[Timofmars]

TLDR: I found some data and used it for calculations, and I found that every 32 Ks you avoid (but the batter still gets out) will result in 1 extra run gained. But the data is incomplete, and the game may not even reflect real life in this area.

I'd be happy with a ballpark figure, because right now I'm not giving my players any value for avoiding Ks, so I'm likely undervaluing them.

Using the GIDP info for one season, I found roughly that men are on (any base) 43.3% of the time, and double plays happen 4.5% of that time (of course, about 1/3 of the time there are 2 outs, making double plays impossible). And with men on first base (other bases may or may not be occupied) with less than 2 outs, GIPD happens almost 11% of the time.

So that gives me the negative outcomes of better Avoid Ks ability.

Actually, I just now found that before 1940, all times that a runner advanced when the batter hit into an out were counted at sacrifice hits, not just on bunts. And in some years, sacrifice flies were added in as well.

I took data for 1930, when SH included non-bunts and SF even if they only advanced a runner but did not score them. There were 2606
SH in 97262 plate appearances. So I took PA, subtracted hits, Ks, BB, HBP, which should give outs on balls-in-play. Then multiplied by 2/3 since that's the average time there should be less than 2 outs. Then multiplied by 0.433 to find times that men are on base (2012 data). That gives 16070 instances where runners are on base with less than 2 outs.

So divide SH by 16070 to show a 16.2% chance of advancing a runner on a ball-in-play that gets the batter out. If that data is still roughly reflective of baseball today, it probably overestimates the SH chance slightly since you're probably more likely to have runners on the closer you get to 3 outs. On the other hand, there can be more than 1 runner on base, so you can advance 2 or 3 runners in some of that 16.2% chance. So if I use average # of baserunners (0.622 is some rough data I have on that from 2017) and divide by the 0.433 of times runner are on, it should tell me that 1.436 runners are on base on average when there's at least 1 runner on. I assume the SH data only credits a maximum of 1 SH each PA, even if more than 1 runner advances. Sometimes only 1 of the baserunners will advance, but for simplicity, I'll assume they all advance. So 16.2% chance of getting a SH on a ball-in-play out, that moves an average of 1.436 runner gives 0.233 bases gained on balls-in-play with runners on where the batter doesn't get a hit.

Based on my data, each base gained (but not scoring) on the SH is about an extra 0.10 or 0.11 runs, compared to just a strikeout, while a runner scoring from 3rd is a 0.42 or 0.76 run gain (depending on whether you are left with 1 or 2 outs). Runner are on 3rd about 16% of the time that any runners are on, but that's where your biggest gains are from. If I multiply these values out by the expected chance of baserunners on each base, I get 0.404 runs gained per SH compared to a K. And multiply that by the chance of that ball in play being a SH instead of an out (16.2%) give you an average 0.0654 runs on each ball in play with less than 2 outs that is not a hit (nor a double play), compared to just a strikeout.

Doing a similar calculation for GIDP, there's a 0.139 chance of a GIDP on balls-in-play with runners on that are not hits. Compared to just a normal out, this takes away an additional out and a baserunner. Comparing this to a strikeout, assuming the baserunner was on 1st, taking him off the base results in a loss of 0.229 expected runs (if there was 0 outs before) or 0.111 expected runs (if there was 1 out before). The penalty from the additional out lowers the expected runs of other baserunners by about 0.2 each (though they may advance a base to offset penalty), and maybe like a 0.15 loss of expected runs on the batter that doesn't get to bat now (or slightly less, since he surely has at least 1 runner fewer to have a chance to hit in, and I already calculated the loss from that). Multiplying these numbers by the expected baserunners (just as I did with SH before), I get a 0.41 loss of expect runs per DP, but then assuming any runners on 2nd and 3rd advance at that time, it reduces the penalty of a DP down to 0.247. Multiply by the chance of a GIDP for a ball-in-play with runners on that are not hits, with less than 2 outs, and get an average of 0.034 runs lost. Subtract that from runs gained (due to SH), and you are left with 0.031 runs gained for hitting a ball in play for an out instead of striking out. This all works out to give you an extra run every 32 Ks you avoid.

If I didn't make any mistakes in the math, there's a few other issues. The GIDP data only includes standard double plays, so every DP gets the batter and 1st base runner out. So there should be more DPs that what is shown in the data, though they are much more rare I think. Also, I have no idea how accurately OOTP models these stats in particular. They may do a good job on making hits and HRs appear in realistic amounts, but who knows what they used to figure out how often baserunners advance on an out.