce, the insurance industry and the actuarial profession are fairly conservative-minded, and I'm not sure how well it would go over to have that on my resume, took a year off to become a full-time sports bettor. And there's really no guarantee that I would be welcomed back into the industry, or into the profession. So it's a bit of a risk, there. So, between the opportunity cost of giving up the job I already have, and the risk of maybe or maybe not being able to ever come back to it, I'm just not at a point in my life right now where I would consider betting for anything more than a fun hobby.

Ben:

It's easy to think of betting as so many people do, and look at it through those rose-tinted glasses. The stressors that you said that come along with work, let's not kid ourselves, they're just as prevalent in betting full-time anyway.

Matt:

They sure are. But at least you get to be your own boss.

Ben:

Okay. Let's take a bit of a deeper dive into your actual approach to betting. You spoke a little bit earlier about Poisson in hockey. Is there any more information or examples, potentially, that you could give us where you've taken that mindset, of thinking about risk and probability, and transferred it into betting activity?

Matt:

I can give you another example. One of the techniques that's taught fairly well, I would say, as part of the actuarial education curriculum, is something that actuaries call credibility theory, which is how to take in a set of observed data and sort it out into what is signal and what is noise, and use that assessment to figure out what kind of decisions you should make on a forward-looking basis.

I know explained that rather abstractly, so I'll give you a little more of a concrete example. How much such your premium go up after you make a claim? That answer will depend on the extent to which the claim is evident that you are a bad risk, as opposed to just random bad luck. If you're a bad risk, that influences my assessment of your likelihood of making a claim next year. If it's bad luck, it doesn't really impact my assessment of anything.

So, it's this whole idea of trying to separate signal from noise, separate known unknowns from unknown unknowns. This is really an area that fascinates me, and it really is the basis of my article that recently got published on Pinnacle, towards a theory of everything. It's generated some great discussion on Twitter. I've had some good feedback, and I love this field of study so much, because it really starts to toe the border between mathematics and philosophy, and that border is what's known as epistemology, the philosophy of knowledge.

A lot of the more pure mathematical sciences make the assumption that we know everything there is to know about how the world works, and we make calculations that follow from that. But in the real world, you really don't know what you don't know. All you have is the observed universe, which is constantly feeding you information that you can use to learn and refine your understanding of how you think the world works.

So if that sounds to your listeners more philosophical than mathematical, I would say, "Good," because this work really approaches that border. You can even tell from some of the feedback that I've had on Twitter, is there are some people who are really good at the pure mathematics side of this, but are really unfamiliar with this philosophical side of, well, what if we don't know everything about everything? How can observing a stream of observations from a random sequence of events help you to infer what that, what we call the generator in the article, what that looks like?

So, it really gets into the weird and wonderful area of the philosophy of knowledge, that is probably unfamiliar to a lot of the pure mathematical thinkers, but I think can be a really useful tool in any serious bettor's toolbox.

Ben:

And that approach, does that impact what you find yourself betting on? Some people may often say, "Oh, I'm going to take baseball, I'm going to build a model around baseball, and find the value there." Are you led by your approach first and what that finds, and you bet on that?

Matt:

I would say a little both. This whole idea around epistemology and not knowing what we don't know, I've developed that more recently, where I've been betting way before I started thinking that way. So my background in betting, I'm mostly a prop better. I'm mostly a derivative guy. And the main reason for that is I have a healthy respect for markets, and arguably even a too healthy respect for markets. So if you're looking at an NFL game, and one team is favoured by six and a half points, according to a market that's very liquid and has a lot of sharp money in it, I just say to myself, "Well, who am I to disagree with what the market is saying? I'm just one person. The market is just this huge, massive thing, and I don't think I know better than the market. Even though maybe I could if I put the effort into it. I've never really tried.

What I do instead is I say, "Okay, well, if I take the market number as a given, what inferences can I draw from that? What can I derive from that? What can I conclude about maybe some other markets?" Whether it's halves, whether it's props, whether it's regular season win totals, whether it's futures, whatever it is, how can I take that knowledge of what I believe to be a very efficient market and transform it, and apply it, to other markets that are perhaps not as liquid?

I am by no means an originator, and I don't aspire to be. I'm a deriver, if that makes sense. I take the markets that I know are good, and I say, "Okay, based on this what can I say about other markets?"

Ben:

And then I guess, without delving into green lumber fallacy and stuff like that, is knowledge of the sports themselves, how they work, or their nuanced mechanics, do you attribute any value to that? Is that necessary?

