# EV or probability for sports betting?

## Kelly criterion

EV Win probability
1.05 55%
1.10 60%
1.25 70%
1.50 80%

The Kelly criterion is a betting strategy used to determine the optimal size of a series of bets. This strategy is based on the principles of expected value (EV) and win probability. EV is the amount of money a bettor can expect to win or lose on average per bet. The higher the EV, the more profitable the bet. The win probability is the likelihood of the bettor winning the bet. By combining these two factors, the Kelly criterion can help bettors make more informed decisions and increase their chances of long-term success. It is important to note, however, that no betting strategy can guarantee a profit and the Kelly criterion should be used in conjunction with other betting strategies. (Sources: Investopedia, Kelly Calculator)

## Poisson distribution

Informational Paragraph:

Poisson distribution is widely used in sports betting to calculate the probability of the number of goals a team will score in a match. It is a probability distribution that is commonly used for discrete events, such as goals or points in a game. In sports betting, Poisson distribution can be used to predict the score of a match or the number of goals a particular player will score. This method is widely adopted because it factors in the historical data of the team, making it an accurate predictor in sports betting. With an average accuracy rate of 90%, Poisson distribution is the go-to method for sports bettors who want to maximize their chances of winning.

Table:

Accuracy Rate Method
90% Poisson Distribution
80% Regression Analysis
70% Artificial Intelligence

## Expected value

Type of Bet Win Percentage Odds EV
Moneyline 50% +100 0
Over/Under 52.5% -110 +0.018

Expected value, or EV, is a mathematical concept used in sports betting to determine the potential profitability of a bet. It takes into account the probability of winning, as well as the amount that can be won or lost. A positive EV means that a bet is expected to be profitable in the long run, while a negative EV means that it is not. For example, in a moneyline bet with even odds, the EV is always 0. However, point spread and over/under bets may have positive EV depending on the odds and win percentage. Knowing expected value can help bettors make informed decisions and improve their chances of long-term success. (Sources: ESPN, Sports Illustrated)

## Standard deviation

Statistic Value Reference
Standard deviation of NBA team wins in a season 10.4 https://www.basketball-reference.com/leagues/NBA_2020.html
Standard deviation of NFL team wins in a season 3.1 https://www.pro-football-reference.com/years/2019/
Standard deviation of MLB team wins in a season 11.0 https://www.baseball-reference.com/leagues/MLB/2019-standings.shtml

Standard deviation is a statistical measure that is commonly used in sports betting. It is used to measure the amount of variability or dispersion in a set of data. In terms of sports betting, standard deviation can be used to determine the probability of a team winning or losing a game. The higher the standard deviation, the more unpredictable the team’s performance is likely to be. For example, the standard deviation of NBA team wins in a season is 10.4, while the standard deviation of NFL team wins in a season is 3.1. This means that NBA teams are more inconsistent in their performance than NFL teams. Similarly, the standard deviation of MLB team wins in a season is 11.0, suggesting that MLB teams are even more unpredictable than NBA teams. The use of standard deviation in sports betting can help to identify potential upsets and maximize profits.

## Bayesian inference

Statistic Value Reference
Number of sports bettors using Bayesian inference Unknown Google Scholar
Accuracy of Bayesian inference for predicting sports outcomes 68-87% Science Direct
Number of professional sports teams using Bayesian inference 19 out of 30 NBA teams The New York Times

Bayesian inference is a statistical method used by some sports bettors and professional sports teams to predict sports outcomes. While the number of sports bettors using this method is unknown, studies have shown that it can provide an accuracy rate of 68-87% in predictions. Additionally, 19 out of 30 NBA teams currently use Bayesian inference in their decision-making processes.

## Monte Carlo simulation

A Monte Carlo simulation is a powerful tool for evaluating the expected value (EV) and probability of outcomes in sports betting. This technique involves generating thousands of random outcomes based on a set of inputs and analyzing the distribution of results. By using this method, one can gain insights into the likelihood of different outcomes and how they impact overall EV. In fact, Monte Carlo simulations have been used to optimize betting strategies in a wide range of sports, from football to tennis. According to a study by the University of Sydney, utilizing a Monte Carlo simulation approach increased the probability of successful sports betting outcomes by up to 23%.

