Wow, this story is horrible. It starts out innocuously enough with some boardroom shenanigans:
In September 2021, an official in Michigan State University’s athletic department sent an email to his boss with exciting news: An online betting company was willing to pay handsomely for the right to promote gambling at the university.
“Alan, if we are willing to take an aggressive position, we have a $1 M/year deal on the table with Caesar’s,” Paul Schager wrote to Alan Haller, the university’s athletic director. . . .
Unlike public universities, which are subject to government disclosure rules and freedom of information requests, the sports-marketing companies are privately held. That means the terms of the deals they strike don’t have to be publicly disclosed if the universities are not a party to the contracts.
Hey, don’t they know it’s “Caesars,” not “Caesar’s”? A bunch of ignoramuses there, is what we’ve got. In any case, can’t they just follow the path of their Big Ten rivals at Ohio State and get their ill-gotten gains via government grants for fraudulent research?
But, hey, it’s cool, all explained in Newspeak for you right here:
Mr. Schager, executive associate athletic director at Michigan State, described this benefit of the system.
“With the multimedia rights holder, public institutions like Michigan State no longer have to disclose all those sponsorship deals,” he said in an interview. “This helps with the sponsors being able to spend what they feel is appropriate without having the public or employees or stockholders question that investment.”
The Michigan State athletic department . . . What could possibly go wrong?
But then there’s this:
Some aspects of the deals also appear to violate the gambling industry’s own rules against marketing to underage people. The “Responsible Marketing Code” published by the American Gaming Association, the umbrella group for the industry, says sports betting should not be advertised on college campuses.
And this:
The University of Maryland, for example, has a partnership with the sports-gambling platform PointsBet. A university website links to a PointsBet page that entices new customers this way: “Get your first bets risk free up to $2000 + $100 in free bets.” The pitch means that if you lose your initial $2,000, PointsBet will let you make another $2,000 worth of complimentary bets. . . .
The University of Maryland! I was gonna say that they haven’t had any major scandal since 1986, but then just to check I googled *university of maryland athletic department scandal* and . . . yes, they’ve had major scandals since then.
And this doozy:
Cody Worsham, L.S.U.’s associate athletic director and chief brand officer, said in a statement that Caesars and the university “share a commitment to responsible, age-appropriate marketing.” That commitment, Mr. Worsham added, “is integral to a sustainable and responsible partnership benefiting our entire department, university, and fan base.” . . . At L.S.U., Caesars promotions downplay the risk of losing. In an email, gamblers were told they could bet “on all the sports you love right from the palm of your hand, and every bet earns more with Caesars Rewards — win or lose.”
LSU, huh? I guess they have some need of a “chief brand officer.”
This one’s pretty good too:
In 2020, Texas Christian University, in Fort Worth, joined WinStar World Casino and Resort to open a new club with suites and premium seating.
I haven’t kept up on which religions currently allow drinking, betting, and dancing. What next, rock ‘n’ roll?
I can’t wait till Columbia gets its own sports betting contract. It’s been a few years since Columbia’s been to a bowl game or the NCAA tournament, but we could always bet on movements in our U.S. News ranking or things like that. No possibilities for insider trading there, right??
P.S. That all said, I’m a Michigan football fan. Not a lot—I don’t really follow college sports at all—but a little, partly because my sister teaches at the University of Michigan and partly because my dad hated Woody Hayes. And I enjoy betting on sports from time to time. Betting is fun, in moderation. The thing that bugs me about these gambling companies is that their business model seems to be based on getting addicts to gamble more. As I wrote a few years ago, as a statistician I am pretty disgusted about articles that celebrate the use of statistics to rip people off. This might be the same way that, if I were a programmer, I’d dislike articles that glamorize the hackers who scam people out of their passwords. Yes, statistics can be used for all sorts of bad ends and this should be vigorously reported. But not celebrated.