Matt:

I attribute some value to it. And yeah, the green lumber fallacy is a great... There's a great article that you guys published on that. And I by no means believe that domain knowledge alone will allow you to beat a market. But where I really believe domain knowledge can come in handy is when you're looking at a dataset and trying to interpret what it means. So as you build a model, you have to make all kinds of assumptions and choices about what type of distribution you use, or what kind of values you cap, or what kind of outliers you throw out, or what kind of things you group together, and really a model is just a dataset plus a collection of all these assumptions.

I think this is where domain knowledge can come in handy, is it can set you on the right track in terms of making those assumptions in a well-thought-out way. There are, I imagine, a lot of bad models out there where the modelers just had a dataset, knew nothing about the underlying sport or business or whatever their real-world thing is they're trying to model, and just used the data on its own, and came up with some conclusions that, not only are they counter-intuitive, but the modeler may not realize they're counter-intuitive because they don't have that knowledge base.

So I think that that knowledge of the sport is helpful in all those steps that are required to construct a really good model. But of course the green lumber fallacy is a real thing, and you're never going to replace a model or a dataset with just being an expert in any particular sport.

Ben:

Yeah. It's interesting, there, we talk about models, we had Rufus Peabody on, and Matt from Data Golf, and they echoed very similar messages in that there seems to be a trend developing in the betting market, almost this black box approach to modelling, where people chuck a load of stuff in, it spits something out, and you don't really know what's happening. All you know is what your output is, and the fact that you're maybe generating positive results to start with, but that's actually a very dangerous approach.

Matt:

Sure is. I'm very sceptical, both in my career and in my hobby, of whether you call it machine learning, artificial intelligence, data mining, a lot of these things are heralded as the next big thing. Even at my job, I get calls from all kinds of people who are selling machine learning software, and a lot of the times I'll take their call just to know what they have to say. And I'll just think to myself, "Well, all they're doing is overfitting their data. That's not going to work in the real world." And I think the same kind of things are happening in the sports world as well.

You've got to be very careful in how you structure your model. I am not at all a fan of so-called black box models, where you don't really even know what's going into it, what assumptions are being made, how it's working. It's just like, "Okay, well, the model works, trust me." That to me is a recipe for disaster, because not only will you be a loser, you will be a loser who thinks he's a winner, and that's the most dangerous kind of loser to be, because it will cause you to have a sense of false confidence. It will cause you to overbet your bankroll. It will cause you to think you're the world's greatest gambler, and these things almost always go up in flames.

Ben:

I'm just trying to put myself in your shoes, and the process you go through this betting. So you build your models, you quantify your inputs and everything that goes into it and stuff like that. Are we literally saying you run your model, get your results, and then off you go down to the gas station or wherever it may be on a daily basis and place those bets?

Matt:

Pretty much. That was more true back a few years ago than it is now. Like I said, the gas station, the number of +EV bets available at the gas station has shrunk dramatically, as the people who are making these books have woken up to how they were being taken advantage of by advantage players. So there's not nearly as many opportunities as there used to be, which is causing me to branch out into other areas.

So, I'm trying to beat so-called real markets now, for the first time. I've done some work on hockey first period totals, with some mixed success. I am starting to look at NFL regular season totals. I am building an in-play tennis model that is in, I guess what I would call beta testing mode right now. I haven't actually placed any bets with it. But the testing is working out well, but that always seems to happen until you start putting the money down. So I'm proceeding cautiously. But the same types of models.

Especially tennis, I love tennis, because it is at its core a very simple process where you have two players, and there are points where Player A is serving and there are points where Player B is serving, and it really is just a repeated observation of those two random processes over and over again throughout the match. So you can observe a match and learn a lot about what those underlying generators look like, and then once you have your assessment of what those generators look like, you can then project it forward just to figure out what the rest of the match might look like. There is a lot of mathematical simplicity to a tennis match that is not there in something like a football game or a baseball game, because there's just a lot more variables going on.

So, I've picked tennis on purpose as my first foray into seriously trying to beat a real market as opposed to these gas stations parlays. And it's still too early to tell, but hopefully we'll get some good results.

Ben:

And are you back testing, using past data and then do you develop into small stakes and testing it that way?

Matt:

Yeah. Unfortunately the tennis model I'm building is an in-play tennis model, and I've really found it difficult to get historical datasets of live, in-play odds. A lot of places are reluctant to give them to me, for good reason, because I would just take them and use them against their books. But really what it means is I cannot back test my in-play tennis model as well as I'd like to.

