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I am trying to understand how game odds work. One scenario I came across was the over/under scores for football (soccer) games in the form of a table like this:

Date        Home Team   Away Team   Handicap    Over    Under   Payout
4/17/2016   Team A      Team B      +0.5        1.03    12.41   95.20%
4/17/2016   Team A      Team B      +0.75       1.04    10      94.20%
4/17/2016   Team A      Team B      +1          1.03    11.5    94.50%
4/17/2016   Team A      Team B      +1.25       1.12    6.13    94.70%
4/17/2016   Team A      Team B      +1.5        1.21    4.31    94.40%
4/17/2016   Team A      Team B      +1.75       1.24    3.93    94.20%
4/17/2016   Team A      Team B      +2          1.29    3.6     95.00%
4/17/2016   Team A      Team B      +2.25       1.48    2.64    95.00%
4/17/2016   Team A      Team B      +2.5        1.68    2.18    94.80%
4/17/2016   Team A      Team B      +2.75       1.86    1.96    95.40%
4/17/2016   Team A      Team B      +3          2.16    1.73    96.00%
4/17/2016   Team A      Team B      +3.25       2.42    1.57    95.00%
4/17/2016   Team A      Team B      +3.5        2.66    1.46    94.10%
4/17/2016   Team A      Team B      +3.75       3.04    1.37    94.20%
4/17/2016   Team A      Team B      +4          3.9     1.26    95.20%
4/17/2016   Team A      Team B      +4.25       4.25    1.21    94.20%
4/17/2016   Team A      Team B      +4.5        4.85    1.17    94.60%
4/17/2016   Team A      Team B      +4.75       5.95    1.13    95.00%
4/17/2016   Team A      Team B      +5          7.7     1.08    94.70%

I understand that 2.5 goals per game (handicap here) is generally the average goals scored, but I want to know from this data exactly what the market is thinking. We may also call it the tipping point or break-even point.

How would I calculate that value?

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I have worked in a London sport hedge fund for 6 months so I will have a few things to add to the previous answer.

In general, the odds reflect what the odd makers think about the market in the sense that each odd can be converted to implied probabilities for each outcome. However, the odd makers also change their odds depending on which event the bets are placed, to mitigate their loss/risk. So in that case, the odds would also reflect what the people (i.e, the betters) think rather than what the odd maker thinks.

The human factor is taken into account too. For instance, in big games, say Chelsea vs Arsenal, most betters actually have a favorite team and bet with their emotions. Therefore they tend to bet much more on a win from either team than a draw (betting draw is boring). So all the bookmakers have to do is to bump the odds of the draw a bit and reduce those for the win.

I mostly just tend to bet against my favorite team when they play a big rival so that I maximize my happiness: if my team wins I don't care I lost money, and if they lose, well, then I've made some money at least.

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My answer is USA based. Your mileage may vary.

First off, the "over-under" is usually a single number. You are betting the score is >= that number. You can be sure that statistically, the final score of the game is likely to be that number. I don't know what the numbers you posted refers to.

I don't think there is a single canonical answer for computing this. In the USA, staticians in Vegas usually sets the odds and bookies are required to balance their bets around this. The algorithm they use is certainly complicated and proprietary. But other agencies could compute slightly different numbers and you could have bookies around those too.

The answer is complicated because it's not purely additive. You can't just say "on average Team A usually scores X ppg, and team B usually scores Y ppg, so the over/under is X+Y. That is because you can have ways of categorizing defenses, and you may then say "On average against teams with defenses like B's, A scores X ppg". Then there are other factors like "A scores more points when home than away".

Most betting agencies probably use a propietary algorithm of:

  1. PPG by A
  2. PPG by B
  3. Points allowed PG by A
  4. Points allowed PG by B
  5. Who is home/away
  6. Weather (And looking at past scores in those settings)
  7. PPG by A against B historically
  8. PPG by A against B historically
  9. Injuries.

    ...etc. Many factors like this. It is probably a giant regression equation, but the feature set is vast.

EDIT: in conclusion, you cannot simply re-create this value. It is some proprietary algorithm that the sports betting agencies compute. It will change daily, or even multiple times per day, up until a cut off point, as new information is assessed (e.g., a player gets hurt during training that week).

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