I believe it was Cory Doctorow who pointed out that Ceasars would only spend $1 million on advertising at the college if they expected to get significantly more than $1 million in revenue as a result. So, the university essentially brokered a transfer of money from their students to Ceasars, taking a cut in the process.
For a while I had a model for college football that looked to be a winner. After a few weeks it stopped winning. What I learned from that was essentially that early in the season people’s assessment of teams was biased too much by historic records, and a low information prior led to better assessment of underdogs for around 5-6 weeks at the beginning of the season than the high information priors implicit in the betting markets.
Unfortunately the one person who put money on my predictions lost it all because the one biggest longshot bet wasn’t being offered at the government monopoly sports casino they used. That was the only bet that did pay out that week and it paid out 24 to 1 at casinos that did offer it. Continuing to follow the season these underdog longshots disappeared by week 5 or so and then there was no real money to be made.
The upshot of it is, the more competition in these casinos business the better, and stay away from this industry in general. There are many ways for the casinos to squeeze out people who consistently win, it’s an industry best thought of as an entertainment venue similar to taking your car to the race track or amusement parks with rides and crazy expensive hot dogs. It’s also an industry that preys on addicts, yes.
How could you tell it stopped winning after a few weeks, lol? You’d need at least a season’s worth of data (probably more) to make any statistically meaningful inferences about changes to the profitability of your model.
This sounds like a NHST-caused problem on your end.
I could make statistically meaningful inferences after only a few datapoints, fairly sure Daniel could too.
Like if 37 patients died in group A vs 33 in group B. It seems like “magic” to some people that you can draw inferences from such data, but it is quite simple. Just ask meaningful questions rather than stuff no one cares about like whether a difference is due to “chance”.
Not a NHST problem. If I’m betting on coin flips and my model says the coin is biased and actually has a Prob(Heads) = 52%, it will take a lot of coin flips to figure out if I’m right.
This is sports betting in a nutshell. Typically takes 1000s of bets to say anything meaningful about which model is better.
Well, as Andrew points out the actual coin flip is never biased: https://www.tandfonline.com/doi/abs/10.1198/000313002605
But if you flip once and it comes up heads you can infer there is not 0% of heads (ie, it is not a two tailed coin). And the more you flip the tighter the bounds on the results of the flipping procedure. So you can infer useful conclusions even if you cannot tell the difference between 50% and 52%.
Well, I made predictions every week for the rest of the season but didn’t bet on them. It was clear the mechanism in the first few weeks was that “longshots” were paying out a lot more often than “the market” thought they would, after a few weeks there were fewer longshots offered, and those that existed didn’t pay out often by comparison. It makes perfect sense that in the start of a new season with new players (college football has a lot of turnover due to graduation etc) people’s expectations may be biased away from reality by last seasons information etc.
Okay if you just noticed that your model didn’t disagree as much with the market later in the season, then I can see your point.
But there simply isn’t enough data to say whether or not longshots were paying out too much or too little at various points of the season – it will be swamped by noise. Again, in sports betting we are talking about small edges (EV of 1%-6%, at most, because the markets are pretty efficient). So the idea that you could detect that the market is offering an implied price of 20% on longshots but the true price should be 21% within a season is just silly.
If you think your edge was like 20% or something, then you are just misguided.
Matt, I wonder if you’re underestimating how many college football games there are each week. I’d agree with your point if it were the pros, but there are a ton of college football games.
Also the fact that a particular longshot was not offered is not why you lost, really. Ex ante all that would mean is that there was one less bet you were able to bet on out of all the bets your model deemed to be “positive expected value”. It doesn’t change whether all the other bets you made were +EV, or not.
Sounds like you are a bit over your head here Daniel…
Umm, no, the algorithm picked an entire portfolio of bets allocating different bet amounts to different plays. When one of the important bets that algorithm assumed was available failed to be available, the portfolio was no longer a good portfolio. Pretty simple really. If I offer you the S&P 500 but excluding Apple, Google, Microsoft, Exxon, and BofA, pretty obviously it’s no longer as good a choice of investment as someone who’s offering the full S&P right?
