Tuesday, August 03, 2010
Odds Ratio Method: track runners and baseball
Let’s say you have a runner that runs the 100m, and we observe his running time as 10.0 seconds, with one SD = 0.2 seconds. Let’s call this runner Aurora. And we have a second runner who averaged 10.1 seconds, witth one SD = 0.2 seconds. This runner is called Bolt.
How often will Aurora beat Bolt? Running a simulator 10,000 times, I get .640. I’m sure there’s a nice probability calculator that will give us the same result (if so, please share).
Let’s say we have a third runner, called Canuck, and he runs in 10.2 +/- 0.2. Bolt will beat him .640 times.
What are our expectations of Aurora beating Canuck? Well, the Odds Ratio suggests the following:


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