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I'm reading a paper about predicting baseball games, and I'm having trouble figuring out what one of the variables means. It's the "r1, r2, and r3" variables in the following passage:

It is unreasonable to expect that all three ratios affect the probability of winning in the same way. We therefore adopt unknown contribution parameters r=(r1,r2,r3) where we define the relative strength of the home team over the visiting team at time s as

λs=α^r1∗β^r2∗γ^r3

We assume that the contribution parameters are constant across all MLB teams and arise from independent prior distributions with ri ∼uniform(0,ai)where ai is prescribed, i=1,2,3. The value ri close to 0 implies that the corresponding ratio has little effect on the relative strength. For the MLB data considered in this paper, we let ai =2 for i =1,2,3. We view these as subjective priors where we use our knowledge of MLB to impose effects based on the current winning percentage, batting and pitching. Note that in the context of the models described below, ai = 2 is a realistic upper bound for the value of ri , i=1,2,3.

I don't understand what they mean by

ri ~ uniform(0,ai)

This r variable is responsible for weighting the particular variables involved in this prediction, so it seems to be pretty important that I know how to calculate it. Thank's in advance.

Edit: Here is the paper in question: http://people.stat.sfu.ca/~tim/papers/mlb.pdf

Community
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jstewartmitchel
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1 Answers1

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It means they expect the $r_i$ to be uniformly (http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29) distributed across all possible match-ups with a mean of $\bar{r_i} = \frac{a_i}{2}$ and $r_i \in [0, a_i] = [0, 2]$.

Also, for better understanding, please provide a link to the paper in question.
AlexR
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