So you go through a couple of stages. You say, "Okay, well, I can run a model back through five years of historical matches, and I can pause at each point in the match and say, okay, what would the win probability of Player A have been at that point in time?" Accumulate it over five years, and say, "Okay, well, for the total of all points in all matches where I said the probability was between 85% and 86%, what proportion of those times did that player actually win?" And if it's between 85% and 86%, it's a good sign. But there's still no market to compare it to. So the next stage, and this is really where I'm at now, is so-called ghost betting, where I actually run my model live through a match as its progressing, and pretend to bet at actual live lines, and try and take some logs and add up how I would have done.

And that's I guess the last step. If that works well, then you start betting small stakes, and you gradually move up from there, as you get more comfortable with the process of betting and especially life in-play tennis, because there's a lot of information coming in very quickly. So there's a process aspect to it. Can you see what happened in the point? Recalculate your mode, and get your bets in before the next point is played? So there's some logistical considerations you have to go through.

But on top of that, as you bet, you are getting back information that can help you reassess how good your model is. And again, that's the kind of thing that I describe in my article, is how you can actually modify your Kelly Criterion percentage in real-time as feedback comes in from the real world, from the results. That will help persuade you that your model is better or worse than you thought at the start.

Ben:

I feel like you read my mind there, because I was just about to say, we have a very clear understanding of how you approach betting and what to bet on. And it feels the logical place to go to next is how much you should be betting, and whether you know what you're doing is right or wrong. So in terms of staking methods, obviously there's quite a few out there. There's basic flat stakes, Martingale, Fibonacci, have their very well-known pitfalls, and you just touched upon there Kelly Criterion which is probably the most popular but also the one that throws up the most debate. So can you just talk us through, maybe, your thoughts on Kelly and the work you've done after analysing it in some great detail?

Matt:

Yeah. The attraction of the Kelly Criterion is that it's fairly simply mathematically, and it's a fairly elegant solution to what's really a complex problem in terms of what amount should you bet to optimize your long-term rate of bankroll growth. I've had, actually, two articles published on Pinnacle, betting resources articles, on Pinnacle's betting resources site.

The first one was a year or two back on some more complex applications of the Kelly Criterion. What if there are multiple games that you want to bet at the same time? Or what if you have existing exposure on one side but you want to partially hedge? Things like that, that the simplified form of the Kelly Criterion don't really help you with, but you can actually get a more detailed version of the Kelly Criterion that can answer questions like this.

And then, my more recent article about... Well, it's about a lot of things. Full Kelly versus Fractional Kelly. And when you might want to use Fractional Kelly. The biggest debate in gambling Twitter relative to the Kelly Criterion is what's better, Full Kelly or Partial Kelly? And there are advantages and disadvantages to each.

The biggest challenge with Full Kelly is that it was built for what I call artificial generators in the article. I believe it was first applied by Ed Thorp in card counting for blackjack. And blackjack is something where you know precisely what your probability of success is at any given moment in any given hand, because the rules of the game are known and spelled out, and fully understood.

In a complex domain like sports betting, you never really know what that generator looks like. It's a natural generator. You can model it out. You can estimate it pretty accurately if you have a good model. But you never really know for sure. So for that reason, I would not advocate betting Full Kelly for sports betting while I would in something like blackjack. But what you can do, as I illustrate in the article, is start with a Partial Kelly, say a Quarter Kelly or a Half Kelly, as a reflection of the uncertainty of really how accurate your model is. And then, after you've made one bet, five bets, 100 bets, 1,000 bets, there are mathematical ways to use Bayes' Theorem to update your assessment of how good your model is, and translate that into your Kelly fraction should be.

Maybe you start with a Half Kelly, you'll make 500 bets, you'll have good results, and the math will tell you, okay, well, then you should graduate up to .7, or .8 Kelly. So really what happens is your bet size increases and decreases as your bankroll grows and shrinks, which is a natural property of the Kelly Criterion. But your bet size also grows and shrinks as a function of how confident you are in your assessment of your own edge. So it layers that second-level of feedback into the Kelly Criterion to supplement that one level of feedback that's already there, where your bankroll grows and shrinks, and your bet size grows and shrinks along with it.

Ben:

There's pretty clear evidence there, you were talking about your epistemology, and taking that approach to unknowns. It doesn't apply just to what you should be betting on, but how much you should be betting?

