Crunching the NumbersJanuary 13, 2010
Why You Shouldn't Bet on Baseball
By Chris Moore

Alternative title to this post: Why Tango Tiger still has a day job

I really enjoyed the feedback to my last article on why umpires should be biased in favor of control pitchers. Most of the folks with a solid statistical background responded favorably, while the unwashed masses thought I was ridiculous and should be run out of the blogosphere on a rail. (Perhaps I don't give the detractors enough credit; if they were washed and educated, then it was an equally entertaining Ask Marilyn-esque experience.) Anyhow, I thought I'd repeat the experience by picking on another low hanging fruit: betting on baseball games. I know a fair number of people who bet on sports. They don't understand that betting on sports is an investment in entertainment, not a viable means of turning baseball knowledge into cold hard cash. This post should be far less iconoclastic than the biased umpire post, but the central point doesn't appear to be widely known.

So here's the skinny: you should not bet on baseball. In the long run, you'll lose. No model that you can develop can be anticipated/demonstrated to beat Vegas. I don't care how good you (think you) are. I don't care how much you think any given line is outrageous. You can't be expected to win. You might think (as I did) that many people who bet on baseball may make poor predictions, and that the intelligent bettor may be able to profit off of them. You'd just have to be better than the average bettor, right? Wrong. I'd argue that Vegas profits off of these folks (because they set the lines), but the rest of us shouldn't get involved.

A couple caveats: First, I've been recording the Vegas odds for a couple years, and have analyzed data for 2007 and 2008. I forgot to download them this year before they disappeared off of the web service I use, so I don't have this year's odds. But I'd be happy to wager that nothing has changed because the system Vegas uses hasn't changed. Second, I am only looking at betting on who wins individual games; there are a number of other bets one could place, and maybe you could make money betting on which pitcher is most likely to start the top of the 7th inning, or which batter is likely to adjust their cup first. I'm not touching those wagers.

In 2008, Vegas came really close to being perfect. The variance between the actual outcome of all regular season games and Vegas' prediction for those games was within the range that one can attribute to random chance. If we start by assuming that Vegas' lines perfectly reflected the likelihood of each team winning each game, the variance between the predictions and the actual outcomes would be greater than it was in 2008 75 percent of the time.

That doesn't mean that Vegas is 75% likely to be perfect. We'd have to go all Bayesian and start assuming silly things to figure out precisely how good Vegas really is. But think about that statistic: if Vegas were perfect, they still would have had a 75% chance of making a worse set of predictions than they did in 2008. So somehow, by hook or by crook, they made some ridiculously accurate predictions in 2008.

It is still possible that the bookmakers got lucky, and that there is money to be made in betting on baseball. So I ran a couple more simulations. According to my numbers, it is crazy unlikely (p<.01) that Vegas is off more than 4% per game. This is because almost all baseball games have a true home-win probability of somewhere close to 50%. Even when the Yankees meet the Royals, the odds aren't far from 50%.

So let's run with my rough estimate that Vegas is off by no more than 4%. In order to make money betting on baseball, you'd have to do better than that. You won't make money if you're just better at chance (i.e., by picking the Yankees every time, or picking the home team every time). If you matched their 4% inaccuracy, you'd lose money a little more often than you won money (on a year-by-year basis). If you barely beat the 4% inaccuracy, with, say, 3.8% inaccuracy, you'd be expected to make a little money each year, but the likelihood that you would lose money each year would still be very high. If you removed 25% of the error in Vegas' estimates, so that your estimates deviated from the true probabilities by 3%, you'd make a profit 73% of the time (again, on a year-by-year 2-3 years out of every ten, you'd net a loss), for an average return of 3 cents on the dollar. I make more than that in my checking account (granted, it's a great rate for a checking account, but still...).

There are enough variables out there that there's a distinct possibility that I'm wrong. If you have the data to demonstrate that you can win reliably, I'd like to see it. But until then, I'm sticking with the numbers, which say that Vegas is really, really good, and you'd have to be considerably better (25% better) to even make a decent return on your investment.

I also have a novel answer to the question: "If you're so smart, why aren't you rich?" Because I'm smart enough to know it's a scam. Flame away :)

Update 1/14/2010

Following this post, there were a number of replies, mostly harsh ones. I expected nothing less, since there are far more people invested in baseball betting being a sound investment than the alternative. In fact, I was hoping for it; my initial analyses were run to see how large the margin for potential profit was for my own practical purposes. In the comments, I promised that if someone posted verifiable data that demonstrated that I was wrong, I would say so. I'm going to relax that standard and give Umaga credit for making a reasonable argument that I found convincing along with his own purported ROI.

