Predicting Baseball: Demystifying Bayes' Theorem

PREDICTING BASEBALL Demystifying Bayes' Theorem Nate Silver CREATOR OF PECOTA, THE MOST ACCURATE BASEBALL PLAYER PERFORMANCE FORECASTING SYSTEM IN THE WORLD The "king of quants" While the math behind Nate Silver's predictive system is unknown to the public, it is understood to be based on Bayes. "Aggregate or group forecasts are more accurate "In the past ten years, it's hard to find anything that doesn't advocate a Bayesian approach." than individual ones." THE MAN WHO CORRECTLY PREDICTED: PRESIDENTIAL ELECTION SENATE RACES NCAA BASKETBALL Champion teams 2012 and 2013 49 of the 50 states all 50 states all 35 races 31 of 33 races in 2008 in 2012 in 2008 in 2012 What Is Bayes' Theorem? A probability theory to measure the degree of belief that something will happen using conditional probabilities. PROBABILITY THAT PROBABILITY EVENT A OCCURS, GIVEN THAT EVENT B OCCURRED CONDITIONAL EVENT EVENT B Bayes' theorem was first published in 1763, 2 years after Thomas Bayes' death EVENT HOW TO PLAY BALL! THE BAYESIAN WAY Hypothetically, let's say that The Yankees are having a great season. Let's use Bayes' Theorem to see if The Yankees win their next game. START WITH THE HISTORY OF THE EVENT YOU ARE TRYING TO PREDICT BAYES' THEOREM p(A,) p(B|A,) V EVENT A p(A,|B) = p(A,) p(B|A,) + p(A,) p(B|A,) Probability The Yankees will win based off past performance So far, out of 100 games played, 72 have been wins. A=72% p(.72) p(B|A,) p(A, |B) A:=28% That means that so far out p(.72) p(B|A,) + p(.28) p(B|A,) of 100 games, 28 have been losses. EVENT B FACTOR IN ANOTHER RELEVANT VARIABLE PAST PREDICTED WINS AND LOSSES When Sports analyst Bob predicts that The Yankees will win, he is correct 55% B=55% Given A, occurs (win) .72 x .55 of the time. p(A,|B) = .72 x .55 + .28 x .45 That means when Sports analyst Bob predicts that The Yankees will win, he is B=45% .----> Give A, occurs (lose) incorrect 45% of the time. THE CHANCES OF EVENT A OCCURRING AGAIN ASSUMING EVENT B DOES OCCUR IV RESULT Based on: The Yankees' past performance and Bob's win prediction, there is a 76% probability of The Yankees winning their next game. > p(A, |B) = ( 76% p(A, B) ADDING ADDITIONAL VARIABLES The more variables taken into consideration, the more accurate the prediction will be. .76 x .60 Let's say that The Yankees win 60% of night games. p(A,|B) .76 x.60 + .24 x .40 B=60% B=40% When A1 ocCurs When A1 occurs 83% p(A,|B) Source SPORTS-MANAGEMENT-DEGREES.COM http://bayesball.blogspot.com/ http://skepticalsports.com/?tag=bayes-theorem http://stattrek.com/probability/bayes-theorem.aspx DEVELOPED BY N NOWSOURCING http://www.baseballprospectus.com/article.php?articleid=7652 http://www.hardballtimes.com/main/article/bayes-theorem-and-prospect-valuation