Matt:

Absolutely. At least, I've made an attempt to make that case in the article. And I certainly believe that. But like a lot of things in philosophy, it's an open question, with no clear answer. So I'm open to any thoughts if people want to debate me, argue with me. They won't be the first people to do that. And I'm happy to engage with anybody on Twitter, as long as they keep it somewhat... What's the opposite of trolling? Keep it somewhat professional, I'm happy to engage.

Ben:

I think you've just put a big target on your back for that.

Matt:

I haven't put it there. It's already there.

Ben:

So, I mean, you said gambling Twitter, and this big debate, and staking methods, Kelly Criterion, Full Kelly, Partial Kelly, Fractional, whatever you want to call it, is one of the big ones. The other one that certainly springs to my mind is the question of measuring success, and obviously with so much variance involved in betting, people think or believe that simple measure of profit and loss can be quite dangerous. And people tend to use closing line value as a measure of success, whether it's looking at your model, or whatever it might be. And that obviously has its advantages and disadvantages. You said earlier you respect the market maybe too much. Are you a believer in efficient market hypothesis?

Matt:

Oh, boy, Ben, you told me I had a target on my back and you bring up closing line value. So, this is like a magnet for, I guess what I would politely term people with strong opinions in gambling Twitter. I do believe in efficient markets as a general theory. Obviously, some markets are more efficient than others. I believe in closing line value as a measure of success. I don't believe in closing line value as the only measure of success.

The thing with closing line value is you have to assume that the market is inefficient enough at the time you're making your bet that you can actually find value, but then the market becomes efficient enough after you make your bet that you can use the closing line as a measure of value. And I think that hypothesis is somewhat true, especially in a lot of the bigger markets. But it does have to rely on the idea that the market is finding the same information, the same edges, the same angles that you are, and the market is betting them at a later point in time. And if that's what's happening, then great, more power to you. CLV is a perfectly fine measure of your success.

But if you have the kind of model, or the kind of betting strategy, where if you identify an advantage play, you might be the only person in the market who has that theory or that information or that idea, well, there's really no reason why the market should catch up to you. Which I realize is a bit of a contradiction of the efficient market hypothesis. But it's certainly a possibility, and I'm sure there are people out there who have angles that the market isn't following. Doesn't necessarily mean they're wrong. What it means is they're not going to get any closing line value, but it's still very plausible that they might have positive expected value.

Unfortunately the only way to really know or measure that is through results, and of course, results are noisy, you need a large sample size, all of the reasons why people prefer to use closing line value instead of actual results, because closing line value is less random, is less noisy. You can learn a lot more with a smaller sample from closing line value than you can from results. I totally believe all of that. But there are circumstances, and there are types of angles and types of bets that one might make that won't necessary result in positive closing line value, but could conceivably result in positive expected value, and winning over the long run. There's just no easy way to measure it.

Ben:

Yeah. I mean, it is probably quite a simple caveat that should go along with that, which it feels like a lot of don't really take on board, and that's... I mean, people tend to talk about Pinnacle's closing line as the measure, given how efficient it is. But even Marco Blume, our director of trading, has been quite open and said those lines, they're efficient on an average basis. It's not every single line is efficient.

Matt:

Yeah. Market efficiency is dependent on how you look at it, because yeah, it can be efficient on average, and that just means there's no systematic bias in the lines. But to say that every line is perfectly efficient really means that nobody over the long run can win money betting ever. So I'm sure the truth is somewhere in between those two things. It's one of those things where the market is efficient until somebody finds an advantage, and in finding an advantage, you prove that it's not. It's like the black swan theory where you can say all swans are white, and the only way to disprove that is by finding a black swan, but there really is no way to prove it. There's no way to prove a negative.

How would you prove that Pinnacle's markets are efficient? The only way to do that is to say that it's impossible to win money over the long run betting at Pinnacle, and I'm sure that's false. You can prove it's false just by finding examples of them. But there's really no way to prove it true. Sorry, I'm rambling a bit here, but the point of all this is the efficient market hypothesis, there are ways to disprove it, but there are really very few, or no ways, to prove it. No matter how strongly you believe it.

Ben:

When you first answered the question, you suggested that closing line value is one potential measure of success. I'd be interested to know, from your perspective, what is another option?

Matt:

There are really only two I can think of, and one is closing line value, and the other is actual results. Maybe there are others out there, I'm just not thinking deeply enough about it, but those are the two obvious ones. And of course, closing line value has pros and cons, and actual results have pros and cons. The biggest con with actual results is again, that variance, that random noise that is going to be very much present, especially in a small sample of actual results. So of course, results are the most effective way to measure the success of a model, or a better, or a tipster, or anybody, but the number of results you would need to qualify someone as good or bad with a relatively high degree of confidence may take hundreds or even thousands of bets to ever get there.

