How do bookmakers set their odds?

Question

I am and always was fascinated by how oddmakers set their odds.

With almost everyone I have previously discussed this question, they always say something along the lines of:

'Duh, they set the odds in a way that they 'split' the bettors in half (the total potential payout) and they, the betmakers, get their profit by setting their odds (slightly) smaller than their final payout will be.'

And this sounds, to me, not that logical (on the other hand it does sound pretty smart).

If we take the (presumably fair) coin-toss as an example, the most logical (to me) offered bets would be something like 1.98€ for each outcome (only tail or head is possible), for each 1€ bet.

But, according to the logic above, oddmakers would set the odds at any point which splits the pot, and that could be anywhere (if for any reason the bettors would almost entirely prefer one side of the coin).

I get that the oddmakers probably would set their odds not completely even and move them in the direction of the 'split-pot' to decrease their risk (by not having to pay out more than they previously amassed in the event of the unfavorable outcome).

I hope this illustrates my disconnection to the answer above.

So how does this work in reality, where it seems to be way more difficult to built a model to realistically evaluate the chances of specific games (e.g. soccer matches, who seem to be very close/coincidental/luck-dependant)?

1. Do bookmakers just resort to the 'split the pot'-approach?

2. Are there some (betting) reinsurers?

3. Is there scientific literature (regarding the approach of oddmaking)?

4. How does this affect potential arbitrage opportunities (in my opinion the above 'answer' leads almost surely to some sort of arbitrage opportunity at specific points in time; but my minimal experience has shown me there is, obviously, none)?

I appreciate any answer and would welcome any discussion (in a sense, if there is a place where something like this can be rather discussed than answered I would love if someone can point me that direction), thanks in advance.

---

Note: bet makers, oddmakers, betting providers, bookmakers all means the same to me.

Answer 1

As far as I know, a simple explanation:

The odds are usually not presented as percentages, but as "decimal" odds, which can be obtained dividing the percentage by 1: 50% / 1 = 2. In the case of X 62%, -X 48%, the decimal odds are: X 1.61, -X 2.08.

The decimal odds indicate what you would get as reward in case you win. Notice therefore that outcomes with higher estimations of happening pay a lower reward, and outcomes with lower estimations of happening pay a higher reward.

1. They make an initial informed estimate of probabilities of a given outcome given their expert knowledge of the sport, they definitely have some expert analysts as well as some statistical models -based on previous results-. In this case, let's say, they predict X has a chance for them of 50%, so the odds so far are: X 50%, -X 50%. It is secret what method each bookmaker uses exactly, so you will never know unless you become the bookmaker yourself, or work with them as the expert; however many possible methods, beyond the intuitive informed opinion, are well known: looking at league standing, categorizing the teams by recent performance, seeing previous encounters of the same teams, using the statistics of the goals scored in previous games to make a poisson distribution, calculating an ELO rating for each team or even each player, etc.

2. They add a premium (also known as "vig"), to their prediction, which they might win. This is actually their earning in the long term. Notice that in the previous step, both possibilities, X winning and X losing added to 100%, they just add to that total some percentage points, let's say 10 points, so they will add to 110%. That 10% is their long term earning because, they are actually paying, in the long term, getting 10% more than they would to get even odds (long term). The way they distribute this premium (vig) among the outcomes is unknown and probably different for each particular bookmaker, some may add it equally (which would be the intuitive way) so it would be: X 55%, -X 55%; some may add more to some option, like X 52%, -X 58%; and some may want to compensate for the favorite, PERHAPS (a very speculative perhaps) even giving better odds than they even estimated originally to one that is not a favorite, like X 62%, -X 48%.

3. As the days pass and the game is about to start, the odds get adjusted according to new information and according to the market demand, to compensate each side in case one is getting many bets and another is not.

The art of betting systematically, is therefore about trying to find odds that are better than the "reality" offered by the bookmaker. For example, if the bookmaker is offering these odds: X 55%, -X 55%, which seem to indicate that both outcomes have same chance, your way to beat them would be to find out that some outcome has different chances than these estimations, for example, if we know that actually X has a chance of 60% of winning, we should bet for X indeed, as the actual reward (if it were even with the probabilities) in decimal odds should be 1.67 (corresponding to 60% chances of happening), but it is actually paying 1.82 (corresponding to 55% implied chances).

This means, we will bet ¤1, and if the odds were exactly as the probabilities, it should pay back the same ¤1 we bet plus ¤.67; and this way in the long term, if we played infinitely in average we would end with ¤1 anyway, because the reward is even with the chances. However, given that the odds are in our favor, we will bet ¤1 and we will get ¤1 plus ¤.82, which is ¤.15 higher than what would be even, that, in the long term, is our earning.

Even if we lose this bet, if we only bet to favorable odds like these, we will have an earning in the long term.

Now, this sounds easy but there are 2 details:

1. It is VERY HARD to find actual mistakes on their estimations or, as they call them, market inefficiencies: it is very hard to calculate the chances of an event, and very hard to calculate exactly how much is their "mistake". Even if we know they are wrong, without knowing how wrong they are, it is hard to calculate how much to bet.
2. If we somehow manage to find out how much is our advantage, we still have to know how much to bet on each bet, which is actually not as intuitive as it sounds. Luckily there exists an already mathematically proven formula to know what percentage of your bankroll you have to gamble on each bet, depending on the advantage you have, which should, in the long term, give you the highest possible profit. This is called the "Kelly criterion". However, this only works if you know well what is your advantage, and if you don't, this bankroll management will lead you to loses and bankruptcy very fast, because this is a precise calculation based on your advantage: if that number is wrong you will lose a lot.