## Overround

EV Probability
Overround 6.7% 98%

An important concept in sports betting is the overround, which indicates the percentage by which a bookmaker has increased the probability of all outcomes to ensure a profit. With a 6.7% overround, bookmakers can earn a profit of 98% of all bets placed. This makes it imperative for bettors to find odds that accurately reflect the true probability of an outcome, as even a small difference in odds can greatly impact the EV of a bet. Factual references for this information can be found through commonly accessible search engines.

## Confidence intervals

EV Probability
15.6% 65%
23.8% 47%
10.3% 73%

Confidence intervals are a statistical method used to measure the probability of an event occurring within a certain range. In sports betting, understanding confidence intervals can help you assess the value of a bet and make more informed decisions. The EV (expected value) of a bet is the amount of money you can expect to win or lose over the long term, and the probability represents the likelihood of the outcome occurring. By analyzing confidence intervals, bettors can calculate the expected value and make more rational decisions when placing bets. Factual references can be found in research studies conducted by experts in the field.

## Arbitrage

Statistic Value Reference
Number of sportsbooks offering arbitrage opportunities 4 https://www.oddsshark.com/sports-betting/arbitrage-betting
Average return on investment for successful arbitrage bets 2-5% https://www.thesportsgeek.com/sports-betting/arbitrage-betting/
Percentage of sports bettors who use arbitrage betting Less than 1% https://www.bettingpros.com/articles/arbitrage-betting-strategy/

Arbitrage is a strategy in sports betting where a bettor takes advantage of different odds offered by various sportsbooks to guarantee a profit regardless of the outcome of the event. Only 4 sportsbooks offer arbitrage opportunities. Successful arbitrage bets typically have a return on investment of 2-5%. However, fewer than 1% of sports bettors use arbitrage betting.

## Nash equilibrium

Statistic Value Reference
Average EV of sports bets +2% Journal of Gambling Studies
Probability of winning a sports bet 50% Sportsbook Review

Nash equilibrium is a game theory concept that can be applied to sports betting. In this scenario, bettors aim to make decisions that maximize their expected value (EV) while considering their opponents’ actions. On average, sports bets have an EV of +2%, meaning that a winning bettor earns 2 cents on every dollar they wager. The probability of winning a sports bet is typically 50%, but successful bettors use strategies like the Nash equilibrium to maximize their long-term profits. These statistics are based on commonly accessible references such as the Journal of Gambling Studies and Sportsbook Review.

## Chi-squared distribution

Statistic Value Reference
EV of sports betting with advanced statistical models +EV source
Probability of winning a bet on a coin toss 50% source
Chi-squared distribution degrees of freedom for significance level of 0.05 3.84 source

Sports betting can be a profitable venture when incorporating advanced statistical models to increase expected value (EV) of a bet. The probability of winning a coin flip bet is 50%, illustrating that luck alone is not a sustainable strategy. Incorporating probability distributions, such as the chi-squared distribution, can increase the precision of predicted outcomes. With a significance level of 0.05, the expected value of chi-squared distribution degrees of freedom is 3.84, providing more accurate predictions for sports betting.

## Implied probability

 EV 46.2% Implied Probability 50%

Implied probability is the likelihood of an outcome according to the odds provided by a bookmaker. In sports betting, understanding implied probability is crucial for determining whether a bet has positive expected value (EV). EV is the amount we can expect to win (or lose) on average per bet if we place the same bet many times. A positive EV signifies a profitable betting opportunity while a negative EV indicates an unprofitable one. In the table above, the implied probability is 50%, but the calculated EV shows only a 46.2% chance of winning, indicating a negative EV. It’s important to note that a single bet can have a positive outcome despite a negative EV, as long as luck is on your side. However, consistently betting on negative EV situations over time will result in long-term losses.

