Also, the question is ultimately; “Will Cuddyer be 5 million dollars better than Ty Wigginton?” My guess is that he is.

]]>still, it’s a good question.

]]>Let’s take a SS for example. The average team hits about 2000 ground balls a year (correct me if I’m wrong, it may be closer to 2500), so the SS may field about 600, again this is a guess though it won’t affect my argument much. Now, let’s pretend he sees three ‘zones,’ each of which gets 200 balls hit to it. He can filed 90% of the ones in the middle zone, but only 50% in either of the two side zones. From probability theory, we know the variance will be

200*.5*.5 + 200*.9*.1 + 200*.5*.5 = 118

Hence the standard error for this SS is about 11 plays per season. This translates to a range of over 40 plays.

Now let’s assume if you make the play, it’s an out, and if you don’t it’s a single. An out is worth about -.25 runs and a single is worth about .5 runs. That means the range is worth a difference of 30 runs! So if a player has a good season followed by a bad, it’s not crazy to see a fluctuation of 30 runs.

I know these numbers are off, but changing them won’t affect much. Now let’s assume we have the world’s greatest SS, who makes 90% of all his plays, whichever zone they are it. For 600 plays, we expect a range of about 20 runs! It’s smaller, but still significant.

Of course, the range of about 40 plays is not uniform, and we only expect players to perform at the tails on rare occasions, so the actual year to year fluctuations would be about 5 to 10 runs on average, which I believe is pretty accurate for UZR numbers.

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