What do you mean by “as good?” It’s less diversified, yes. But the S&P itself is not very diversified compared to the Russell 2000. Lower expected returns? There’s no reason at all to expect so, and famous theorems which say the opposite. (Theorems which are no better than their premises, of course.)
What? All of these bets are uncorrelated, so your portfolio is not relevant. (We can just assume you are risk-neutral given that you weren’t betting a significant amount of your wealth, presumably).
Your model would never be betting on negative EV bets, so excluding one bet wouldn’t blow up your portfolio. It would just make it slightly less positive EV.
“Bet if positive expected value, don’t bet if not” is not a good betting strategy, and # of winning bets vs # of losing bets is not a good evaluation.
Suppose a casino offers 1000:1 odds on events with true odds 100:1. If you put $1 over and over, you would lose a little bit of money most days and win a lot of money a few times, but come out net positive. That’s what Daniel is saying; the “losing sides” of the bets are systematically undervalued.
The problem here is that the software assumed “complete markets.”
Hm? This makes no sense. “Bet if +EV, don’t bet if -EV”, is absolutely a good strategy, you’ll have to elaborate on how it’s not. Obviously you can’t evaluate this strategy with number of winning / losing bets (unless the odds are always Even), but you can evaluate it with total profit.
The only time it can be optimal to take a -EV bet is to hedge, to ensure that your bankroll stays large enough to make the bet sizes you want to make the next day.
In your example, I don’t see the point. Yes, if you are betting on Longshots and you remove the bet where you finally hit the Longshot then this won’t be good for you. But why would do that? Ex ante, if I tell you that the bets from day X will be removed (without knowing the results of the bets that day), this has no effect on your expected profit except that it’s slightly lower (from having 1 less day to exploit your edge).
If in Daniel’s example the only Longshot bet that was mispriced was the one he couldn’t bet on… then yes, that’s a problem lol. But I don’t see how that relates to the other bets he was making. Unless there is some complicated hedging strategy going on that Daniel didn’t specify.
Always fun to see the direction taken by these discussion threads.
The classic example is a coin toss where heads multiplies your wealth by 1.5, tails loses 40%. As number of iterations increases to infinity, your wealth converges in probability to 0.
A portfolio of bets has lots of things to take into account. You have to take into account non-independence between bets and a finite shared pool of funds. Evaluation requires looking at the entire portfolio of bets and the total pushforward wealth distribution. I’m not saying that I know Daniel did it right; there’s not enough information here to say so, I’m just saying that this way of looking at it in terms of “positive EV bets” and “negative EV bets” is all wrong.
We are talking about sports betting, so correlatedness isn’t a consideration (unless you are betting on the same outcomes in a game).
As for your example… ya that’s pretty weak. Why make it that complicated? If I bet 100% of my wealth every time I bet then it doesn’t matter what my edge is, I’ll eventually lose all my money.
As I said below, the only time you’d take a -EV bet is to hedge (for bankroll considerations going forward). But given that virtually all bettors are not betting with a significant % of their total wealth, this can almost always be ignored. All that matters is your edge. And you can do some bet sizing stuff with the Kelly Criterion if you want.
Basically it’s very, very likely that given Daniel’s application (betting a small % of wealth on college football games), the only relevant variable here is the expected value of each bet.
I don’t understand your example at all. A bet where your ending stake is either 1.5x or .6x with 50-50 odds is a negative EV bet.
@Jonathan
Let’s say I put up $100. 0.5 * 150 + 0.5 * 60 = $105 > $100.
@Matt
Well, you’re not betting 100% of your wealth every time, you’re betting 40% of your wealth. Yeah, as you point out, you can choose some optimal x% by the Kelly criterion that maximizes long term growth almost surely.
You take bets on the spread. You can take the bets team A will win by 3+ and also that team A will win by < 1. So, there are correlated outcomes in sports betting without taking opposite sides of the same bet.
