Monday, December 2, 2013

Odds of a hit or a home run -- Cal Ripken 1996 data

This post explains and illustrates the concept of odds.  It uses the Cal Ripken 1996 batting data.


Data for Cal Ripken 1996 Season
Singles
111
Doubles
40
Triples
1
Home Runs
26
At Bats that Did not end in a hit
462
At Bats
640
Batting Average
0.278


Example 5.2:  On the basis of this 1996 regular season data, what are: (1) the odds of Cal Ripken getting a hit or not getting a hit on a specific at bat; and (2) the odds of a home run or not getting a home run on a specific at bat?

Definition of odds:  The odds an event will occur is defined as 

P/(1-P) where P is the probability the event will occur and 1-P is the probability that the complement of the event will occur.

Answer to Example 5.2: The odds of a Cal Ripken hit are 0.385 (0.278/(1-0.278)) and the odds of not obtaining a hit are the reciprocal 2.60. Home run odds are 0.043 (0.041/0.959) while odds of not getting a home run are the reciprocal 23.4.

Note:  Note that odds of events are often positively skewed.   The odds of an event is often used as the dependent variable in a regression analysis but regression models often assume the dependent variable is normally distributed rather than skewed.  Often in these regression models the analyst will use the log of the odds as a dependent variable because it is less skewed than the odds. 

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