I created a semi-normal (i.e. symmetrical) distrubution of ten batting averages, assuming .250 is average:
[.200, .220, .230, .240, .245, .255, .260, .270, .280, .300]

Then, based on each average, I roll once for a hit (loosely simulating a single at-bat). If it’s a successful hit, I “predict” that I’m looking at a good (above-average) hitter. If it’s a miss, I “predict” that I’m looking at a bad (below-average) hitter. Since I already know the hitter’s “true” average, I can compare the prediction to the actual value.

My hypothesis is that a hit is a better predictor of a “good” hitter than a miss is a predictor of a “bad” hitter.

So I run the sim for 10,000,000 hitters.
Hit correctly predicts good hitter: 54.64%
Miss correctly predicts bad hitter: 51.54%

You can fiddle with the input values all you want to change the variance, but until the average average gets up to .500, then a positive outcome will always be a better predictor of an above-average hitter than a negative outcome predicts a below-average hitter.

Huge disclaimer: none of this implies any statistical significance whatsoever! These outputs are still very close to 50%. Looking at a single outcome (or a small sample) to guess a hitter’s performance is not a good idea.

Small sample sizes are small sample sizes, whether they produce the result you’re “expecting” or not.

Can you then tell me how loaded it is, and in which direction?

Of course not.

But let’s say we’re pulling coins from a jar where we know the average coin is weighted such that it flips 25% heads and 75% tails (w/ normal distribution). We randomly grab two coins from the jar and flip each coin only once. Coin A lands heads, Coin B lands tails. Clearly, neither result will have any statistical significance, but:

Hypothesis 1: Coin A is a “heads” coin (> 25% heads)
Hypothesis 2: Coin B is a “tails” coin (< 25% heads)

Wouldn’t we have slightly more confidence that H1 would prove true if we repeated the coin flip 999,999 more times? Doesn’t the occurrence of an improbable event give us slightly more information than the occurrence of a probable event?

No it’s not. That’s the definition of “small.” Say I have a loaded coin. Say I flip it twice. Say it comes up once heads and once tails. Can you then tell me how loaded it is, and in which direction?

But the time he ends up in the majors they probably won’t be. See Clement and the catching position, for example.

But unless the FO undergoes an honest-to-god revolution, Raben will get traded for some overpriced relief pitcher or $10M/year bottom-of-the-rotation starter before he cracks the roster anyway.

Dennis Raben, Everett (45 PAs)
429/556/743 (1.299 OPS)

Craig Wilson, Tacoma (18 PAs)
500/611/929 (1.540 OPS)

Food for thought: in a game where batters experience failure more often than success, a small sample of unusual success is slightly more meaningful than a small sample of unusual failure.