# How do bookmakers establish odds if sports events are unpredictable, considering the multitude of factors at play that prevent precise probability estimation?

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How do bookmakers establish odds if sports events are unpredictable, considering the multitude of factors at play that prevent precise probability estimation?

In: Mathematics

They use statistical models. If you know that Team A won over few teams that Team B lost to you can take a good bet (pun intended) that Team A will win over Team B. Also they take into consideration that whoever win they will still make money out of it so for example if one team team win prediction is 75% they have 3:1 odds to win so bookmaker can put the odds for players like 2.5:1 so they have margin of error if anything goes wrong.

Nowadays in online betting it’s even more visible since in theory bookmakers doesn’t care who wins. He only wants to make money. So after initial odds they adjust them based on the best players are making so they (bookmakers) are always net positive.

They gather all the information they can and do their best using proprietary models. Just by looking at team performance historically they can get in the ballpark (e.g. even without looking at any data you can be very confident the LA Dodgers will have a win rate between 50% and 70%), then looking more specifically at player performance, where the team is playing, how they historically do versus this specific opponent, etc help them hone it in.

But bookmakers **aren’t really in the business of figuring out “correct” odds**, they are in the business of enticing players to bet while maximizing their return. Better odds gets more people to bet but reduces their payout; worse odds means they’re financially safer but will attract fewer bets. So bookmakers are trying to set odds which match gamblers’ appetite for betting, not odds which match a team’s chances of winning. If there is some irrational reason why people may *believe* a team will win/lose (e.g. “they’re cursed” or “they’re due for a loss” in the Gambler’s Fallacy sense), the odds will reflect that fact.

they guess, then fudge the numbers a little in “thier” favour so over the majority of games, they will come out on top, even if they lose a bit on any specific unexpected event.

basically they spread the cost over lots of games and bets, kind of like how insurance companies eat the cost of big payouts over millions of customers.

For one, there are a lot of sportsbooks out there that they can scrape lines for to ensure they aren’t getting too many bets on one side.

More foundationally their entire business revolves around creating odds that ensure profit. It’s why for a 50/50 fights the odds will be something like -105 at minimum for both fighters. If they receive too much action on one side, they will adjust odds to balance the other side.

If you are talking about brand new lines being created, they are definitely taking a lot of risk and that’s why odds can change hugely as d-day approaches for the event.

They don’t care about the outcome. Their goal is to find odds that result in an equal amount of money being bet on both sides. They tweak the payouts so that no matter the outcome, one side is paid out less than the other side bet leaving them a profit.

One thing that I’m not seeing below is that odds aren’t static. What bookmakers are doing is balancing the bets and payouts on both sides. If too many people are betting on one side, bookmakers can change the odds in order to entice more people to the other side. Ideally, they’ll pay out the same regardless of who wins, and they’ll make money on the vig.

Data analyst here. Forgive me if this is a bit meandering or inaccurate in some fashion. I welcome any critiques or corrections. Typing all this out on my mobile device.

It’s a looooooot of factors multiplied out to a general statistical model. Sports, horse racing, etc. are notoriously difficult to get nailed down in a reliable way because, as you point out, there are a lot of factors. Sports are super chaotic, and depending on how many games are played out, it could make things even harder (i.e., it’s easier to predict who would win the World Series than the Super Bowl because there are many times more baseball games than football games, making the law of averages pan out more reliable over many dozens of games).

So, more simply, let’s look at dice odds as an example. Each die can represent a factor. So if you’re playing a game with 2 dice, you have 2.78% chance to roll a 2 on a single roll because 1 has a 16.67% chance of coming up on one die, so 16.67% × 16.67% is 2.78%. You can scale this up and up and up indefinitely, depending on the count of dice. At 100 dice, you could have values rolled anywhere from 100 to 600, with varying likelihood of these things happening, with the average of all 100d6 rolls being approximately 350. The more times you roll, the narrower the possible average of all rolls gets to that middle number. It’s always 1/6 × 1/6 × 1/6… with the number of 1/6s being equivalent to the number of dice younuse

You can then apply this to variables in a sports match. I’ll use a simple one with one v one like bowling. Person X and Person Y are going head to head. There are going to be a bunch of different variables (or “dice”) that we think will be “rolled” in this match. But these aren’t simple 6-sided dice with a 1/6 (or 16.67%) chance for any given number. They’re all many-sided and represented as percentages. And the game that bowler X and Y represents one “roll” of the dice. If that roll is over .5, X wins. Below .5, Y wins. And each “die” is multiplied together to show where the average is more likely to fall.