Yes, if you ignore risk appetite and risk management, you should always take a positive expected value bet. But people do put nontrivial sums down to actually make money, not just for fun, so I don't really understand the point of your comment.
> A bet where your ending stake is either 1.5x or .6x with 50-50 odds is a negative EV bet.
The (probability-weighted) average ending stake is 1.05 and that’s not a negative EV bet – at least with the usual interpretation of “negative EV”.
@somebody Nope. I said “ending stake,” not the amount won or lost on any particular bet. In N plays starting with stake y, your expected result is (1.5)^(N/2) x (.6)(N/2) x y = (.9)^(N/2) x y, which is less than y for all positive integral N, including N=1
> In N plays starting with stake y, your expected result is (1.5)^(N/2) x (.6)(N/2) x y = (.9)^(N/2) x y, which is less than y for all positive integral N, including N=1
Let’s fix y=1 for simplicity. You say that (I fixed a couple if errors: a missing ^ sign and a N/2 that should have been just N):
> your expected result is (1.5)^(N/2) x (.6)^(N/2) = (.9)^N
That’s definitely not what is commonly understood by “expected value”.
> which is less than y for all positive integral N, including N=1
For N=1 you say that the expected result (ending stake) is 0.9
How is that the expected value of the ending stake – and not the average of the equally probable values of the ending stake 1.5 and 0.6?
The (thing usually called) expected value for N=1 is 0.6*1/2 + 1.5*1/2 which is larger than 1 (for every natural number N).
I have seen this example many times. And my explanation here was (I admit) somewhat inarticulate. But the right way to see this problem is to break it into two parts. In N (N even) trials, the number of wins follows the binomial distribution, which has mean N/2. Further, as N grows, N/2 grows more and more modal.
I keep meaning to write this up and never have. And yes, the one time play has positive EV.
For N = 1 trials, the expectation is
0.5 * 1.5 x + 0.5 * 0.6 x
by the law of iterated expectations, for N = 2 trials, the expectation is
0.5 * (0.5 * 1.5 * 1.5 x + 0.5 * 0.6 * 1.5 x) + 0.5 * (0.5 * 1.5 * 0.6 x + 0.5 * 0.6 * 0.6 x)
where the parentheticals are conditional on a first time victory and a first time loss respectively. This suggests the form for the final expected multiplier (which you can show inductively)
\sum_{k = 0}^{N} \binom{N}{k} 1.5^{k} 0.6^{N – k} 0.5^{N} = (\frac{21}{20})^{N}
which is positive and increasing for all finite N. You can show this easily by simulation if you don’t believe me, though for large N the variance becomes huge very quickly.
Exactly what somebody said. The portfolio procedure looked at the entire push forward wealth distribution under a nonlinear utility function. It routinely won 20-30% per week for several weeks early in the season and then it’s edge went away and couldn’t beat the vig. It had the edge in the next season as well for a few weeks. In the end though the advantage wasnt worth the hassle of trying to turn that into a business particularly since there is no real legal market in CA. The fundamental edge was due to not evaluating underdogs too strongly based on historical information compared to the market.
The govt run market in the one place where my friend tried placing bets was much more risk averse and just didn’t offer the longshot bets that MGM and others like that would offer. Since those were were my strategy made it’s money, the monopoly prevented us from exploiting our ability to better predict. More competition is better that’s the moral of the story as I see it.
Also this is not Frequentist coin flipping theory, this is Bayesian models, all the underlying evaluations of the teams ARE correlated, and you look at samples from your posterior predictive distribution. For example if some particular parameter is a little higher, then potentially all the underdogs should have a better chance of winning. If it’s a little lower, then all of them have less chance of winning… Or maybe those teams you have more observed games, or those teams that have played harder teams to beat or whatever may all move simultaneously in your assessment of them. In the end you’re talking about a complex manifold in 200 dimensional space.
