wT(n(Ip – ppT))w

For my example, that comes out as 10.859, so our standard error is 3.295.

Thanks!

]]>For example, let us assume a batter only has two possibilities: get on base or produce an out. The latter is good for +0.5 runs, the latter for – 0.25 runs. Now pretend a player gets on base at a rate of 0.350 of the time. Over 500 plate appearances, we expect this player to accrue

175*.5 – 325*.25 = 6.25 runs.

The variance of a single event is n*p*(1-p), which is equivalent to

175*.650*.25 + 325*.350*.1025 = 40.1

Take the square root to get a standard error of 6.33

Note the variance will increase as n increases as we are finding the variance of a sum rather than a mean. Furthermore, power hitters will have considerably more variance, as their more probable outcomes are associated with large weights. A small change in HRs will have a much bigger change than a small change in singles, leading to more variance.

]]>How can you talk about error without knowing the margin of error for a specific statistic? This is my problem with many stats; I know they have flaws but don’t know the magnitude of those flaws.

2 runs difference could be huge if the margin is .2 but tiny if the margin is 10.

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