Based on responses like those made by Umaga, I'll change my position: (1) No one can make money betting on the closing line, or lines that end up looking very similar to the closing line; (2) if you can predict which opening lines are particularly poor, and you bet early enough, you may be able to make money. In summary, I'd say that there are a small few (yes, likely financial quants, or ex-quants) who can leverage the peculiarities in the system to make money. I have no data for this, but I'm convinced that it's true. But for a vast majority of people, betting on something that looks like the closing line, you're not likely to make money.

Some have commented that a bookmaker's job is to balance the books, and to some extent to exploit known biases in bettors (such as to exaggerate the probability of a favorite, like the Yankees, to win). The story is that this pushes the moneyline away from the "true" probability of each team winning, creating a margin for people to put "smart money" in. I'm fully aware of how these lines are set, and how they change, but it doesn't change the story. If there are any biases such as these, the "smart money" is completely canceling them out. We know this because the closing line is as close to being a perfect measure of game outcome as is practically possible. It does not show the systematic bias that we would expect to see. Thus, if a bettor is going to exploit this, he would have to do so early, before the line drifts towards the closing line.

Others commented that I was being dense, and that "of course" the moneyline makes a "ridiculously good prediction" of game outcome. They argue that baseball betting is essentially a prediction market for baseball game outcomes. These comments absolutely miss the point: (1) a prediction market is not guaranteed to converge at a perfect prediction; (2) even if it *did* converge to the perfect prediction, the 2008 closing lines were better than you would expect a perfect prediction system to be 75% of the time. Kyle is wrong when he says "of course" bookmakers are that good; by random chance we would expect them to be measurably worse even if we predictive markets to converge to a perfect prediction (which seems to be Kyles other point, which, of course, is some combination of silly and naive).

The reason is this (in answer to TomC's question): every baseball game is a Bernoulli trial, that is there are two possible outcomes, home team wins and away team wins. There is a probability, p, that the home team wins, and a probability, q=1-p, that it loses. Thus, each baseball game is essentially a weighted coin flip. A perfect prediction system would have access to the "true" probability of each team winning (p and q). If you were to bet on whichever team has the greatest chance of winning, the outcome of your bet would also be a Bernoulli trial. This means that the variance between your optimal guess and the actual outcome has a known distribution: a binomial distribution. If we know the number of games we bet on, and we know the true odds of winning each of those bets, we can calculate a probability distribution for the variance between the actual outcome and our optimal guess. Thus, we can say things like "There is a 75% chance that the variance between our optimal guess and the actual outcome is less than some number, k."

In 2008, the variance between the bookmakers' closing line and the actual outcome was very small. In fact, it was less than we would have expected by chance 75% of the time.

What does that imply? If you were betting on the closing line, and you had perfect access to the true probability of each team winning, you would still have a 75% of being outperformed by (the average) bookmakers in 2008. If you can't outperform the bookmakers, you can't make money. Thus, you can't play the closing line, or lines that end up being similar to the closing line, and win.

But Umaga's point is a good one and well taken: I said both that you can't make money betting on baseball, and that you can't make money betting on the closing line. But these two claims are not equivalent. In the end, I'm convinced he is correct: I'll stand by the latter claim and back off of the former. You can't make money on the closing line, but you may be able to make money on the opening line or rogue lines (of which there are many). According to this story, making money on sports betting requires the bettor to be clever and look for opportunities to exploit, because the predictive market is really good. So for the vast majority of the sports bettors out there--the ones who don't have MBAs; who haven't had quant jobs at hedge funds; and who don't try to jump on opening lines before they drift away--those folks are buying entertainment every time they bet on a game.

Lastly, I'll point out that since bookmakers take a percentage of the action, this isn't even a zero-sum game; it's a negative sum game. One commenter, Garrett Weinzierl, doesn't like the implication that sports bettors are "all sailing off the edge." But since this is a negative-sum game, most bettors are sailing off the edge. For this system to work, most have to be sailing off of the edge. If you're a sports bettor, I'm not saying you're sailing in the wrong direction. Only Garrett knows where his boat is going. But if you're not at risk for going over an edge, you're an exception to the rule.


Chris, is your dataset available online?


Do you think this holds true for betting on team over/unders before the season. (72 wins for the Rays in 2008) I think there's money to be made there.

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If you want to state a dissenting opinion, that's fine as long as you do so in a civil manner. Calling a writer an "idiot" is not acceptable conduct on this site.

