Uneven Distribution

If you’ve taken an introductory math class, you’ve probably seen the bell curve graph that explains how the distribution of things are grouped around the average and thinner at the extremes. National League second baseman have decided to band together and disprove normal distribution in 2008, however.

As a group, they are hitting .267/.335/.415 for a .750 OPS. Normal distribution would suggest that we’d find a cluster of players with an OPS between .700 and .800, but in reality, only one of the 13 qualified second baseman falls in that range – Luis Castillo. The other twelve are split into two distinct groups – tremendous and terrible. This morning, we look at the guys excelling, and tonight, we’ll look at those who are dragging the average down.

We’ve talked about the amazing years Chase Utley and Dan Uggla are having. Both are having historically tremendous seasons for a second baseman, and they’re mortal locks to represent the NL at the all-star game. But behind those two MVP candidates are four pretty good players in their own right.

Orlando Hudson: .303/.372/.503, 0.82 WPA/LI
Brandon Phillips: .287/.336/.529, 0.55 WPA/LI
Kelly Johnson: .299/.362/.495, 0.34 WPA/LI
Mark DeRosa: .297/.384/.449, 0.66 WPA/LI

All of these guys are having seasons that would create a strong case for an all-star bid in any other year. Hudson and Phillips both add terrific defense to their offensive value, while Johnson and DeRosa continue to be the under the radar stars for their respective teams. You really can’t go wrong with any of these six guys, as all of them are having tremendously valuable seasons.

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Dave is a co-founder of USSMariner.com and contributes to the Wall Street Journal.

7 Responses to “Uneven Distribution”

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  1. Scott says:


    How about showing the actual graphic while discussing it so we can visualize the spread?

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  2. Brandon says:

    Can you explain what you mean by “One standard deviation from that .750 OPS is .015 points” and how you came up with that number? Thanks!

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  3. Chris says:

    Standard deviations are supposed to account for huge deviations from the mean. If what you say is true, namely that one group is freaking awesome and the other group is terrible, then the standard deviation should be huge also. There must be something in the data that is skewing the data towards moderation, maybe a large chunk of back-up second basemen that have collectively had a lot of at bats and that fall within the required 3 standard deviations.

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  4. Zach says:

    I ran the data myself, and it looks like you misread the standard deviation. It should be .157, not .0157. So three standard deviations from the mean (.786) would put the norm between .315 and 1.257. All thirteen 2Bmen fall in this range.

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  5. Dave Cameron says:

    Whoops – good catch, Zach. I just put the decimal in the wrong spot. That’s what I get for writing this post in the wee hours of the morning. I’ll update the post.

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  6. Brandon says:

    “Normal distribution would suggest that we’d find a cluster of players with an OPS between .700 and .800″

    To be more specific, in a normal distribution with a mean of .750 and a SD of .157, you’d expect 24.3% of the curve to fall between .700 and .800. So you’d expect about 3 of these 2Bmen to fall within that range. You’d expect most players, about 68.3%, to fall within one standard deviation, which ranges from .593 to .907. What would be mildly interesting is knowing whether the percentage of players performing outside of this range is considerably larger than 68%. In all, though, I don’t really get why this is valuable. We already have other metrics to show us how good some of these players are doing. In the long run, the data will probably normalize.

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  7. Dave Cameron says:

    There was no intent on my part to have this post be valuable from a player valuation standpoint. It stands on its own as an interesting tibdit, and that it doesn’t advance the quantification of value doesn’t really matter to me.

    It’s interesting, I think, that the division line between good and bad second baseman is so obvious this year. That’s the whole point of this post.

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