There is a big debate at SOSH about roster construction. Coincidentally, I just wrote a computer program which allows for very quick, simply analysis of a similar question.

The question is as follows. Will a team with an uneven distribution of player talents score more runs than a team with an even distribution? Put another way, would you rather have 3 players with a 130 OPS+, 3 with a 100 OPS+ and 3 with a 70 OPS+, or 9 players with a 100 OPS+? Clearly, the two teams have nearly similar OPS+ numbers. They won't be exactly the same, though, since I assume that both teams will also maximize lineup effectiveness. Therefore, the lineup for team 1 will be, by OPS+, 130, 130, 130, 100, 100, 100, 70, 70, 70, and as a result, team 1 will actually have an OPS+ closer to 102 than 100.

I ran some numbers. I computed that last year, a 130 OPS+ was very close to .380/.493 OBP/SLG, a 100 OPS+ was .330/.430, and a 70 OPS+ was .280/.370. I assumed, for all teams, that no basestealing, sacrifice flies, double plays or productive outs occurred (it's a real bitch to write those things,) and also: no one goes first to third, or scores from first on a double, but they always score from second on a single. Finally, the starters play every single at bat of every game. Park effects are obviously not included.

What I do is for each batter, find the likelihood of an event (for a walk, for example, it's BB/PA.) I then run a random variable. If it's in the correct range, it's a walk, or a single, or a double, or a triple, or an out. Obviously, this leads to the possibility that the two teams will have wildly different OPS+ numbers. This program simply looks at how these teams will fare given their actual level of talent, and with the luck that occurs every year.

Here's what I found:
I've run 200 season simulations. Team 1 scores, on average, 775 runs, with a standard deviation of 44, a maximum of 889, and a minimum of 678. Team 2 scores, on average, 761 runs, with a standard dev of 42, a max of also 889, and a min of 650.

Some issues with my study: I need to reduce Team 1's OPS+, and that will be very easy if I just input 64 OPS+ for the 70 OPS+, which will give Team 1 an OPS+ of 100. 2 points of OPS+ can probably describe 14 runs, so when I finish that, I'll write about it, if people are interested.

Also, ignoring double plays probably helps Team 1 a little too. That team will get a couple of more base runners on, and their crappy players are more likely to hit double plays (because they hit more balls in play.)

So, what does everyone think? Is my method alright? Intuitively, which team should score more runs? What does all this mean? Any other questions?