I wouldn’t exactly call a 2010 xFIP of 3.32 struggling…”less dominant” is more accurate.

]]>If not, I have no problem as well going with a closer by committee with either just Broxton and Kuo, or the three of Broxton, Kuo, and Jansen.

]]>What does the distribution look like if you break out the fastball speeds by month?

]]>For proportion measures (batting average, OBP, strikeout %, etc.) all you need to add is the sample size; the margin of error for a 95% confidence interval is 1.96*sqrt(p*(1-p)/n), where p is the observed (sample) proportion and n is the sample size. We see that in 2009 Broxton faced 300 batters, walking 1 intentionally, so he pitched to 299 and struck out 114. That’s 38.1% (.3813), so for a margin of error we have 1.96*sqrt(.3813*.6187/299) = .0551. Our 95% confidence interval is thus 38.1 +/- 5.5, so we estimate with 95% confidence his true talent level in 2009 was to strike out between 32.6% and 43.6% of batters pitched to.

Repeating for 2010, we get 73/266 = .2744, and MOE = 1.96*sqrt(.2744*.7256/266) = .0536, so a strikeout rate of between 22.0% and 32.8% . There is a small overlap in the ranges here; we should compute a formal estimate of the difference (the math is somewhat more extensive) but we can be comfortable saying we are highly confident the difference was real and not a fluke of sample size.

For interval measures (things that can’t be expressed as a percentage) we need sample size and standard deviation, and basically use standard deviation in the formula instead of p*(1-p). We also must use a t-value which varies with the sample size instead of the fixed 1.96; for 2010 (265 “degrees of freedom, or n-1) this would be 1.969.

These calculations are trivial to do in Excel, and the authors on this web site should do so for every statistic reported. If anyone needs help, email me at paul hightower 84 at hot mail dot com .

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