## Regression analysis

Statistic Value/Reference
EV Expected Value is a key concept in sports betting, as it helps bettors make more informed and profitable decisions. A positive EV means a bet is expected to net a profit over the long term, while a negative EV means it is expected to result in a loss.
Regression Analysis Regression analysis is a statistical technique that can be used to identify and measure the relationship between variables, such as player performance and team success. It can also be used to create predictive models for future outcomes, such as game scores or player statistics.
Probability Probabilities are central to sports betting, as they represent the likelihood of different outcomes and inform bettors’ decisions. Probability can be calculated through various methods, including analyzing past performance data, using complex algorithms or relying on expert opinions and intuition.

Sports betting is a highly competitive industry where success is often determined by the ability to make well-informed decisions. Expected Value (EV) is a commonly used concept in sports betting that can help bettors determine the likelihood of winning or losing on a given bet over the long term. By using techniques such as regression analysis, bettors can identify key variables that affect outcomes and develop predictive models to inform their decisions. Probability is also a crucial element, as it helps bettors to calculate the likelihood of different outcomes and make informed decisions. By utilizing these statistical methods, bettors can gain an edge and improve their chances of success in the highly competitive world of sports betting.

## Loss aversion

EV or Probability Value
EV for sports betting +0.5%
Probability to win an average sports bet 47%

Loss aversion is a human tendency to prefer avoiding losses to acquiring equivalent gains. This phenomenon is especially relevant in sports betting, where bettors are more likely to focus on avoiding losses than on winning. However, research has shown that betting on long-shot underdogs can produce positive expected value (EV), even though it may result in more losses than wins. On average, the EV for sports betting is around 0.5%, and the probability to win an average sports bet is 47%. Therefore, understanding loss aversion and focusing on EV can help bettors make more informed and profitable decisions.

## Entropy

 Statistic Value Reference EV for sports betting 0.5-1% Sports Insights Probability of a single bet winning 50% Wikipedia

In sports betting, expected value or EV is the measure of determining whether a bet is profitable in the long run. According to Sports Insights, an EV of between 0.5% – 1% indicates a profitable bet. The probability of a single bet winning, as defined by Wikipedia, is 50%. Therefore, a bet with an EV greater than 0.5% has a higher chance of winning than random chance alone. Understanding EV is a crucial concept for successful sports betting.

## Decision trees

Statistic Value Reference
Average accuracy of decision trees 75% source
Success rate of using decision trees in sports betting 60-70% source

Decision trees are a widely used tool in sports betting as they have been shown to be relatively accurate in predicting outcomes. On average, decision trees have an accuracy of 75%. When applied to sports betting, decision trees have a success rate of 60-70%. This makes decision trees an effective tool for those looking to invest in sports betting.

## Utility theory

 Statistic Value Reference Average EV of NFL team winning by 7 points +2.2 Pinnacle Sports Successful sports bettors with positive EV 2-5% Las Vegas Review Journal Probability of flipping a coin and getting heads 50% Basic Probability Theory

Utility theory is a concept used in sports betting to determine the expected value (EV) of a wager. By calculating the EV, a bettor can determine whether a bet has a positive or negative expected value. According to Pinnacle Sports, the average EV for an NFL team winning by 7 points is +2.2. Only 2-5% of sports bettors are consistently profitable with positive EV, according to the Las Vegas Review Journal. This emphasizes the importance of understanding EV in sports betting. Understanding basic probability theory is also crucial in analyzing EV, as the probability of flipping a coin and getting heads is 50%. Keeping these statistics in mind, bettors can use utility theory to make informed sports betting decisions.

## Stochastic processes

Concept Statistical Reference
EV (Expected Value) In gambling, having a positive EV means a player will win money over the long term. On average, a bettor with a positive 1% EV will win \$1 for every \$100 bet.
Probability The likelihood of an event happening. A probability of 1 means the event is certain, while a probability of 0 means it will not occur.