The idea isn't to bet every game, it's to look for inefficiencies in individual lines....and there's enough volume of games to have enough total product with bad lines (e.g. games with national teams - Yankees, Cubs, Dodgers) set to work out a decent amount of the variance over the season. Which is why baseball is the only sport that is beatable over time if you have the skill set and are willing to put the work in.



Thanks for writing this. Do you know anything about how they set the line? How important are the starting pitchers? The old conventional wisdom was that baseball is 75% pitching. Is anything like this reflected in how Vegas sets the odds?


1) Um, you are wrong.
2) What lines are you using - opening, closing,etc? 3) Do you think line moves are instantaneous?
4) Do you understand how closing lines are set?

David, I take data from, but they only keep it until the end of the season. I'd be happy to send you the data I have from 08.

Jeremy, possibly, but why? There isn't enough data to analyze those types of bets, but I don't have any strong intuitions about which types of bets have the greatest margin for nerdy types like us to exploit. Why season wins?

Garrett, how much have you lost betting on sports? :)

Big Dog, in my analysis, I assumed that the bettor bet on every game proportional to the "badness" of the line. In previous versions, I looked into only betting on a subset of games that looked really bad. Vegas still did really, really well. But I guess the point of my analysis is this: that I didn't find any evidence for bad lines. One would expect them to add up in aggregate, but they don't. Have you had reliable success betting using your system?

Cy, I'm not sure how sophisticated the models are for setting the initial line (My guess is they are all very good, but vary in their methods), but the line moves to roughly balance out the value of the bets for the home and away team. If the initial line is poor, it is quickly corrected. Also, since it is risky for Vegas to make bets itself, it's primary goal is not to predict who will win, but predict who will bet on each team (there are other things it can do to improve profits, but these are riskier than balancing the betting).

Umaga, I'm using the closing line. I'd be really intrigued to be wrong. So please, prove it. What makes you so sure? Opinions are entertaining, but since we're talking money here, we need facts. What facts do you have that make you so sure it can be profitable? Open challenge: I'll update the post to include responses from anyone who can back up their positions with data. The Garrett Weinzierl's of the world need only email me their data, and I'll publicly admit they are smarter than I am. I'll bet that doesn't happen, though. :)

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Calling a writer or one of our readers an idiot or a moron serves no useful purpose. If you want to express your disagreement and engage the writer or a reader who has left a comment, then I suggest you do so in a civil manner and by stating the facts or stating an opinion and backing it up with substance rather than hatred. If you can't conform with this simple request, then we will blacklist you from making comments in the future.

I believe the proper title of this article was "Why *I* shouldn't bet baseball." You, quite literally, have zero understanding of how sports betting works. Zero. None. Zip. Nada. Your argument for how good vegas lines are.. is utterly incoherent. However you think you're measuring the accuracy of the lines.. you aren't measuring the accuracy of the lines.

And VEGAS lines, seriously? The first sign of somebody completely ignorant about sports betting is that they think Vegas is more than a drop of piss in a swimming pool in today's betting climate. Vegas doesn't originate numbers. Vegas won't even take a decent bet.

My cat- the one that likes to clean up after me when I drip spooge on the floor- could make money betting baseball. People dumber than that cat make money betting baseball.

1) I'm so sure because I've bet sports as my sole source of income for 3+ years and have made a living at it. I'm a real grown up with a mortgage, property tax, etc - so I'm not talking beer money while living in mom's basement. Previously, I was a quant investment/financial engineer guy with an MBA in Finance/Stats from a very good school so I have a decent understanding of price setting, volatility, etc. I'm part of a loosely affiliated group of ~10 people all of whom are doing the exact same thing as me.

2) MLB moneyline bets only - no run lines, totals, or derivative bets - in the period of Aug 2007 - Aug 2009 I made 2,241 bets and had an ROI (Net Profit/Total $ Bet) of 4.2%. Disclosure: sample size is actually smaller because the same bet at two different books is double counted in the quick calc I did.

I agree with you that the closing WA ( widely available) line is the best predictor of the outcome. However, there are a number of factors you are missing in the price setting process.

a) The existence of rogue lines where books deviate from the market consensus. In other words getting -105 on the favorite, when the market has the favorite at -115.

b) The fact that opening lines are not equal to closing lines and market driven adjustments that move the opening line to the closing line are not instantaneous.

c) You have the very common misconception of how the lines get set (1) over emphasizing Vegas (2) attributing too much of a role to the bookmaker and too little to the market. The scale of Vegas sports betting is a joke compared to the overseas/online market.

