Let's do this bullet point style!
- I was surprised at how close the two outcomes were with respect to multi-run innings, about a 2-4% difference historically. One of the great things about studying baseball is that you are surprised by the results and you learn things. That's part of why I write this blog. If I wasn't leaning anything, I would just be up here pontificating. In this case, I found that I was guilty of attributing more import to the home run than it deserved. Obviously, the home run is far more valuable because it is one guaranteed run, but with respect to multi-run innings its value is marginalized relative to the walk. I did not recognize this, and thus my initial approach to the problem was incorrect.
- We can definitely conclude that Tim McCarver is totally wrong. Whether we examine the problem from the perspective of history or probability, both correct ways of examining the problem, the weight of evidence is greatly against him. Even thought the difference in probabilities is seemingly small, it's over such a large set of samples that it takes on much significance. It's nearly impossible to conceive of a scenario in which the walk is more valuable than the home run, which was McCarver's basic assertion.
- We reaffirmed a basic baseball truth: outs are your most precious commodity. The difference between the two events with respect to multi-run innings has nothing to do with their relative value to each other from a run expectancy point of view. The home run is more valuable with respect to multi-run innings not because it scores a run, but rather because it precludes the possibility of an out.
- Finally, we provided a tad more evidence for the Markov property in baseball. The conjecture about the walk being more likely to lead to big innings is largely based on the assumption that indicates more about the game state than it actually does. Baseball is largely dependent only on the current state of the game, not on how each state was reached.