My guess is that the formula was based on empirical evidence. If you wanted to adjust the formula so that it fit the model more closely, you'd need to come up with a statistic that says "How hard does this player hit the ball on average?". The closest thing we have to that above is SLG.

Sharks 2.57 (4.5 hits, 31.5 AB)
Piranhas 5.50 (15.25 hits, 42.25 AB)

Most likely, that just shows the formula breaks down at the extremes.

I suspect he was (is) also counting on Mauer to have a monster 2nd half.

What made this one strange was that the Twins strutted out of Kauffman Stadium one night earlier with an 11-4 victory, thinking their scoring troubles were over.

"One of those days where you just kind of shake your head and wonder what's going on," Twins manager Ron Gardenhire said. "You score that many last night. That's the way the game is. You come back [Thursday] and can't find a way to score a run."

I mean, hey, they scored 11 last night. Problems over, right? Heh.

Bingo! This is also on the slate for part 2.

And another problem for the Twins comes into view — in games when they get few hits (today), they absolutely cannot score. This year, they are 10th in the AL in BA; last year, as Dick points out nightly, they led the league in BA. No surprise that the run scoring is down significantly, and they are back to getting shut out regularly (as in 2004).

Yep, when you rely on singles to score runs and don't get any, it's essentially a crap shoot. If you manage to clump them all together, you might do ok. Unfortunately, this will normally not be the case and you will not get much of anything.

Now if he can just stay with the theme and find one or two young, cheap power hitters for 3B and DH, the Twins could survive having no power out of SS and 2B. (CF is going to be a problem regardless -- it's either going to be lacking power, or very expensive.)

For the sharks it was easy. I just need them to have 4.5 HR for every 27 outs they made. So their average becomes 4.5/(27+4.5) = 1/7.

For the Piranhas, I just had to do trial and error until I got something really close. Eventually I got .361174 to be a close enough mark which scores the piranhas 0.500001 runs/inning.

And another problem for the Twins comes into view -- in games when they get few hits (today), they absolutely cannot score. This year, they are 10th in the AL in BA; last year, as Dick points out nightly, they led the league in BA. No surprise that the run scoring is down significantly, and they are back to getting shut out regularly (as in 2004).

Same trend per inning. Fewer 0 run innings for the sharks, more 1 and 2 run innings, fewer of everything else.

Interestingly, the Guppies have a marginally higher OPS than the Sharks. Although the margin is really razor-thin, one could conclude that it takes a higher OPS to score the same number of runs if you are doing it all by singles. And then the real problem with the Twins' offense comes into view -- their OPS is sub-standard, so there's no way in hell they can score an average number of runs with their complete lack of power in 6/9ths of the order.

It's good to know that what's happening is exactly as I would have predicted it. The Twins hitting problems go a bit deeper than just this, but I think this problem is at the heart of it. The Twins marginally winning record this season is obviously a result of their fantastic pitching. Some hitters with even a marginal amount of power at the bottom of the order would greatly improve the Twins consistency and could have very likely contributed to 6 (or perhaps many more) wins so far this season.

If I feel up to it, I may try to run some of those numbers before part 2, or maybe even make it into a part 3.

Do you have data for the Sharks and Piranhas per inning? That seems important for the purpose of the general "small ball" vs. "smash ball" debate. One of the main advantages to small ball is that it's supposed to be better in close games where you might just need one run. The number of shutouts for the piranhas suggests that they probably get shut out per inning a lot, but...while it seems unlikely to me that the per inning distribution is much different than the per game distribution, I'm curious.

This is exactly what's happening. Great post, GH.