The online market is where the prices are set. The process is very market driven - a few books open with lines for the next day's game. They adjust lines as bettors identify edges. Gradually other books post their lines based on their observations of the market. During the rest of the day fluctuations occur due to new bettors, news, etc - resulting in the closing, market consensus lines which you find to be accurate. Successful betting consists of getting numbers during the betting period that are better than the closing WA lines.

This is a rather simplified description ignoring the fact that books also are taking positions vs their customers. The classic case is forcing bettors who favor "public teams" ( Yanks, Red Sox, Cowboys, etc) to take worse odds than an emotionless market process would come arrive at. Obviously, if they deviate too far from "true" this creates opportunities. It also ignores book's desire to adjust for unbalanced action greater than their risk tolerance will accept.

In summary, I agree that the closing WA lines on non-niche bets in general are not beatable after transaction costs. However, your conclusion that baseball isn't beatable is flawed because it ignores the opportunity to get numbers better than the WA closing lines.

(Commenting on your "Bayesian Umpires" pieces, since I don't see an email address for you?)

You said "Under *any* non-flat true pitch distribution, these conclusions hold."

To put the problem in statistical terms: you're assuming that pitch location is a well-defined distribution at all. I.e. that the pitcher, as a stochastic process, is stationary. The pitcher, if he has any brains, is not a stationary process.

Without all the terminology: if you call my borderline results as strikes, then I'll shift my target an inch off the zone.


Wah wah wah. Your comments about substance are rather hypocritical as its rare that someone writes something on the internet that is so absurdly wrong on virtually every front with a complete lack of understanding of the subject. Do you have any clue what he's discussing, since Chris has no clue? Let me list some loltastic errors:

1) Assumption of Vegas as representative of the current betting market
2) No clue how a market works
3) Assumption you bet all games
4) Terribad use of statistical methodologies
5) The assumption that his modeling is superior to all others

And the list goes on. I don't need to e-mail Chris my data, I can instead just go to the local bank, fill my bathtub up with the money, and the send him a picture of myself Scrooge McDucking through it.

Something as simple as the fact that opening lines differ from closing lines illustrates that baseball can be beaten (if the other arguments aren't persuasive in any way).

Chris, I say season wins because it seems to me like PECOTA's projections of the 2008 Rays and 2007 White Sox were actually deadly accurate, and Vegas was off on them. Normally guys make money (or break even) by flat out betting against the public. But when you have a sophisticated projection system that strongly differs from the public, I like to think that there might be value betting on the projection system. I haven't done a study into the matter or anything, but I (have been) willing to put money on it that I'm right .

I don't bet and have no practical (as opposed to theoretical) knowledge of betting.

But it is my understanding that the aim of the house isn't to set a line that correctly predicts the outcome, but to "balance the book."

That said, one can imagine a process that would result in the final line being a very good predictor of the actual result. That procees would look very much like the process described by umaga in his comment above - the line would converge towards an accurate predictor as the "smart money" identifies deviateions from the "true" line.


Thanks for your response. It's hard to take the Garrett Weinzierls of the world seriously, but I find your response well reasoned and interesting.

I am not suffering from any of the misconceptions you mentioned: I used the term "Vegas" as synonymous with bookmakers for this audience; most of the bookmakers I looked at were not in Vegas. And of course, the bookmakers aren't prescient. The reason the closing lines are so good is because of the wisdom of crowds. The bookmakers have an incentive to set a good initial line (that is most profitable), but they don't nail it.

The first sentence of your summary is all I set out to argue. The second sentence is intriguing. I have no data to support or refute it.

I'm willing to assume that if you jump in immediately, and you have a fantastic model, you could beat the opening line. But if you make 1000 bets per year, and expect a 4% ROI, my numbers would suggest you have something around a 30% chance of losing money any given year. That's some sizable risk, given the amount of money we're talking about here.

Further, now the only way to make money betting on baseball is to beat everyone else to making a bet. The vast majority of bets are made when the line is somewhere between the opening line and the closing line. My guess is that it makes most of its movement quickly, and then settles down. So a vast majority of the bettors are betting against the closing line or something very similar, and we've agreed they can't make money.

I'd love to see some data on the opening lines. Do you have historical data?

Yes, please send me the data.

Would you actually outline your methodology for saying bookmakers are "perfect"- what exactly you're measuring? Would you show your work on the 30% chance of losing money?

"Loltastic" is a terribad word, dude.

cdm -

1. Please don't take the following as an attack. But I think part of the problem is a failing common to many smart, analytical people expert in a certain area when they venture in to an area outside their expertise. You are used to being the smartest, most analytical, most nitty-gritty guy in the room. However, in this room you are the ones making implicit assumptions without realizing it, drawing conclusion on common knowledge that is wrong, etc. There's a bit of the 13 year old virgin lecturing on sex going on here.

