# How do betting houses determine betting odds for sports?

Let's take football (soccer) for example. There are 3 possible outcomes, home win, draw, away win. I took a random game from bet365

Turkey vs Ukraine
hwin, draw, awin
2.20  3.40  3.20

So for investment of 100\$on given result, you either loose 100\$ or win: 220\$, 340\$ or 320\$. Their probability assessment doesn't add up to 100%, they take extra 5%-12%, but how did they come to these numbers (2.20, 3.40, 3.20)? Is it the betting patterns of people that bet, for example, if 90% of people put money on Turkey, hwin coefficient would be lower, or is it some kind of a calculation? The problem with calculations is that the sample is very poor, national teams play very few games in long periods of time, between whole range of teams of different strengths, many outside parameters contribute, like injuries, current form and motivation of individual players, etc. Is their strategy for national championships any different, you could find more regularity as the games are more frequently played, though 4 national league games per month isn't that much (and are also played home/away, which are two very different things). So basically, the question is on what do they rely the most, how do they come up to these numbers, is it the calculation, betting patterns of other players, combinations etc? One sub question, if other gamblers have a strong influence how coefficients are put, it seems to me that such assessments would be with significant error. I don't know if you can tell the difference between 65% and 70% for a given outcome, but that difference to me is indistinguishable. To be clear, I believe that Turkey in given example is a favorite, mostly because they play at home, but are their chances for a win 45% or 55% is too abstract, if they played against Monaco national team, then I'd give you a probability for the win with much more confidence. • Hint: Do bookmakers really need to know probabilities in order to be profitable? Concrete example of hint: suppose you decided to build a book and, at the stated odds, got 10 people to bet on a home win, 6 on a draw, and 7 on an away win, for total pay-in of 2300 dollars. Under what circumstances would you lose money? – whuber Jun 5 '12 at 14:40 • Yes, of course you're right, but I'm just suggesting the assessment is in terms of money, not probability! Suppose, e.g., I have already collected 10K in bets and somebody comes along who wants to bet$100 on a really remote possibility. If I give them better than 100:1 odds, I could lose money. So I only offer lower odds that I can afford. If they don't bet with me, I lose some business--but no money; if they do bet with me and win, then I'm guaranteed to make money. If there's a competitive market, the odds I offer will be close to 100:1. This is how a market prices in probabilities. – whuber Jun 5 '12 at 16:47
• In a nutshell: this is why huge banks in the US have needed bailing out. They said they were hedging risk (the no-lose strategy I described) but they were secretly estimating probabilities--and (eventually, inevitably) getting them wrong or just getting unlucky. One lesson: if you want to stay in business, get out of the probability-guessing game. Let other people win and lose money and just take your (small?) cut for facilitating the process. – whuber Jun 5 '12 at 18:25
• (+1) whuber. Profitable bookmaking is an accounting problem rather than a statistical problem. – Gschneider Jun 5 '12 at 18:32
• Actually, I never bet in my life, but I'm interested in subject. :) And I'll agree that most people who're guessing probabilities are loosers, but someone must be better at it, and I wouldn't be surprised if betting houses employed few of those. – enedene Jun 5 '12 at 18:33

How odds are set is a really interesting subject that I have done some research into, and in a similar way sports analytics.

The first paper I would refer to covers the NFL specifically "Why are Gambling Markets organised so differently from Financial Markets", Steven.D.Levitt (The Economic Journal 2004). This illustrates that the odds on the NFL are rarely set to generate 50/50 action because the bookmaker can exploit "square" action by skewing odds against their traditional bias (i.e. the point made above about the Ohio State Buckeyes - if the bookmaker is aware that they are going to take a larger % of the bets, they can either adjust the odds or the spread so the better has to pay a premium to bet the Buckeyes - e.g. the -7.5 or more than one touchdown instead of -6.5 - especially if the true rating for the game was around -5 or -6). It also makes the point that bookmakers/sportsbooks rarely make the odds themselves they are usually paying influential odds makers who set the line for a lot of events. The bookmaker will then rarely adjust these odds greatly as they will effectively handicap the market against other bookmakers and sportsbooks (generating a profitable opportunity for "sharp" action).

In the case of the game quoted by the OP, the prices quoted by Bet 365 is consistent with the over-round % that they have run on most football games this season of between 105-107% (I have an interest in this - their over-round% on the English Premier League is typically 5-6%). That 5-7% margin will look after them in the long run as it increasingly means unsophisticated gamblers have to be more right than average in the long run to make a a sustained profit. How the actual odds are generated is another matter in the case of Bet365 a lot of their competitors use the Bet Genius group for Odds Data (e.g. Sportingbet, Paddy Power, Sky Bet). They will probably then make small adjustments to this based on their typical clients betting preferences (e.g. what type of action they take and biases).