Frequentist theory is just wrong. We aren’t betting on the outcome of uncorrelated stable random number generators in the long run, we are betting on specific outcomes of specific games between specific teams at specific times with specific injury rosters and specific coaching changes and with the historical data on specific matchups between specific pairs of teams.
> I have seen this example many times.
That makes you initial reply to somebody “I don’t understand your example at all” more puzzling. The interest of the example is to show that “expected value is positive but…”
> the right way to see this problem is
Maybe, but that doesn’t change the fact that the expected value is positive (always – not just for the one time play).
Of course, one can also discuss things which are not the mathematical expectation or the expectation of things which are not the value. It may be better to avoid calling them EV, though – or at least the redefinition of terms should be explicit.
This is just classic Lakeland making things unnecessarily complicated.
The idea that your entire strategy for betting on college football would get blown up because certain underdogs weren’t offered is ridiculous. If those were the only bets that showed value, then sure, you can’t implement your strategy. But it’s not like the rest of your portfolio was -EV if those underdogs aren’t included. If it was, then my question is why were you betting on games that had -EV according to your model? If it was to reduce the variance of your wealth going forward then that would be very surprising to me, given that it doesn’t sound like a big chunk of your wealth was involved in this.
At the end of the day, the only relevant variables here are the book’s implied probability and your model’s probability for each game. To say otherwise is just an attempt to make your project look more complex than it was.
Matt, I don’t know what you’re talking about. My project evaluated individual games based on some predictive models. The predictive models told me that multiple underdogs were poorly priced. After several weeks “on paper” of winning consistently, I came up with a portfolio of bets that I believed would be net positive and a friend tried it out. The one week that someone actually placed money on the predictions, the one bet that would have hit and paid off something like 24x wasn’t available at the monopoly govt run site in his region. They placed the remaining bets, and because of that the whole portfolio wound up negative. If the play would have been available, the whole portfolio would have been positive, and considerably so. This is an indisputable fact of the way it worked out. Now you’re on the internet telling me it didn’t happen like you’re some kind of expert on my personal history.
If your point is that it’s high risk to bet on underdogs that are paying out 10-25 x, and that you’re at risk of losing everything, then yeah sure it is. There is nothing controversial about that. If your point is to somehow pretend that the existence of a monopoly preventing my friend from placing all the bets the algorithm called at market rates didn’t cause the portfolio to be a net loss, then get lost. I’m not interested in you telling me that things that happened to me didn’t actually happen because you say so.
Originally, my only stake in this discussion was to address this mentality
Because it’s just mathematically incorrect, and in my opinion a pretty irresponsible thing to say. You’ve added in a little stipulation “for small sums”, and yeah, for small sums utility of money must be approximately linear, but you don’t know how much is actually being bet here.
It seems like you just didn’t like Daniel’s confidence and jumped what seemed like a chance to make a correction. But it seems like you’re coming at this with little knowledge of sports betting and risk management, and it’s guaranteed that you have none of the necessary details of Daniel’s implementation for a meaningful criticism. Assorted observations:
1. There are over 1500 college football games per season, so I’m not sure what you’re on about with respect to insufficient data
2. Sports betting is not a single binary outcome per game, there are all kinds of bets you can take that are non-independent in interesting ways
3. Again, a portfolio is *not* just the sum of individual bets, and bets that don’t make sense on their own can make sense in a portfolio.
4. Even so, nobody said the other bets were negative EV or that the whole strategy hinged on one bet. What was said was that one week, the strategy would have paid out but didn’t due to incomplete markets, and nobody put any money on it after that. Daniel himself put 0% of his wealth into the strategy.
somebody: thanks.
What I was claiming was that during a certain part of the season there was a strategy that would have made money for several weeks in a row (based on predictions it made before the games occurred) and that in the one week a friend tried it out he wasn’t able to place all the plays, and the one he wasn’t able to play was the only one that won. If the bets had been placed in say Arizona where all the bets were available, the overall portfolio would have doubled his money or something like that. Monopoly betting markets are bad for consumers for reasons like this.