2. You are over estimating the speed at which the opening lines converge upon the closing lines. Across all the games and all the books there are plenty of opportunities to grab numbers before they fully adjust. The market is far less efficient and slower moving than investment markets.

3. Like almost every non-professional gambler you are GREATLY overemphasizing the importance of handicapping. Understanding how to bet, the true value of deviations from the market, the interrelation between bets, etc is far more important than what we derisively call "pickin' winnahs". There is a lot more I could say here, but teaching others how to win is counter my financial interest.

4. If you are defining a "good initial line" as one that is either a) best predictor of future or b) splitting action evenly you are incorrect. Many books regularly take positions by shading their lines to attract action to a specific side. Basically, they are looking to take advantage of the dumb public swayed by recent performance, name recognition, team loyalty,etc. Obviously, if they shade too much it creates an edge. The competing influences between shading lines, market enforced adjustments for deviating too far, and the need to make sure that book exposure to individual bets isn't greater than risk tolerance, helps prevent the rapid movement to the closing lines that you envision. Also, there is good old fashioned stupidity and sloth.

5. Across all sports I make far more than 1k bets a year, and have a historical ROI of 2.85% - which is in line with other successful bettors I know. Over an arbitrary time period there is a significant chance of losing money - losing months are not uncommon. Even with an edge, having both a sufficient monetary bankroll and the emotional stability to absorb negative volatility is necessary.

Like all sports betting, being successful betting baseball requires lots of work and is 99% of the time completely unglamorous. So yes, the vast majority who try fail. Partially because of misdirection of effort, but mostly, I think, due to an unwillingness to put in the hard work/grinding necessary to succeed.

Good god this article is horrible. It doesn't take someone who knows an ounce about gambling to know that this particular phrase doesn't pass the "is this ridiculous?" test.

"So somehow, by hook or by crook, they made some ridiculously accurate predictions in 2008."

This is like saying the stock market makes "ridiculously accurate predictions." Of course it does. It's an aggregate of people with vested interests in not losing money. Does anyone think that the "lines" in Vegas are made out of thin air just like the prices of MSFT, GOOG, and other assets?


Anyway, he also goes on to consistently talk about "the model." I know most of the posters in this thread personally and I can attest that they all make plenty of money betting on baseball (amongst other sports).

Your failure is assuming that a "model" is necessary. Why do you think we must model the games with a better version of PECOTA to beat bookmakers?


I'm sure it was hard to take the first round earther seriously as well. Try for a minute instead of just steadfastly insisting we're all sailing off the edge.


Don't ask any tough questions. They will be casually brushed aside with snarky comments like "But how much did you lose?" and "Its hard to take the Garrett Weinzierls of the world seriously."

I promised that if someone made a convincing argument for why I was wrong, I would update the post, and so I've done just that. I also tried to address the substantive points, like TomCs question and Kyles comment which seemed to be related to the glory of prediction markets. I think I was also less snarky to Garrett. But just a little.

Ok- first off.. good try sounding smug on your math dropping all the technical terms I was already familiar with, but, well, it's better to be right than to be smug. The real chance of losing money over 1000 baseball bets, each with 4% edge (ROI, return on investment), is much closer to 10%. 30% is totally wrong. Anybody with excel (or a real knowledge of math) can verify this. At even odds (+100), a bet with a 4% edge is one that wins 52% of the time. So plugging into excel (or using the normal approximation, but excel is easier), the odds of losing money- winning 499 games or fewer at even odds- is given by =BINOMDIST(499,1000,0.52,TRUE) which is about 9.7%. Checking -200 and +200 lines, which is a reasonable bound for most games, gives a range of 3.3% to 19.1% (bigger dogs have a bigger chance of coming out behind). Still nothing even in the ballpark of 30%.

So now your (note the spelling) premise is that because most people are losing bettors, that no one should bet baseball? How absurd.

Most people who bet baseball would think a baseball model was a baseball player posing for a magazine. Now this doesn't mean anyone who has a model will be a winning bettor, but it is ridiculous to think that the people reading this article are representative of the general betting population.

Second.. your attempt to quantify how good the lines are is utterly horrible. I actually expected that you were counting the total wins of home teams, but instead you're counting the total wins of favorites. So, across all the games, you figure out the percentage of the time that the line says the favorite will win, and add them up. Then you count the number of times the favorite did win. Then you compare. And since the numbers were close, you conclude that baseball betting is unbeatable. Really? C'mon man.

