THE BOOK--Playing The Percentages In Baseball

Friday, February 25, 2011

Humidor effects

Alan gives us a primer on the effects of humidors:

The experiments found that when the relative humidity is increased from 30 percent to 50 percent, the weight of the ball increases by 1.6 percent and the COR decreases by 3.7 percent. Together, these results can be used to calculate that for a hard-hit ball typical of home runs in Major League Baseball, the BBS is reduced by 2.8±0.5 mph (or about 2.8 percent), where the error bar is due to the uncertainty in the COR measurement and its affect on the BBS. More on this a little later. Most of the reduction comes from the reduced COR (2.2 mph), with the remainder coming from the increase in weight (0.6 mph).
...
The mean home-run distance at Coors is 414.8 ft. After applying our 2.8 percent reduction in BBS and 1.6 percent increase in weight, the mean distance is reduced to 401.6 ft, a change of 13.2 ft, or 3.2 percent. With those changes, the number of home runs in Coors is reduced from 336 to 235, a (30±6) percent reduction. Most of it (27 percent) comes from the reduced COR, with the remainder (3 percent) coming from the increased weight. Another way to express this result is that for each 1 ft reduction in the fly-ball distance, the home-run probability is reduced by 2.3 percent.

Note: Alan started with each HR, of which the mean is 415 feet.  He reduced each HR individually, and the mean of those flyballs is now 402 feet. 235 of those remained as HR and the other 101 were now flyballs (outs or hits).  The mean of the 235 still-HR, unreported here and unimportant for Alan’s point was likely pretty close to 415 feet.  I’m guessing maybe 412 or 413.  I just want to make a tangential point that the mean HR distance will not be 402 feet in this case.

In summary, the calculation gives a reduction of (30±6) percent, whereas the actual reduction is 25 percent. The closeness of the calculation to the actual result suggests that it is very plausible that the reduction in home runs at Coors Field can be attributed to the humidor. That is the primary conclusion of this investigation.

Let me turn now to Chase Field, where the typical relative humidity is even lower than in Denver, on the order of 20 percent. Therefore, we need to investigate the effect of changing from 20 percent to 50 percent, an increase that is 1.5 times the increase at Coors.... Putting these things together, I would expect to find a reduction at Chase approximately 1.5 times that at Coors, or a whopping (45±9) percent! That’s not a small number, folks.... As another example, the consequence of moving the fences uniformly closer by 5 ft would be an increase in home-run production by 13 percent.

I liked the Q from one of the commenters:

How long does it takes for a baseball to equilibrate to ambient conditions? I assume that as soon as the balls are removed from the humidor they start to lose/gain moisture depending on the relative humidity. I don’t know how long the average ball is exposed until it is put in play, but this must affect it’s moisture content.

Maybe the 30% in lab conditions compared to the 25% in real-life conditions may be instructive.  So when Alan says 45%, maybe it’s really 37.5%?