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The editors at Sports Management Degrees decided to research the topic of: Predicting Baseball: Demystifying Bayes' TheoremThe 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 Bayesbased.  "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 2020:  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  http://www.baseballprospectus.com/article.php?articleid=7652  http://bayesball.blogspot.com/  http://www.hardballtimes.com/main/article/bayestheoremandprospectvaluation  http://skepticalsports.com/?tag=bayestheorem  http://stattrek.com/probability/bayestheorem.aspx 