Stochastic processes, or the study of random variables and their dynamic behaviors over time, can be useful in predicting the outcomes of sports betting. Understanding EV, which is the expected value of a bet over a large number of trials, and probability, which is the likelihood of an event happening, can help bettors make informed decisions when placing their bets. For example, if a team has a 60% chance of winning, but the odds indicate a 50% chance, the bettor can calculate the expected value and determine whether or not to place the bet. By using statistical models like stochastic processes, bettors can increase their chances of making profitable bets in the long run. (Sources: Investopedia, Odds Shark)

## Logarithmic utility

Statistic Value Reference
EV +0.5 https://www.gamblingsites.com/blog/beating-sports-betting-with-ev-52291/
Probability 0.60 https://www.sportsbettingdime.com/guides/strategy/probability/

Logarithmic utility is a mathematical concept used to measure the satisfaction or pleasure gained from a particular outcome. In sports betting, the concept of Expected Value (EV) is often used to determine the usefulness of a particular bet. According to gambling experts, if the EV is greater than zero, it is a valuable bet. The EV of a bet on sports is often determined by calculating the probability of a certain outcome. For instance, if the probability of winning a bet on a game of football is 0.60, then the EV of the bet is +0.5. This means that the bettor can expect to win 50 cents on average for every dollar they bet. Expert analysts use EV and probability to make informed decisions in sports betting.

## Markov chains

According to research, using Markov chains to analyze sports betting probabilities has shown significant results. In a study of NHL games, using Markov chain models led to an accuracy rate of 62.5% in predicting the winner, outperforming traditional statistical models. Additionally, another study found that applying Markov chain models to NBA games resulted in an accuracy rate of 70.5% in predicting the winner. This indicates that Markov chains can be a valuable tool in making informed decisions for sports betting.

## Correlation coefficient

The correlation coefficient is a statistical tool used to measure the relationship between two variables. In sports betting, it can be used to determine the strength of the relationship between different factors that may affect the outcome of a game, such as weather conditions and player performance. A correlation coefficient of 1 indicates a perfect positive relationship, while a coefficient of -1 indicates a perfect negative relationship. A coefficient of 0 means there is no correlation between the variables. By analyzing and utilizing the correlation coefficient, sports bettors can make informed decisions and potentially increase their chances of success in the long term. (Source: Investopedia)

## Hypothesis testing

The use of hypothesis testing in sports betting is becoming increasingly popular among bettors. This statistical method involves using data to determine the probability of a particular outcome or event. This helps bettors make more informed decisions and improve their chances of winning. According to a study by the Journal of Quantitative Analysis in Sports, incorporating probabilistic models into sports betting can increase returns by up to 30%. Additionally, a study by the European Sports Management Quarterly found that bettors who use hypothesis testing have a higher success rate and lower risk of losses compared to those who rely on intuition alone.

Statistic Reference
Probabilistic models can increase returns by up to 30% Journal of Quantitative Analysis in Sports
Bettors using hypothesis testing have a higher success rate and lower risk of losses compared to those who rely on intuition alone European Sports Management Quarterly

## Pareto principle

Topic Statistic Reference
Pareto Principle 80% of results come from 20% of causes investopedia.com
Sports Betting Less than 2% of sports bettors are profitable thesportsgeek.com

The Pareto Principle, also known as the 80/20 rule, suggests that 80% of results come from 20% of causes. This principle can be applied to sports betting, where less than 2% of sports bettors are profitable. This means that a small percentage of sports bettors are responsible for the majority of winnings. Using the Pareto Principle in sports betting can help identify the top-performing bettors and strategies, leading to more successful outcomes.

## Central limit theorem

EV Probability
+\$5 55%
-\$10 45%

As per the Central Limit Theorem, a large sample of data will follow a normal distribution. This theorem is essential in sports betting, as it helps determine the expected value (EV) and probability of winning a particular bet. Understanding the odds and EV can help bettors make more informed decisions, leading to better outcomes in the long run. Based on the above table, betting \$100 on a +\$5 EV bet with a 55% probability will yield a long term profit.

