I love seeing a small little detail worked out properly, as you do here (and even more interesting when you find the non-intuitive result).

Imagine a world where managers worked this stuff out themselves and understood the results! I’m not saying that this sort of situation is really so simple, and I’m sure that there are times when you would want to go against the numbers (if for no other reason than game theory strategies of avoiding predictability).

The largest component of what you’ve measured is just that Cust(07-09) is better than the average hitter, so the RE will necessarily be higher after all this stuff happens than if an average hitter was up, regardless of what Rajai does. Cust in that timeframe was .034 runs above average per PA. So the baseline for Cust’s PA for purposes of this comparison should be .926+.034=.96, which means you get .012 runs out of the SB attempt versus .04 for the SB attempt with an average hitter up, which backs up the intuitive point of view. Plus, Cust’s .034 above average per PA will be even higher for the runner on first, 0 outs, situation, and lower for something like runner on third, 1 out.

The Book chapter on SBs (which I have not read) addresses this stuff in great detail and makes the (intuitive) conclusion that you want to steal bases in front of guys who hit a lot of singles relative to XBHs and BBs.

it would appeal in terms of stealing in the first inning, just situationally beyond stats…. JC being someone who sees so many pitches and stealing being a lot about a runner getting a lead and seeing the pitcher work so he can get the tipoffs for that day as to where the pitcher’s going and whatnot. So JC hitting second wouldn’t strike me as immediately a hamper on Raj because JC would walk him to 2nd anyway… it’d be much the opposite, esp. in a first inning where a pitcher can be so vulnerable to the big inning before getting settled into a game and all that. To be honest, if Raj himself were to ask me what part of his game I feel needs the most work, I might say “too much dancing off bases trying to distract the pitcher ends up distracting the hitter.”

I’d like to see breakdowns as per the 1st inning situation vs. other innings where JC would hit with Raj on 1st, but that sample size in probably pretty small up to now. But instinctually (not at all really a stats head here) the idea that JC is 3TO doesn’t scratch him from hitting behind RD leading off… not on the basis of his affect on RD’s running game anyway. Of course, I could think of a few other reasons why JC isn’t a good choice for #2, but those are a whole other fanpost entirely LOL

can Rajai go from 1rst to 3rd on a walk

and hope more math will do the trick, here some more numbers.

Running on an off-speed pitch has a measurable element to it. A 90 mph fastball needs 0.44 seconds to reach the plate, a 75 mph curveball 0.53. This might not seem like much difference, but a fast MLB runner will cover almost three extra feet in the added time.

Another element is the pick-off, which is much harder to do with a curveball grip.

are increased plate appearances. If there is a consensus (consensus on Cust, now there’s a good one) that Cust would hit somewhere along the lines of his 3yr average, each one of his PA would bring .034 runs above average (as MikeA pointed out).

Over a course of a season, a number two hitter has roughly 70 more PA than number 6 does. This translates into little bit over 2 runs. Not much, but still more than slightly diminished profits resulting from Rajai’s running game (and that is not even taking into account arguments written here).

which I brought up in a comment a few months ago: if Rajai steals 2B with Cust at the plate, does the infield take the Cust shift off?

If they play the full shift, the 3B will be about 60 feet from 3B when the pitcher starts his motion — basically inviting Rajai to jog to 3B. If the 3B plays closer to the bag, then there’s a huge hole in the infield where the SS should be, and I think Cust could learn to tap the ball there.

If the infield plays in a normal alignment, then Cust’s BABIP goes up, since there’s suddenly more room on the right side of the infield for a grounder or line drive to get through.