All you are measuring is the existence (or nonexistence) of a favorite-underdog bias. And, shockingly, you can't get rich by blindly betting all the favorites or all the dogs. What you failed to realize- shockingly, really- is that if bookmakers had set EVERY line identically, you would come to the same conclusion. Let's say the favorites actually won 57% of the time (plug in whatever the real number is). If, instead of whatever line they actually dealt, the bookmakers had dealt every game at -145/+125 (with the same team favored), then you would think the bookmakers had done a near-perfect job of setting the odds, using your ridiculous counting method. Even your average moron degenerate bettor could see that Yankees-Nationals would be a ridiculous value at -145, but your method doesn't do anything to determine how accurate any individual game line is. If one line is off to the favorite's benefit, and another line is off to the dog's benefit, that's 2 good betting opportunities for somebody with circulation upstairs. To you, these even out, and the expected favorite win percentages matches perfectly, and baseball is unbeatable. Again, C'mon man.

It is somewhat funny that this article is now an ongoing joke with the community of bettors, but seriously Chris... You've botched rudimentary math calculations, made some egregious assumptions that border on insane, and then ask people to disprove your argument... as if your nonsense actually supports any sort of conclusion. Apparently "Richard" thinks that your post warrants something more substantial to refute it than the common derision it deserves.

More about this "model" that you used. What does this prove other than your model cannot beat MLB closing lines? How can you make any inferences about any other model without access or knowledge of them?

A very interesting article and posts too. It's sobering to see just how far the odds are stacked against you by the bookmakers but that's part of the game - the real "entertainment" from gambling, if you're willing to put the work in, is the satisfaction from beating that disadvantage.

My belief, based admittedly on "paper trading" rather than actual riches, is that it is possible to beat those odds by system building , selecting parameters that may be under-regarded by the setters of the line.

I would suggest that a couple of seasons is certainly not enough data to uncover the stable patterns of profitability that may exist. My first attempts to do this kind of analysis were based on a single season; when I tried out the promising ones over five seasons only a fraction of the systems still worked.

The two biggest difficulties I have found are (a) sourcing the archived lines in the first place - there is a lot of data that needs to be gathered, and it's not like the bookies want you to have it - if there are any good sites out there, I'd love to know; and (b) combining those odds with the previous game statistics in a working format that can be examined for predictions - a bit of a marathon task, as I only have limited excel skills. I admit I haven't added the last couple of years yet simply due to the massive ammount of work required.

If those five years are a big enough data set for predictions - and I'm no statistician, you'd know far better than me - it would certainly appear that a return of 4% ROI on about 50 bets per year per system isn't unattainable, with the caveat that the yearly returns are indeed volatile and you are correct that the risk of a losing year is fairly high even on a successful system.

Anecdotally, I have heard that baseball is one of the "softest" sports to bet on; this would appear to be backed up by the fact that when bookmakers run promotions offering "free money" based on a certain volume of betting, they will frequently specifically exclude win bets on baseball, presumably on the grounds that knowledgable money is at minimal risk.

You are still completely missing the point. No bookmaker sets any line except the opening line. Beyond, that whatever the line is once you place your bet is set by the market. The bookmakers don't care who wins, if you win or if you lose. They only care if you place a bet. As long as bets are being placed, they are making money. In fact, the very function of the line is to even things out for the bookmaker. In other words, the line serves to create a situation where roughly half of all bettors are betting one way and the other half are betting the other. The book collects the half that lost, pays the half that won for a zero sum transaction overall. But since he gets the vig on all bets, the bookie wins.

The line fluctuates based on keeping that median intact, so if at some point 60 percent of all bettors are betting one way, the line will move until it's attractive enough to bring the formula back to center with half betting one way and half betting the other. That is the only function of the line. They do not set the line as a function of their great predictive powers. They have nothing to do with it. The line is completely controlled by the bettors themselves.

However, your basic assumption that vegas bookmakers are so good at predicting outcomes of games refutes your whole argument. Because if it is possible, to predict game outcomes so accurately, then it is possible for a sports bettor to predict the games just as accurately.

One last note: your argument has a flawed assumption. You present your case as if the line were unbeatable because it is so accurate which to you is proven out through how accurate the final outcome is. But every bet has a winner. No matter what the line is, you can either bet with or against the line, i.e. taking the favorite or the dog. Every bet has a winner. Your argument paints the picture that the bookie wins every bet no matter what because he is so good at predicting the line. That's just not true. As I stated earlier, he fully expects to lose half the bets he accepts, That's his business plan. that's why the vigorish exists.