For a lot of sports the Cantor Fitzgerald group have created the Midas Algorithm to set up odds in the same way they would deal on Wall Street and they are getting an increasing presence in Las Vegas running several sports books - http://m.wired.com/magazine/2010/11/ff_midas/all/1. This has allowed them to set spreads for the entire NFL season (http://www.grantland.com/blog/the-triangle/post/_/id/27740/nfl-win-totals-hot-off-the-sportsbook-press) before the pre-season has taken place (which is not a typical case as most bookmakers seems to react on week to week action and player injuries and performance).

How are the actual odds generated? This is the more difficult question. Going on Mathletics (Wayne L.Winston 2009), some sports e.g. the NFL can be governed by a simple least squares algorithm based on margins of victory and points scored which can then be finessed (e.g. to give more weight to recent games). This can then be used to generate win percentages based on the ratings derived. In the case of the NFL, Hal Stern "On the Probability of Winning an American Football Game" (American Statistician 45, 1991) showed that the probability of the final margin of victory for home NFL team can be well approximated by a normal random variable with mean = home edge+home team rating-away team rating and a standard deviation of 13.86. Plug the ratings generated by your least squares work in and you have a set of percentages against a given spread. I believe that this can also be applied to a lot of other sports (e.g Australian Rules Football). In the case of football though I believe that oddsmakers also have done some regression analysis into player statistics to allow them to make a more rational rating based on the players that will actually be on the pitch rather than past team performance in terms of margins of victory (e.g. the Dtech group who analyse European football for the Times Newspaper base their ratings on the Team shots and goals data http://www.dectech.org/football/help_info.php - rather than a least squares model based purely on margin of victory). Given that sports could and should be viewed as an academic subject, I believe this is why we have seen increases in the number of the groups such as the Accuscore group who have a largely academic background (from interviews on the ESPN Behind the Bets Podcast) and have used their knowledge to generate opportunities from odds skewed to exploit gamblers that bet with pre-conditioned biases (e.g. the home team favourite wins more than 50% of games). If you can remove bias from the team that you pick, I believe this will generate opportunity.

• In your opinion which is the the best way to remove bias in the odds? – emanuele Jun 4 '14 at 19:38

The following is for entertainment purposes only. Sports betting is a very interesting academic topic, and I recommend you keep it an academic topic. You incur your own financial (and legal, in some jurisdictions) risks by acting upon anything I say :)

The process is more complicated than many people make it out to be. First of all, there are examples of sports books that are explicitly based upon the public's actions...basically they are matchmakers for those willing to offer bets and those willing to place them. Those generally aren't what we are talking about though. As for the others, one school of thoughts is for the houses to expertly determine the "true" odds, and set the line accordingly. As many in the comments pointed out, another school of thought is that the house can manipulate the line so as to receive balanced action on each side and guarantee profits (as was noted, the implied probabilities do not sum to 100%, so the difference is accounted for by the juice or vig). However, legitimate betting houses handle thousands and thousands of events every year, so they don't have to be overly concerned with guaranteeing a smaller profit if a larger profit can be had in expectation. As handled by sports books, this is not purely an accounting problem.

It's important at this point to make a couple distinctions. First I'll note the difference between opening lines and closing lines. Betting houses have to have some line before the market has acted on their lines, and these opening lines are considered less efficient than the closing lines just before an event starts. It's also important to note the difference between so-called "sharps" and "squares" in the betting world. Despite what they might think, most bettors are so-called "squares" that don't really have much if any discernible skill in picking a side on which to bet. "Sharps," on the other hand, are well-funded experts that know what they are doing. Whereas a square probably has a set limit that he will bet, independent of the odds, a sharp is very different. A sharp won't bet at all if he feels the odds are unfavorable, and he will bet a great deal if the lines do not update to reflect his actions. This is not pure irrational greed on the sharp's part; there is a statistical basis known as the Kelly criterion for determining how much to bet when one has an advantage.

So the existence of sharps makes it surprisingly non-trivial to simply set a 50/50 line and happily lock in profits. If the line is bad, sharps will hammer it over and over again. To maintain the 50/50 action, the house would have to adjust the line to the point where sharps no longer feel they have an advantage. There are lots of forces at work here...market forces, arbitrage between different books, and lots of information, but these are going to tend to make that closing line fairly close to the true odds, whether that was the original intention or not. Of course it's complicated since the house might have non-public information or might think they are smarter than the public. There's not really a simple answer, but just keep in mind that a) sports books want to maximize profit and b) there are smart people out there who bet more when the line is worse.

As for how they might determine the lines aside from actual betting (which might be important for instance in setting opening lines), there are numerous things they can do. First of all, they might look to other books and assume some variant of the efficient market hypothesis. However, they might also employ the same types of techniques that sharp bettors employ. In the 21st century, sports analytics is a growing field. There are numerous academic journals, conferences, and blogs dedicated solely to sports analytics. There's also a ton of data out there, beyond just which team won or lost. In Major League Baseball, for instance, data exists on just about anything one might want to track. Every play of every regular season game for roughly the last 60 years can be downloaded by anyone with an interest. There are also people that are quite knowledgeable at ascertaining relative skills of players by observing them play. I can't say what a specific book does, but the potential combination of analytics and scouting on behalf of the sports book is quite formidable.