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Does A Player Own A Skill Or Was It Just Sample Size?

Once a player demonstrates a skill, he owns it. This adage is attributed to Ron Shandler at Baseball HQ and frequently used to project a rebound from a worse performance level to a better one - assuming that player has been at that better level as some time in the player's past.

I hear it frequently enough on various fantasy sports shows and podcasts that I conclude it to be an accepted piece of fantasy intelligence. What I wonder is how it jibes with the arguments of small sample size when applied to players who have had a particularly good stretch of performance.

Does the hot stretch of performance mean the player now "owns" the skill? If it does, doesn't that negate the small sample size argument?

How about a bad stretch of performance? Doesn't that mean he owns the ability to be especially crappy or is that just a small sample size argument against the players not being good?

The hamster on the wheel in my head just collapses whenever I try to reconcile the acceptence of the Shandler adage and my knowledge of sample sizes. Can this be resolved?