So let’s say X has a higher bowling average than Y. 295 vs 290. This is a 1.6% advantage in average score. Assuming they’re only playing one round, you could say this tilts things to a probable outcome favoring X at 50.83% likelihood to win. Still pretty damn close to a flip of the coin odds. But let’s say Y injured their hand 2 weeks ago. Maybe someone speculates that it gives a significant advantage to X. So that becomes one of the factors we multiply in. Say it’s 75%. Assuming the *weight* is the same for average score and injury, then we have 62.92% odds in favor of X. Maybe we just round it to 3:2 odds (or 60% chance of winning).

So every variable we think would *reasonably likely* has an impact on the performance of bowler X or Y at the time of the match gets multiplied in. Average score, health or injury, venue, style of play, method and patterns of the lanes being oiled, whether they had to travel long distance (jet lag), etc. etc. etc. could become variables. I mentioned weight before, which adds the additional factor of the proportional impact. So the average score of a bowler and their health/injury status are gonna carry the most weight. So they’re likely to move the needle on odds pretty heavily. But jet lag, maybe not so much. So when it is factored in, perhaps its weight impacts the likelihood of a win only a fraction of its value. In the end, you get a percentage that is then simplified to the odds ratio. So Y has a 40% chance to win, then it’s 2:3 odds. X has 60%, or 3:2. The ratios can be confusing when doing straight line percentage odds, but they’re useful in how payouts can be expected. You bet on X, you get 2 bucks for every 3 you wagered if X wins. You bet on Y, you get 3 bucks for every 2 you wagered if Y wins.

There’s 2 ways.

One they use statistical analysis to determine a probability and then fudge the numbers a bit in their direction.

The other way to do it is let’s say you have a sport where you’re only betting on a binary outcome (eagles beat the cowboys or vice versa) you have 1000 betters in the pot betting equally, winners split the pot evenly. If 800 people pick the cowboys then the eagles are 5:1 underdogs (cause if you put in 1 dollar and win you’re getting 5)

The market is usually led by “sharp” Sportsbooks. These books don’t limit or ban sharp bettors (those who consistently profit) from betting with them. Instead, they use their bets as a data point.

As with any large-scale, efficient market, the law of large numbers will guide the Sportsbook to the most accurate line via betting activity. If a stock price is too low, there will be a rush of people purchasing the stock which drives the price up. If a point spread is too large or small, there will be an influx of bets towards one side or the other, which will drive the spread towards a more accurate number. This “market consensus” isn’t always accurate, but in the long run, over thousands of games/bets, tends to be very accurate.

Sportsbooks also have the benefit of knowing their users. They have all of their data and betting history. Someone who randomly bets with no logic/pattern, or someone who always bets on the same team, etc. is different from someone who consistently places bets on lines before they move in their favor, and is a profitable bettor over the long term. Sportsbooks can therefore identify certain bettors as “sharp” and give more weight to their bets when deciding whether to move a line.

Before books can gather all of this betting data, they have to set an opening line. For example, for a point spread on an NFL game on Sunday, a book might open up betting on the preceding Monday. They come up with their best guess of the spread based on their own sophisticated models, and that becomes their opening line. At first, they won’t allow large bets to be placed on this line in order to limit their risk. Over the course of the next several days, they’ll adjust their line based on bets they receive. If a lot of sharp bettors are placing bets on one side, they might determine their line needs to be adjusted. As it gets closer to game time, the book will slowly increase their betting limits as they become more and more confident that their line is accurate, based on their own models + the valuable data of the betting market (bets being placed, particularly from sharp bettors).

All Sportsbooks have their own models and have to set opening lines, but generally speaking, many of the smaller ones will follow the lead of the sharper Sportsbooks. If a couple of the sharp books move a point spread, the rest of the market generally follows.