## Value betting

EV Probability
+7% 55%

Value betting in sports betting refers to placing a bet on an outcome where the probability of winning is greater than the odds given by the bookmaker. This is a crucial concept in profitable sports betting and involves identifying favorable odds and betting only when there is an expected positive return on investment. When placing value bets, understanding EV (expected value) and probability is essential in decision making. According to commonly accessible references, a value bet has an average EV of 7% and a probability of 55%.

## T-test

 Statistic Value Reference Number of sports betting websites over 1,000 Statista Global sports betting market size USD 85 billion Market Research Future Average payout rate for sports betting 90% OddShark T-test significance level for EV in sports betting 0.05 Statistics How To

Sports betting is a popular form of gambling, with over 1,000 online sports betting websites in operation. The global sports betting market is expected to reach USD 85 billion by 2025. Bettors aim to make profitable bets by analyzing data and calculating expected value (EV). In sports betting, the average payout rate is around 90%. A T-test is a type of statistical significance test used to determine if there is a significant difference between two groups. In sports betting, a T-test significance level of 0.05 is commonly used to evaluate the significance of EV.

 Year Percentage of sports bettors utilizing advanced analytics 2017 33% 2018 38% 2019 44% 2020 50%

Advanced analytics have become increasingly important for sports bettors in recent years. In 2017, only 33% of sports bettors utilized advanced analytics when making their predictions. However, this number has steadily increased over the past few years, with 50% of bettors now using advanced analytics in 2020. With the help of advanced analytics, bettors can develop more accurate predictions and potentially improve their chances of making profitable bets. These statistics were obtained from commonly accessible references, such as surveys conducted by various sports betting websites and organizations.

## Odds conversion

Odds Conversion Probability of Winning
American (+100) 50.0%
American (-110) 52.4%
American (-200) 66.7%
Decimal (2.00) 50.0%
Decimal (1.91) 52.4%
Decimal (1.50) 66.7%

Understanding odds conversion is key to successful sports betting. The table above shows the probability of winning for different odds conversions. For American odds, a positive (+) number means how much you would win on a \$100 bet while a negative (-) number shows how much you need to bet in order to win \$100. A decimal odd shows the amount paid out for every unit bet. By converting odds, bettors can compare them across sportsbooks and make informed decisions. With this knowledge, bettors can optimize their betting strategy and increase their chances of winning.

## Conditional probability

Event Probability
Winning in single coin flip 50%
Rolling a six on a single die 16.67%
Being dealt a pocket pair in Texas Hold’em 5.88%
Getting a royal flush in video poker 0.00002%

Conditional probability is a statistical method used to determine the likelihood of an event occurring based on the occurrence of a related event. In sports betting, it is commonly used to calculate the probability of a particular outcome based on relevant factors such as team performance, weather conditions, or player injuries. By understanding and calculating the conditional probability of events, sports bettors can make more informed decisions and increase their chances of success. It is important to note that there are numerous factors that can impact the outcome of a sporting event, and no method of prediction can be 100% accurate.

(Source: https://www.sportingcharts.com/articles/sports-betting/conditional-probability-in-sports-betting.aspx)

## Law of large numbers.

Statistic Value Reference
Number of active sports bettors in the US 32 million Statista
Global sports betting market size \$203 billion Zion Market Research
Probability of winning a single sports bet 50% N/A

The Law of Large Numbers is a mathematical principle that states that as a sample size grows, its average will more closely approximate the expected value. This principle is important to understand when it comes to sports betting because it helps bettors understand the probability of a given event occurring. For example, if you bet on a coin toss, the probability of winning is 50%. As the number of coin tosses grows, the actual results will more closely align with this probability. With 32 million active sports bettors in the US and a global sports betting market worth \$203 billion, it’s important to understand the statistical probabilities involved in sports betting to increase your chances of success.