So if it is true that the bookmaker will as a function of his business model, lose approximatley half of all bets placed with him, then it is possible for you or I or anyone with enough scholarship to figure out which side of the bet is most advantageous to be the one who is winning the half of the bets he pays out. In other words, the bookmaker has no ability, other than the aforementioned proclivity to give an unfavorable line to a sentimental bettor, to affect your success. The success or failure of a sports bettor is only hindered or aided by his own abilities or lack thereof.

Just remember one thing - the people making money betting baseball (or anything) derive no value about letting you (and the tax man) know about it.

Not saying I did this because I dont bet on sports. But in Ontario Canada, when proline first started out and allowed betting on individual baseball games, in the first year the odds seemed to ignore the effect of the starting pitcher. So if you waited for golden opportunities such as great pitchers on bad teams against a good teams 4th or 5th starter you did well. This was corrected quickly of course.

You only beat the oddsmakers if they make a blatant mistake, and they dont make many.

I would be interested in any data on historical betting lines that you had. Please feel free to contact me off-line at aortim at yahoo dot com

Even if we accept Umaga's response and dismiss CDM's article entirely, what is the point of gambling on sports for a historical ROI of

Unless one enjoys spending their time placing bets among numerous sports books and doing the work that is unglamorous 99% of the time, what is the motivation? OK - so maybe it is a way to thumb your nose at the system forcing us all to become working stiffs with banal jobs. I get it, sort of. The life of a "successful" sports gambler seems pretty banal, too, and devoid of the entertainment the masses at least receive in return for their "investment" in gambling.

If any bettors care to respond I am sincerely interested...


I'm an academic in a quantitative field, so I know nothing about your average working stiff, and I'm not an expert in financial matters.

But I do believe a 4% ROI is far more lucrative than it may appear at first. Unless I'm grossly mistaken, since your bet is only tied up for a short period (couple days?), you can be very highly leveraged. If you place two thousand bets of $1000 over two years, thats two million dollars total. As Umaga pointed out, ROI is total profit / total $ bet. So 4% would be $80k. If you start with $80k (wild guess as to the amount of capital you would want to have on hand), that would be equivalent to a 100% APR.

My guess is that anyone who could make a living betting on baseball could a *lot* of money working a quant job in industry or finance. Well more than 80k. So from a purely financial standpoint, you'd have to have a total bet in the millions (+$5 million?) to earn more betting on baseball than applying those same skills elsewhere. And that says nothing of the risks of having a bad run of luck for a year.

The impression I get is that such highly paid jobs in finance and industry are often highly caustic work environments. I can understand people wanting to work for themselves.

Please correct me if any of this is wrong.

2.85% ROI would get the gambler about 50% expected gain over 1,000 independent 1:1 bets, assuming that gambler was betting using kelly criterion.

The risk of that gambler losing money would be about 33%.

Correct me if I'm wrong, but if I was making a 2.85% ROI on average, then to make a $50k per year profit, you'd have to average over $9700 in bets each day during the season.

For a gambler using this as their income- how many games do you actually bet on, and how much do you spread it out? IE are you betting multiple thousands on games you feel fairly strong about?

If someone can model baseball successfully, they can also probably do the same for other sports. At the very least, they are likely smart enough to figure out how to make decent money in other sports even if they don't model them.

Of course one would need to reduce those bets made simultaenously. Assuming 5 bets made per day over the course of a 200 day season, gambler should reduce bets about 0.5%. This would reduce expected gain end of season a small amount as well.

1. Justin - Why the hostility? When did I sneer at people who work more conventional jobs? Like most endeavors, successful sports betting requires hard work and most of the time is without glamor. It takes a certain weird/anal/obsessive type of person who gets thrilled when they identify a way to have a small edge that may not even be realized.

2. As cdm pointed out my bets are generally settled the same day I bet them, so , theoretically, your money can be rolled over every day earning (on average)~3%. Of course, it is frequently impossible to get my whole bankroll down everyday so the daily ROI of the portfolio will be less since some portion is sitting at a book unbet, earning nothing.

3. When possible most of the folks I know bet 1/2 Kelly - accepting reduced return for reduced volatility. For most of though , the real limitation is how much action a book will take from us. Kelly calcs may be saying bet 5k on something but if a book is limiting you to 1k and another book to $500....

4. On a typical day I have 30-50 bets. This includes derivative/prop bets where the limits are pretty low. I'm more of a grinder than some though because I'm wimpy and like the diversification benefit. Some of my peers may bet far bigger than me spread out on only 10 bets.