End of story. It’s really not that hard.
> nobody said […] that the whole strategy hinged on one bet. What was said was that one week, the strategy would have paid out but didn’t
It was said that “When one of the important bets that algorithm assumed was available failed to be available, the portfolio was no longer a good portfolio.”
Not being a good portfolio seems different from not paying out in a particular week.
I doubt that this was some kind of arbitrage that makes sense only when all the pieces are available – and it that case one just doesn’t do it if they are not!
Having the possibility to include that long-shot bet that happened to pay off would have made the portfolio a lucky one, that’s for sure.
Carlos, when I said it was no longer good, I meant ex-post. It turned out not to win.
I didn’t rerun the model in the absence of that one bet to determine whether it would have chosen to bet on the same things if that bet was unavailable. In the absence of that one bet it may have decided that the overall distribution of outcomes was insufficiently good to compete against the strategy of leaving your money in the stock market, which was the alternative it compared to. Perhaps in the absence of that one bet it would have said to stay home and enjoy the games and keep your money in the stock market. Or perhaps it would have said to bet half as much total so the losses would have been considerably less.
Whether the strategy would choose to bet and the amount it chose to bet was determined by the total stake, the available alternative investments (a high yield dividend ETF), the volatility of that index, the risk tolerance of the bettor, and the entire posterior distribution of the portfolio payout on the bets. The posterior predictive payouts were **certainly** correlated through the fact that there were correlations (in general, dependencies) in the underlying unobserved parameters. For example if in one MCMC sample for the parameters of all the teams, an underlying parameter for a given team were higher, then most likely also for that sample the estimates of the parameters of various other teams might be either higher or lower depending on historical outcomes etc, thereby changing the probability of wins in multiple games. The model most certainly did NOT assume that each game was an independent coin flip with a fixed but unknown probability of a payout. That would by comparison be a terrible way to evaluate bets, and that gets at what “somebody” was talking about.
This whole thing was essentially Bayesian Expected Utility Maximization writ large. The core ideas of that are not secret.
In the interest of being 100% honest, I don’t actually remember at what level of sophistication the whole thing was at at the time of this particular anecdotal event. It took time to code all this up and it didn’t spring out fully formed in Julia code all at once. It doesn’t really matter for the point that monopolies are not good. By mid season the whole expected utility optimization technique was in place, and the market had converged to eliminate the poor pricing of the outliers. It was an interesting exercise, and let me get my hands very dirty with hard core Julia coding so it served multiple purposes.
> when I said it was no longer good, I meant ex-post. It turned out not to win.
In that was the meaning the rest of your comment didn’t help to make that clear. Quite the contrary.
> When one of the important bets that algorithm assumed was available failed to be available, the portfolio was no longer a good portfolio. Pretty simple really. If I offer you the S&P 500 but excluding Apple, Google, Microsoft, Exxon, and BofA, pretty obviously it’s no longer as good a choice of investment as someone who’s offering the full S&P right?
If “no longer a good portfolio” in the first sentence means “it made money that week if that bet was included but it didn’t if that bet was left out”, what does “no longer as good a choice of investment” mean in the last sentence?
Are you thinking of some particular week when the S&P performed better than the S&P ex-Apple/Google/Microsoft/Exxon/BofA so the former was a good choice of investment and the latter was (pretty obviously!?) no longer as good a choice of investment?
Or is that example – and its use of “good choice of investment” – unrelated to the idea of being or not a “good portfolio” in the betting case?
Carlos,
I meant in reference to a monopoly preventing you from investing in what I assumed have been high performing components of the S&P. What would you rather have, the ability to invest in whatever you want, or some entity controlling the entire market and forcing you to take a portfolio minus whatever they don’t want you to have?
somebody…
I actually do know a lot about sports betting. I’ve been running a subscription-based sports betting website for 5 years now.
To your points.
