The same happens with negative feedback. Should your daughter come home with a poor grade reflecting bad luck, you might chide her and punish her by limiting her time on the computer. Her next test will likely produce a better grade, irrespective of your sermon and punishment.

Of course it's impossible to know if the grade is because of luck so obviously you try to determine why she got the grade: didn't do the homework, test was poorly worded, bad noise/odor in the test room, never really grapsed the material, etc. It's pretty mindless to write off results to "luck" without first seeing if they're "trend".

Depends on the way the test is set up. If it's all multiple choice, with many difficult questions that lead to guessing, then luck is a big factor.

Back in my day, after those of us lucky enough to avoid sabre-tooth tigers made it to school, most of the tests were pretty easy if you read what you were supposed to read and moderately tough if you didn't.

In Poker the results = skill + luck works out slightly differently,

because mother ####### donkeys always get way more luck.

Not that it matters much but team outcomes (or batter outcomes) do not strictly meet the assumptions of the binomial distribution. The binomial is (almost certainly) a reasonable approximation. The independence of tests is probably the most "controversial" of the binomial assumptions for baseball (hot and cold streaks).

Also one doesn't normally think of discrete variables in a classical test theory (or "true score theory") way. It doesn't matter much once you're talking outcomes of 162 games or 600 PA but O = T + E is more conformable with continuous variables. For a discrete variable, P(O) = T (not usually expressed as a "true" score but go with it) or in the case of the binomial, E(O) = NT where N is the number of trials, T the true p of success and O the number of successes. As N gets large, the binomial approximates a normal distribution for most baseball-y values of T.

Daniel Kahneman descirbes this quite well in thinking fast and Slow when an Israeli general tells him that positive feedback never works and negative feedback always works. when he praised cadets for a clean execution of some maneuver, the next time they try they usually dont do nearly as good, and whever he yelled at someone for screwing up, they always did better.

Kahneman was quite excited by this as he saw this as a perfect example of regression to the mean, but realized that regression ot the mean is one of the main reasons why people think megative feedback is so effective. This of course is most true in cases where you only praise or reprimand serious outliers. Yhere will always be a distribution of talent of course.