Mathematical sports betting strategy: algorithm for calculating value odds

Mathematical sports betting strategy: algorithm for calculating value odds
Bookmakers don't like mathematical bets. If you assess the risks and bet according to the strategy, the bookmaker's profit will fall.

Mathematical sports betting is a comprehensive approach to betting based on outcome value and bank management strategy. In this article, we will analyze margin and value bets, as well as calculate the expected profit and the likelihood of a losing streak.

Sports betting strategies

Strategy is a systematic approach to financial management in sports betting.

Let's highlight five popular strategies:

  • Kelly criterion;
  • Martingale strategy or catch-up;
  • D'Alembert strategy;
  • Flat;
  • Fixed percentage.

What is margin and how to find it

Odds - the probability of the outcome, taking into account the bookmaker's margin.

Margin is the commission of the bookmaker company. Due to it, the bookmaker remains in profit. At the end of a match or tournament, the bookmaker may be in the red, but at a distance, the margin will bring the office to a plus.

Calculate the probability of an event using the formula:

P = 1 / K , where K is the coefficient.

Determine the size of the margin using the formula:

M = (S - 1) x 100% , where S is the sum of the probabilities of the outcomes of one market.

For example, in the duel Juventus - Milan, the bookmakers put up quotes: 1.60 for the hosts, 4.20 for a draw and 5.60 for the victory of the guests. We calculate the probability:

Victory of Juventus - 0.625: 1 / 1.60.

Draw - 0.2381: 1 / 4.20.

Milan win - 0.1786: 1 / 5.60.


calculate the margin: S = 1.0417: 0.625 + 0.2381 + 0.1786.

The margin that the bookmaker has put into this event is 4.17%: (1.0417 - 1) x 100%.

How to determine the value rate

The bookmaker cannot accurately assess the likelihood of an outcome, although analysts take into account many gaming and non-gaming factors. When analyzing unpopular championships, bookmakers may not know a number of parameters. Some outcomes are underestimated. Bets on them are called values.

Before you value, if:

K x P> 1 , where K is the coefficient, P is the probability according to your calculations.

Here is an example: in the match Athletic Bilbao - Atletico Madrid, the bookmaker offers 3.60 odds for the home win, 3.05 for a draw and 2.25 for the away win.

You analyzed the statistics of the teams and concluded that the probability of a draw is 38%.

We estimate the rate:

3.05 x 0.38 = 1.159> 1. In this case, the rate is valuable. On such events, it is recommended that bets be made according to the Kelly strategy.

The Kelly Criterion is a bankroll management strategy by which the player calculates the size of the bet based on past performance and the current amount of money.

Determine the bet amount according to the Kelly criterion using the formula:

((K x P - 1) / (K - 1)) x R x B , where K is the odds, P is the probability according to your calculations, B is your bank, R is the percentage of bets won.

If 45 out of 100 bets are winning, then R = 0.45. We recommend using R = 0.25 for the first 100 bets.

Expected value in sports betting and variance

The mathematical expectation of profit is the expected profit from a set of bets with the same probability of a particular event.

Calculate the expected profit using the formula:

N x F x (K x P - 1) , where N is the number of bets made, P is the probability according to your calculations, K is the coefficient, F is the size of the bet.

If you correctly estimated the probability of a draw in the match Athletic Bilbao - Atletico Madrid and make 30 bets on a similar basis for the amount of 2000 rubles, the expected profit will be 9540 rubles: 30 x 2000 x (3.05 x 0.38 - 1).

Variance is an uneven distribution of the value of the probability of an event in relation to its mathematical expectation.

For example, when a symmetrical coin is tossed, there is a 50% chance of getting heads or tails. In reality, a coin can fall on one side several times in a row. With a lot of repetitions, the ratio of falling heads and tails will approach 50%.

With risky bankroll management, variance can drive you into the red. Distance eliminates variance.

Determine the probabilities of a losing streak using the formula:

Ms = (1 - 1 / K) ^ N x 100% , where N is the number of losses in the streak.

For example, some professional players prefer to bet on favorites and choose events with odds of 1.25. The chances of success when betting on such events is 80%. But to win 2,500 rubles, you need to risk the sum of 10,000 rubles.

In reality, you can lose several times in a row, and in this case, there is a possibility of losing your entire bankroll. To prevent this from happening, use Kelly's mathematical strategy and take into account the likelihood of a bad streak.

Let's calculate the probability of two defeats in a row when betting on an event with odds of 1.25:

Ms = 4%: (1 - 1 / 1.25) ^ 2 x 100%.

If you correctly assess the probability of outcomes and learn how to distribute the pot according to one of the strategies, then mathematical sports betting can be profitable.

Or you can use this Spreadsheet to analyzer the football match as well as your bets and see the value bet

GO to Spreadsheet