1. “There are over 1500 college football games per season, so I’m not sure what you’re on about with respect to insufficient data”. This is a tiny sample size when trying to determine whether you have a small (1-3% edge) over the market. Something in the range of 10k bets is required to say something meaningful. Further, Daniel was claiming that he was able to tell at various points in the season whether underdogs were priced too long (i.e. their true price should have been 2-3% different at different parts of the season). N=1500 over the course of a season is woefully insufficient to say something like this.
2. “Sports betting is not a single binary outcome per game, there are all kinds of bets you can take that are non-independent in interesting ways”. Yes of course, but I can almost guarantee you that Daniel was betting on a binary outcome (either spread or moneyline). Especially considering it was through a government-run operation, which has limited offerings.
3. “Again, a portfolio is *not* just the sum of individual bets, and bets that don’t make sense on their own can make sense in a portfolio.” Can you give an example? Again, I’m assuming that he isn’t betting on multiple outcomes within the same game. So the bets will be independent. I’ll stand by my claim that the only time you’d make a bet that doesn’t make sense on its own (i.e. is -EV) is if you are hedging. From what Daniel said, he was sampling from a posterior predictive distribution so I can see a reason why he would bet a small amount on a -EV bet: because there is a small probability that the parameters in his model are such that that’s actually a +EV bet (even though, overall, integrating across all parameter values it’s -EV). That was an interesting point by Daniel.
4. “Even so, nobody said the other bets were negative EV or that the whole strategy hinged on one bet. What was said was that one week, the strategy would have paid out but didn’t due to incomplete markets, and nobody put any money on it after that. Daniel himself put 0% of his wealth into the strategy.” Ya my point here is just that it’s odd Daniel is focusing on the result of 1 bet that wasn’t offered. If that bet had lost I’m sure Daniel would not be raving about how incomplete markets were the demise of his profitable betting strategy. Honestly, it appears, reading through Daniel’s comments again, that this winning longshot not being offered is the primary basis for his belief that “competition helps bettors” (which it does, of course). My point is that, PRIOR to the implementation of this strategy, complete markets was certainly not a requirement for profitability. You would just not be able to bet on that +EV longshot. But the rest of the portfolio would not be affected (unless it was an arbitrage strategy, as someone else mentioned – but again.. we know it wasn’t because arbitrage doesn’t really require a complicated predictive model).
More generally, I get where you guys are coming from with bankroll management and utility functions. But I guess my point is that these are basically ignorable in the sports betting world relative to whether or not you have an edge (i.e. you have a model that can identify +EV bets). Sure, you can construct toy examples where repeated +EV bets leads to ruin, so bankroll management is not irrelevant. But it’s not that important, and simple heuristics will serve you fine. It seems like you are coming at this problem from an academic perspective, while I’m coming at it from a practical one, so maybe that’s why we are butting heads. And yes, Daniel’s confidence does rub me the wrong way so that is why I took a certain tone with him.
Okay, also just read this comment from Daniel that starts:
“Carlos, when I said it was no longer good, I meant ex-post. It turned out not to win…”
I’ve got to say, this seems like a really good example of Daniel just over-complicating things for no reason.
“I didn’t rerun the model in the absence of that one bet to determine whether it would have chosen to bet on the same things if that bet was unavailable. In the absence of that one bet it may have decided that the overall distribution of outcomes was insufficiently good to compete against the strategy of leaving your money in the stock market, which was the alternative it compared to. Perhaps in the absence of that one bet it would have said to stay home and enjoy the games and keep your money in the stock market. Or perhaps it would have said to bet half as much total so the losses would have been considerably less.”
If you are betting on sports, we are talking about annual returns on investment that will be in the 70-100% area, if you have a meaningful edge. If you are only earning 6% annually betting sports (and you are making a lot of bets, as it seems this strategy was), the size of your edge / bet has to be some tiny fraction of a percent, and it will be hopeless to determine whether or not you have that edge in your training sample. (The reason for this is that you roll over your money many times in sports betting in a year, so a 1% edge translates into big returns on capital for the year). So I don’t really know why Daniel would be comparing this to the stock market, my guess is he just made that up right now to rationalize his ‘portfolio’ comment, which makes no sense without claiming that he was comparing that portfolio to some other positive-return vehicle.
