I like Mahnken's Heirarchy of Plays.
I think that best puts the Productive Out in perspective.
(as a non-optimal, but not the worst outcome)

But one thing I don't get...
Why is a strikeout a "better" outcome than ball in play out?
(Why is there a difference?)
 

Well, strikeouts can't be sac flies, and can't advance a runner. But they also can't be double plays. So yeah, strikeouts and ball-in-play outs are different.

I'd always read that the net value of a strikeout was slightly worse than a ball-in-play out.

Extrapolated runs (a linear weights formula) puts a strikeout at -.098 runs, and a ball-in-play out at "only" -.090 runs. So yeah, I'd say Mahnken's hierarchy should probably have the order of those two results switched.
 

But I assume that that's based on the assumption that a "ball in play" could advance a runner or be a possible error, right?

When he develops this hierarchy, he specifically lists "reach on error" and "productive out" as other outcomes, eliminating this specific difference, no?

I feel like I'm missing something that would lead to his differentiation of value between a K and a putout...
 

Since Productive Outs and Sacflies are already mentioned, strikeouts are listed higher on the heirarchy because they do not lead to double plays as often. (Even factoring in Strike-em-out Throw-em-out DP's)