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The editors at Sports Management Degrees decided to research the topic of: ## Predicting Baseball: Demystifying Bayes' Theorem## The power of probability- Nate Silver, the "king of quants", - "Quants" is nerd talk for quantitative analysts - 2003 - Released PECOTA the most accurate baseball player performance forecasting system in the world (still to this day.) - Correctly predicted: - 2008 - Presidential election: the winner in 49 of the 50 states - 2008 - Senate: the winners of all 35 U.S. Senate races - 2012 - Presidential election: the winner of all 50 states - 2012 - Senate: the winners in 31 of 33 U.S. Senate races - 2012 and 2013 Champion teams of NCAA Men's Basketball Tournament ## Top Secret Classified- While the math behind Nate Silver's predictive system is unknown to the public, it is understood to be based on Bayes. - It is Bayes-based. - "In the past ten years, it's hard to find anything that doesn't advocate a Bayesian approach." -Nate Silver - Why? - "Aggregate or group forecasts are more accurate than individual ones." -Nate Silver ## What is Bayes' Theorem?- A probability theory to measure the degree of belief that something will happen - using conditional probabilities: - probability event A occurs, given event B occurred - Bayes theorem was first published in 1763, 2 years after Thomas Bayes' death - Bayesian inference - Hindsight is 20-20: - Define the variables based on actual historic data - apply historic probabilities to similar future events - Degrees of belief will change as more evidence is considered ## How to Play Ball! The Bayesian Way- Will the yankees win their next game? - Hypothetically, Let's say that The Yankees are having a great season. - Step 1: Start with the known results that you are trying to predict - Event A (%W and %L) - So far out of 100 games played - 72 have been wins (W 72%) [point and insert into theorem] - P(A.1) = 72/100 = .72 <--(W 72%) - 28 have been losses [point and insert into theorem] - P(A.2) = 28/100 = .28 <--(L 28%) - Event B (Condition) - When Sports analyst Bob predicts a Win! - He is correct and Yankees win 55% of the time - Common mistake! This one stat does not mean the Yankees have a 55% probability of winning. Consider more evidence. - P(B/A.1) = .55 [insert into theorem] - (Bob predicts a win and yankees win 55% of the time) - When Sports analyst Bob predicts a Win! - He is incorrect and Yankees lose 45% of the time - P(B/A.2) =.45 [insert into theorem] - (Bob predicted a win and yankees lose 45% of the time) ## Night Owls- Lets say that the Yankees win 60% of night games - Common mistake! This one stat does not mean the yankees have a 60% probability of winning. Consider more evidence. - Start with the results trying to predict - Event A (1 and 2) aka (%W and %L) - Sports analyst Bob has predicted a Win - 76% chance the Yankees will win - P(A.1) = 76/100 = .76 () - 24% chance the Yankees will lose - P(A.2) = 24/100 = .24 - Event B (1 and 2) [Condition] - When Yankees play at night - Yankees win 60% of the time - P(B/A.1) = .60 - Yankees Lose 40% of the time - P(B/A.2) =.40 - There is now an 83% chance the Yankees will win their 101st game - Breakdown - When Bob says 101st game will be a win, the probability is 76% - Yankees typically win more night games than not: 60% of them - If Bob claims a win 72%-->76% - It's a night game 76% -->83% ## More game changing conditions to consider- line up - DH - Left handed pitcher - Midgame injuries - turf - wall height - humidity - crowd size - home field Sources - https://www.baseballprospectus.com/article.php?articleid=7652 - https://bayesball.blogspot.com/ - https://www.hardballtimes.com/main/article/bayes-theorem-and-prospect-valuation - https://skepticalsports.com/?tag=bayes-theorem - https://stattrek.com/probability/bayes-theorem.aspx |