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Let's go to the "holodeck" for a moment.
We have a pefectly average pitcher - and a perfectly average defense in this simulation.
Baseline: (2700 outs -- 100 games - just for round numbers)
Baseline Simulation:
Pitchers: 700 Ks
Fielders: 2000 outs
Hits allowed: 1000 (.270 BA -- BABIP .333 -- we'll ignore HRs for the moment just to keep the numbers simple)
Simulation A - Plus Pitcher:
Pitchers: 800 Ks -- (100 extra outs). 14% increase in Ks.
Fielders: 1900 outs
Hits allowed: 967 hits (BABIP = .333) -- 33 hits removed
Simulation B - Plus Fielders:
Pitchers: 700 Ks
Fielders: 2000 outs
Hits allowed: 967 hits (BABIP = .326) -- 33 hits removed
The fielders increased their out-producing rate by just over 1%, to achieve the IDENTICAL result of the pitchers increasing their K-rate by 14%.
Tampa from 2007 to 2008 had a 54 point improvement in DER. That prevented 300 hits.
To achieve the SAME reduction in hits through pitching alone, (if BABIP had remained at .334), would require the pitching staff to increase their Ks by NINE HUNDRED (900).
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The problem is outs are a constant. They can *ONLY* be measured by hits allowed.
In truth, for the 2007 Tampa staff, a non-K only turned into an out .67% of the time.
But, in 2008, a non-K turned into an out 72% of the time.
While I don't know the exact number -- each point of DER improvement (or BABIP) from a defense is probably worth something like 6 hits over a full season. (Maybe you can get the exact number, because I'm doing some seriously dangerous ball-parking here). Maybe it's lower than I think - only 5.
But, for the sake of argument, say I'm right. A 20 point improvement in BABIP prevents 120 hits during a season.
It would require a 360 improvement in Ks to achieve the same end, (assuming identical defense).
It shouldn't be too difficult to go and find some teams with very similar K and HR numbers (walks won't matter for the DER examination), but different DER/BABIP numbers -- and get a general read on how many hits a point of DER is worth.
It also shouldn't be too difficult to go and find some teams with similar DER and HR totals, and see what the impact of K differences are on the hit totals.