It's been about almost 2 months since I last looked at whether A-Rod's 2012 HR statistics indicate a player in serious decline, so let's do an update.
If you haven't read the previous posts, this blog has been using binomial distribution as one way of gauging whether A-Rod's 2012 HRs are commensurate
with a talent level of a player hitting HRs in 6.2% of his at-bats. 6.2% is
used because that was A-Rod's HR rate over 2009-2010, when he hit 30 HRs
each year (in less than full seasons).
So far we have found that A-Rod's HR numbers are in the range of what one would expect for someone at that talent level. He has been at the low end of that range - which makes gauging A-Rod's power an interesting enigma.
A-Rod now has 15 HRs in 352 ABs, for a 4.26 HR rate. 15 HRs again is within the expected range of a
player with a talent level of hitting a HR in 6.2% of his ABs. The binomial distribution indicates that 95% of the time a player with that talent level should hit somewhere in the range of 15-30 HRs after 352 ABs.
15-30 HRs is a large range; one obviously would prefer a more precise estimate. However, the breadth of this range is instructive, because it shows the limitations of what we can know about a player's true talent after approximately 4 months of a season.
To further this point, let's flip the numbers around - suppose that A-Rod's 2012 HR stats represents his current HR talent level. He is hitting a HR in 4.26% of his ABs. In that scenario, the binomial distribution indicates we could expect such a hitter to have in the range of 9-21 HRs.
In other words, if A-Rod had hit 20 HRs to date instead of 15, there would have been much less media hyperventilation about whether he is in decline. However, the extra 5 HRs would not tell us that much more about his true talent level these days for hitting HRs.
So while obviously A-Rod's age and his last couple of seasons is cause for concern, it is way too premature to decide that his days as a 30+ HR guy have past.
Note: For reference, I calculated the expected range of HRs using the following R formula: qbinom(c(.95, .05), 352, .062).