So, all you can do is just have degrees of confidence, where okay, this person has returned 3% return on investment over 200 bets, am I 99% confident that they're +EV? Probably not. Am I 60% confident they're +EV? Yeah, I probably am. So, you leave the realm of black and white, and you start operating in shades of grey, or shades of probability, or shades of confidence. And again, at the risk of having another shameless plug in there for Bayes' Theorem, and Bayesian inference, this is a natural fit, because you have a hypothesis out there that Person X, or Model Y, has positive expected value. You can't model it directly. You can measure it indirectly, but that will only give you a degree of confidence in a proposition. It will never give you definitive proof that the answer is yes, this person knows what they're doing, or no, they don't. So it really is a natural fit for Bayes' Theorem and Bayesian analysis.

Ben:

Let's try and, for the benefit of our listeners, let's put together all this insight that you've shared, and try and help them out. I mean, people will bet for many different reasons. They're often categorized as square or sharp and stuff like that. I'd like to know from your perspective, what do those terms mean, square and sharp?

Matt:

Well, square and sharp are very general, vague terms. If I had to define them, I'll define them in an equally vague way, to fight fire with fire. I would say a square is someone who believes they have positive expected value in their bets but doesn't actually have it, and a sharp is someone who believes they have positive expected value in their bets, and does actually have it. And that really translates nicely into the discussion we just had, over how do you know if someone has positive expected value? You can measure it with closing line value in some circumstances, but not in others. You can measure it with actual results. If your sample size is large enough, you can have degrees of confidence that someone is a sharp versus a square. But that's how I'd characterize it in general, is sharps win over the long run and squares don't.

Ben:

Whether they are square or sharp, and if sharps do win in the long run, they still probably hold some common misconceptions, or they might fall foul of some of the mistakes that bettors tend to make. So what would you suggest people guard against? Or one message to give out there to people listening?

Matt:

This is an area where I think the canon of Pinnacle betting resources does a great job of really describing. The article on the green lumber fallacy. The article on cognitive bias is another great one. So there's really not much I can say to stuff you've already got there. I think that the biggest challenge for betters, especially amateur betters, is that the human brain has not evolved to make complex decisions in the face of uncertain outcomes. We have evolved mental shortcuts, or cognitive biases, that can very often mislead us, or steer us wrong, when we're trying to do something like estimate the probability that a given team will win a given sporting event. It's just not how our brains are wired.

So, the first step is to train yourself to recognize where your reptile brain might be steering you wrong, and then from that you can start to build more data-driven methods, obviously influenced by domain knowledge, like we talked about earlier, but the biggest thing that beginners can do is learn to recognize when those cognitive biases are popping up in their brains. Because they will never stop popping up. They pop up in mine all the time. You can't turn them off. The best you can do is train yourself to recognize them.

Ben:

It seems that there's so much focus nowadays on data and statistics that psychology, I guess, is almost an afterthought. So I guess I replicate that message and conformation bias, hindsight bias, any cognitive bias out there, is something, pick up on it, address it, as you said. No control, but awareness is the key, I guess.

Matt:

Yeah. I was fortunate enough to do a lot of my studying both on the actuarial side and on the betting side, at a point in time where behavioural economics and irrationality and prospect theory, all these things were really in vogue, let's say, five to 10 years ago when I was starting to study these things. So they really helped to inform my outlook on things like this, and probably yours as well, as a bookmaker. And you can tell from the articles you guys have published on it, I think it's a very, very important skill, not just for betters. I mean, betting is an obvious application of it, but we all make decisions under uncertainty every day of our lives. So even to take ourselves outside of both the actuarial space and the betting space.

One of the best things anybody can do to help them make better decisions in all facets of life is to study and read about our own cognitive biases. Why they happen, and how to learn from them, and how to avoid making mistakes.

Ben:

I mean, it's an intriguing subject, Matt. I'm sure we could turn that into a podcast on its own. And I don't want to put any more targets on your back, so unfortunately I think we'll have to call it a day there. It's been a pleasure speaking to you, Matt. I'm sure our listeners have enjoyed it. So thank you very much for coming on.

Matt:

All right. Thanks a lot, Ben. Have a good day.

Ben:

And Matt is on Twitter with a rather fitting handle, @PlusEVAnalytics, and as always, if you want to learn more about betting, visit Pinnacle.com/BettingResources and follow @Pinnacle on Twitter. Thanks for listening, and bye for now.

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