Mathematics and sports betting
Date: 2024-03-23 View: 61

In sports betting, mathematical knowledge can help you make wiser decisions, but it does not guarantee profits. Here are five common mathematical strategies:

 

Expected Value Calculation 

 

By calculating the expected return of each betting option, you can choose the bet with the highest expected value. This requires estimating the probability of winning.

Example: Suppose in a match, you estimate the probability of the home team winning is 60%, the probability of a draw is 20%, and the probability of the away team winning is 20%. The odds given by the bookmaker are: home team wins 1.5 times, draw 3 times, away team wins 4 times. 

Expected value = Probability × Odds - 1 

  • Home team expected value = 0.6 × 1.5 - 1 = -0.1
  • Draw expected value = 0.2 × 3 - 1 = -0.4
  • Away team expected value = 0.2 × 4 - 1 = -0.2

As you can see, under your estimation, the expected values of all three options are negative, so betting is not recommended.

 

Kelly Criterion

 

Based on the win rate and odds, calculate the optimal betting amount proportion to maximize profits in the long run. However, it requires a large amount of data to estimate the win rate.

The Kelly formula is used to calculate the optimal betting amount as a proportion of total funds: 

f = (bp-q)/b 

where p is the probability of winning, q is the probability of losing, and b is the net odds (odds-1). 

Suppose you have 1000 dollars and estimate that the home team has a 60% chance of winning with odds of 1.5. Then p=0.6, q=0.4, b=0.5. Plugging into the formula: f = (0.6×0.5-0.4)/0.5 = 0.2. In this case, you should bet 1000×0.2=200 dollars.

 

Poisson Distribution

 

Used to predict the number of goals in a match. Calculate the average goal rate from historical data, then use the Poisson distribution to estimate the probability of a specific number of goals occurring.

The probability mass function of the Poisson distribution is: 

P(X=k) = (λ^k × e^(-λ))/k! 

where λ is the average number of events per unit time, and k is the number of events occurring in a certain time interval. 

Suppose in a match, based on historical data, you estimate the average number of goals scored by the home team is 1.5 and the away team is 1.2. Then the probability of a 0:0 score is: P(home team scores 0) × P(away team scores 0) = e^(-1.5) × e^(-1.2) ≈ 0.0498 Similarly, you can calculate the probabilities of other scores and choose the betting option with the highest expected value based on the odds.

 

Data Analysis 

 

Collect and analyze massive amounts of historical data to discover patterns, build predictive models, and find valuable betting opportunities.

You have collected data on a team's past few seasons, including the number of shots, possession rate, pass success rate, etc. Through data analysis, you find that when the team's possession rate is higher than 60%, their win rate is significantly higher than in other situations. Using this pattern, you can choose to bet on them to win in matches where their possession rate is high, increasing your chances of winning.

 

Arbitrage 

 

Profit from the differences in odds between different bookmakers. Mathematically calculate a set of betting combinations that can lock in profits regardless of the match outcome.

Suppose two bookmakers offer different odds for the same match: 

  • Company A: Home win 1.8, Draw 3.5, Away win 4.0
  • Company B: Home win 2.0, Draw 3.2, Away win 3.8

There is an arbitrage opportunity. Bet according to the following plan: 

  • Bet 100 dollars on home win at A
  • Bet 52.63 dollars on draw and 55.56 dollars on away win at B.

No matter the match result, you will profit: 

  • If home team wins, A gains 80, B loses 108.19, net profit 71.81;
  • If draw, A loses 100, B gains 168.42, net profit 68.42;
  • If away team wins, A loses 100, B gains 211.13, net profit 111.13.

The above are applications of five mathematical strategies in sports betting. However, in practice, more factors need to be considered, such as changes in odds, team conditions, weather, etc. Mathematical strategies are just tools; whether they are used reasonably depends on your judgment. At the same time, bookmakers are also using mathematical models, and the odds are often in their favor. It is advisable to be cautious, treat it rationally, and not invest too much money. Grasp the risks well. The betting system is dynamically changing, and past patterns may not apply. Mathematics is not omnipotent.


 

If you want to actually practice how to make bets, you can try placing small bets at this betting site.