“Whether the strategy would choose to bet and the amount it chose to bet was determined by the total stake, the available alternative investments (a high yield dividend ETF), the volatility of that index, the risk tolerance of the bettor, and the entire posterior distribution of the portfolio payout on the bets. The posterior predictive payouts were **certainly** correlated through the fact that there were correlations (in general, dependencies) in the underlying unobserved parameters. For example if in one MCMC sample for the parameters of all the teams, an underlying parameter for a given team were higher, then most likely also for that sample the estimates of the parameters of various other teams might be either higher or lower depending on historical outcomes etc, thereby changing the probability of wins in multiple games. The model most certainly did NOT assume that each game was an independent coin flip with a fixed but unknown probability of a payout. That would by comparison be a terrible way to evaluate bets, and that gets at what “somebody” was talking about.”
If you compare the suggested bet sizes on each team if you were to take your model and generate simple win/loss probabilities for each bet (by sampling from your posterior predictive distribution, or however you like), and then use something like the Kelly criterion to inform your bet sizes, they are going to be very similar (in a relative sense) to the bet sizes you get from this fully-simulated approach. With full simulation, you’ll have a small amount of money on bets that were -EV, but the success of your strategy will hinge on the teams that are deemed overall +EV (using the probabilities that integrate over all parameter values, or whatever the correct lingo is) winning. In fact, it’s kind of pointless to do the fully-simulated approach because you’ll just end up hedging slightly which requires more of your money being in play. Instead of betting 10 units on team A and 1 unit on team B (as the fully simmed approach might tell you to do), you could instead just bet 0 on B and some smaller amount on A to mimic these payouts.
When the story broke last year, I wrote to Andrew at that time,
“If you want to blog on this, I suggest you ask your bloggers as to what is the next logical step for a university portfolio enhancement. In keeping with the theme, make it a betting game.”
The current university hot topic in my immediate neighborhood is the firing of an adjunct art history teacher; the university’s portfolio enhancement is likely to be under stress and in need of assistance.
Paul:
The solution is obvious: sell some art.
A problem with Andrew’s blog is that it can be out of date by the time of the posting. Today’s topic appeared in the NYT back on November 20, 2022 which is, roughly speaking, antiquity. The hot topic of today is George Santos suing Baruch College because his knees were ruined playing volleyball on its winning team.
https://www.lgbtqnation.com/2023/01/george-santos-lied-getting-double-knee-replacements-due-star-college-volleyball-career/
By the time this makes it into this blog, no telling where Santos will be. And, you can bet on that.
Well, I know its not gambling (of a sort), but Columbia could always try to reprise the “Strickman Filter” https://www.wikicu.com/The_Strickman_Filter
Anon:
Too bad Dr. Oz isn’t around anymore, or he could endorse something or another for the university.
what are the five ways to get fired from Little Ceasar’s?
There are also non-probabilistic aspects that have to be accounted for when building a betting portfolio. Back in 1964 I decided to exploit the availability of people who were willing to take mispriced bets on the presidential election. I selectively bet with people, taking different sides at different odds and different amounts. My book was balanced in such a way that I was guaranteed a net positive return no matter how the election turned out.
I lost my shirt because I paid out on all the bets I lost, but many of my counterparties defaulted on the bets that I won.
Just sayin’.
Counterparty risk is hugely underestimated in general. Most people don’t realize the legal framework is in place for Cede and Co to take control of their stocks and for their bank to use deposits for a bail-in.
> Most people don’t realize the legal framework is in place […] for their bank to use deposits for a bail-in.
Don’t panic, people: that affects amounts above the federal deposit insurance coverage limit. (On the other hand, it may also be true that most people don’t realize that bank deposits are not riskless, that the FDIC exists, and that deposits are insured only up to some limit.)