Leadoff Walks, Homers, Multiple Run Innings, and Stuff

If you're reading this you already know about the great Tim McCarver related debate on lead-off homers versus walks leading to multiple run innings. Conventional baseball wisdom says that base-runners create lots of runs while home runs clear the bases and kill rallies, whereas an unreferenced supposedly large data set says the opposite. A third opinion from "common sense" agrees with said reference, which is that immediately scoring a run to start an inning leads to more runs than just a walk because hey you've already scored a run, so less work to do now. And the slightly more (less?) thoughtful response to common sense says that only what the batters after the first one do matter for scoring 2+ runs, so doesn't matter if the first run is on a homer or a walk and advancement. In conclusion of all those ideas are wrong.

First realize there are two separate questions in this one issue. The first is given a lead-off walk or homer, in which scenario is your team more likely to score 2+ runs? Who the hell knows is the answer. It depends on whether the opposing pitcher is a ground ball or flyball pitcher, how he is pitching that day, whether he is going to be replaced by a better pitcher in one of those cases but not the other, how fast the base-runner is, how good his fielders are, what the score is, whether the manager likes to hit/steal, or not, how much worse the pitcher performs from the stretch, what part of the lineup is coming up behind, whether the runner on first is held on or not, whether the infielders have strong arms (whether they improve out efficiency with the possibility of a fielder's choice at 2nd) and on and on and on. To be safe, you'd probably need 10 years of data from every team out there to average out all of these variables (or 15 minutes and a Fortran compiler, but "the game's played on the field dammit, not a computer" some old crotchety baseball man said (I assume). Personally I'd like to see 100 years of data, but there aren't 100 years of data on modern baseball, so I think that we just need to think a little more, methinks.

Assuming an appropriate sample size, the overall question of what should happen on average is simple:

In case 1 (lead-off homer), that run has already scored safely.

In case 2 (lead-off walk), that runner can still make an out at some point irrespective of what the ensuing batters do.

So given the exact same sequence of hits/outs/walks/etc after both the home run and the walk respectively, you will make more outs on average with just the walk because sometimes he will occasionally be caught stealing, picked off, called for interference, etc etc. And trust me, more outs mean less runs despite what managers think. Only in the hypothetical dull baseball game where all base-runners advanced mono-base-edly and could not make outs would the answer really would be "doesn't matter".

(Note: Yes I know not all the variables listed have 0 weighting on runs scored, but the possibility of making an out on the bases hinders runs much more than anything else listed.)