Aha

I think you might have something here, but I’m not sure yet.

On one hand, I generally hate fake splits data for the following reason: statistical significance entails testing whether the odds of such an extreme difference in outcomes would occur are less than 5%. In other words, 1/20 of all randomly generated splits tests will yield a false positive—and lead us to conclude that such a split is a significant difference, and we’ll go searching for causes.

So, I generally treat this type of stuff with hesitation. The cumulative data is not significant—the differences in day/night AVG and OBP (it’s harder to test SLG since it’s not a percentage) are NOT statistically significant.

However, aggregating data blurs results at times so I did look at individual players. If you check 10 regulars/starters (you skipped Feliz, but I assume you meant to), you will expect that about 0.5 of them will yield a false positive.

However, it looks like Werth does have a significantly higher AVG in the night than the day this year and a significantly higher OBP at night in his career than during the day. His OBP in 2008 and AVG in his career both narrowly missed statistical significance, but are worth nothing at least.

Utley just misses statistical significance for his career OBP, with the odds of his 34-point OBP difference happening by chance falling at about 8%. The sample sizes for 2008 are too small to look at anyway.

Feliz actually just missed statistical significance for the difference between his daytime and nighttime average (.191 day, .290 night), but his career shows basically no difference (.250 day, .255 night).

It could very well be that randomness is generating these results, but I’m not quite sure. There does seem to be some evidence that Utley and Werth probably are better night hitters than day hitters. Still, I’m not completely convinced. It’s definitely worth noting, and it might be useful when deciding on off-days for players.

Sounds good. I’m not quite sure why hitters are worse in the day or night. I’m guessing it has to do with vision and picking up the ball as it’s pitcheed, maybe the same types of comfort that might have to do with homefield advantage.

As for the formula, it’s actually not that bad. If you’re curious (or if anybody else wants to test something), it goes like this:

Say you have {1}: X(a) sucesses in N(a) trials for group a {2}: X(b) sucesses in N(b) trials for group b

Then come up with three probabilities:
(1): p(a)= X(a) / N(a)
(2): p(b)= X(b) / N(b)
(3) p(a&b)= [X(a)+X(b)] / [N(a)+N(b)]

Then the formula is:

[p(a)-p(b)] / square root of [ (p(a&b) * (1-p(a&b)) * (1/N(a) + 1/N(b)) ]

If this number is bigger than 1.96 or smaller than -1.96, you have statistical significance For example, it works very well with batting average. p(a) and p(b) are batting averages in each spit and p(a&b) is total batting average, and N(a) and N(b) are the number of at-bats both ways.

As for whether I’m “bigger brains”, it’s a good thing you haven’t seen me try to remember my high school Spanish! I was so bad that even after taking it for 2 years of middle school and 4 years of high school, I still couldn’t pass out of it for college and needed to take a semester there. My wife is perpetually confused when she asks me what something in Spanish on TV or whatever means, and I still don’t know despite my 7 years of studying it.

LaRoche of the dodgers, would anyone be interested in him?