Anybody know?
Defensive metrics aren't yet that granular, but Defensive Runs Saved is the closest you'll get and the Fielding Bible website, where DRS was created, keeps returning a 404 error, so I can't tell you how it's calculated. The relevant portion of DRS is:
- Fielding Range Plus/Minus Runs Saved based on BIS-trained scorer observations and batted ball timing to determine the velocity of each batted ball.
I think your question requires a lot of context and it's relevant to understand where you want to find the value. Are you asking about an out being worth, in terms of run prevention, the same as hitting a double? Or are you asking about the generalized value to the team or on the FA market? And if it's the former, which I assume it is, do you consider all doubles to be worth equal amounts, or do you want to credit a double that scores a run or a catch that saves a run and penalize an out that wasn't at all productive? And how many outs were there when each occurred?
The best possible answer to your question, IMO, is RE24. RE24, or run expectancy for the 24 possible base-out scenarios, treats a player hitting a double as a + contribution, and last night's Snider double to lead off the 5th was worth 0.61 RE24. An out to start an inning is worth -0.21 RE24. So saving a double for the first out to lead off an inning is worth less in terms of run prevention than hitting a double to lead off an inning, but grounding out to end an inning with men on first and second is worth -0.40 RE24, and that number would go up with a man on third, and doubling with one out and no men on is worth 0.40 RE24.
(All of those figures are from last night's game against the Yankees, and I don't use RE24 enough to know if those are standard or roughly standard)
Lough's catch might have been worth as much as or more than hitting a double to RE24, but it's very much dependent on base-out state. WPA is like RE24, in that it's very much context-dependent. Comparing hitting and robbing a double in a vacuum is also difficult, because then you're really concerned with how often or with what degree of certainty and regularity a player can do one or the other. Delmon Young's robbing of A-Rod's home run, for instance, was a tremendously valuable play, but it's not a repeatable skill for Young, so while it's worth a lot in that instance, that is happened is not really worth much to the Orioles at literally any other time.
I hope that significantly muddies the water.