5. As for why I do this if it requires hard work, has significant volatility, etc - I hated the corporate environment. The disconnect between value produced and rewards. The political bs. I live 5 blocks from the beach and hated putting on pants, shoes, and a preppy shirt. I have the flexibility to work harder and less hard as I please. To play Xbox hockey at 10:00 AM with friends. To see a Tuesday matinee movie. I have a 17 year old dog and instead of leaving him alone all day I'm there to pet him and set him up with a bed on the patio in the sun.

Thanks - I obviously missed the leveraged piece of the equation...


How did you calculate that "the variance between the actual outcome of all regular season games and Vegas' prediction for those games was within the range that one can attribute to random chance." I suspect you are aggregating things that should not be aggregated, but it is hard to know because you don't say how you ran your calculations.

Could you provide a little more information?

A (very) rare internet article where the comments are better informed than the article itself.

Like others here, I've made a living betting on sports (including baseball). I returned about 2.5% on capital invested over approximately 2 years, and the total payoff was enough to provide a more than adequate living - in fact I eventually took a pay cut to go and trade for Lehman Brothers (aha! I'm not so smart after all).

Just because you're not able to come up with a strategy to win doesn't mean I'm not. It's a very standard academic viewpoint (apparently financial markets are efficient and unbeatable too...hmmmm). And of course, as previously pointed out, if I am able to do so I'm hardly likely to publish the details on an online comments page.

PS Having said all that, for me soccer was where the real easy money was...


I took the average closing line from a half dozen bookmakers, and converted the moneyline into a win probability for the home and away team. These numbers do not sum to one (since the bookmakers are raking off the top), so I normalized them to sum to one. So each of the 2000+ games has it's own probability of the home team winning. I then ran a monte carlo simulation, generating 1 million years of outcomes based on these probabilities. For each simulated year, the variance is just the squared difference between the predictions and the simulated outcome. Over the million simulated years, this produces a nice normal distribution (technically, its a mixture model, the sum of many binomials. But it is so close to normal that we can describe it as such). In this distribution, the true 2008 outcomes fell at the 37th percentile. Considering both tails, in 75% of the simulated years, the variance between the actual outcome and the predicted outcomes was less than the difference between the predicted outcomes and the actual 2008 outcomes.


I have to say that I found your article interesting in a limited, academic sort-of-way. As someone who has had consistent success wagering on baseball for more than 10 years, your well thought out and researched article has very little relationship to reality. Only an idiot would wager on every baseball game. Only someone who knows nothing about the sport would buy into a "system". On average, over the past decade I have won 64% of baseball games that I have wagered on against the line. About 40% of my winning plays were on underdogs. My sample size is about 450 games per year. To win on baseball consistently, you have to exercise disciplined selectivity. DON'T BET EVERY GAME. Pick your spots carefully each day. In fact, once you make your picks you should go back to try to winnow your list even further. Those who win on baseball wager on a limited number of plays each day, if at all. Realize that just because a game is being played does not mean you should wager on it. NEVER FORCE A PLAY. Understand that pitching is the key. Limit your plays to small to medium favorites and underdogs of all types. In fact, your first instinct as a player should be the underdog in almost all cases. THE UNDERDOG IS YOUR FRIEND. Stay away from run lines!! Above all, money management is critically important. When you think you have a winner, pound it! Winners are tough to come by, so don't hold back. Even so, remember that there is no such thing as a lock. I learned that lesson the hard way on June 25, 1999. Randy Johnson, in the middle of one of his best seasons, was pitching against a batting practice pitcher named Jose Jimenez of the St. Louis Cardinals. Johnson was on a big streak and a huge favorite. The Diamondbacks were the best hitting team in the league at that point of the season and red hot. Jimenez and the Cardinals? Not so much. I tapped out on Johnson and the Diamondbacks. Johnson did exactly what I expected him to do. Randy pitched a complete game, allowed only 5 hits, walked 2, struck out 14, and allowed only 1 run. Jimenez? Well, here is the AP lead from its game story: "Jose Jimenez, a rookie suffering through one of the worst seasons of any National League pitcher, threw the first St. Louis no-hitter in 16 years Friday night, outdueling Randy Johnson in the Cardinals' 1-0 victory over the Arizona Diamondbacks."

When I lived in Vegas I researched the casino profit on every dollar bet from every type of game. The lowest percent return for the casinos was from the sports book. The lowest return in the sports books was from baseball. I think it was around 3% but I'm not sure.

Great stuff, and I appreciate the back and forth with Umaga.

With you data could you run a similar analysis of over/unders? I'd love to see it. I believe totals in other sports have been shown to be an area of potential exploitation by savvy bettors (as "Vegas" exploits the biases of average bettors) and I'd be curious to see how that plays out in baseball.