Bradley and the Hot Hand

Tom Tango reprints an EMail sent to him by MGL on the hot hand and changing projections. A sample:

How do we define a hot hand as opposed to a normal projection which always weights more recent performance? One way to define it is that it has to be transient, right? It has to slowly dissolve and then disappear completely. But, then again, even in a normal projection, we assume that talent constantly changes anyway, even over and above normal aging. That’s why we have a “recency weighting” in the first place. If true talent never changed, there would be NO reason to weight performance by recency. Performance 10 or 3 years ago would carry the same weight as that from one month ago (independent of the number of opportunities – sample size – of course). Even if we still assumed that talent changes with age, if we adjusted for age using some kind of aging curve, we still would not need to weight for recency.

Right now, Jackie Bradley, Jr. forces us to deal with this issue. As I like to do, I put together a spreadsheet to track the probability of Bradley tying Joe DiMaggio’s record 56 game hit streak. To do this, however, I need to know the probability of Bradley getting a hit.

The probability I use for streak I call Hit Average, hits per plate appearance. Technically, it is batting average without the conditional probability of the at bat. Think about Tony Gwynn and Wade Boggs at their peaks. They had similar batting averages, but Boggs walked a lot and Gwynn was a hacker. Gwynn owned the higher hit average.

I decided to look at three values for Bradley’s hit average:

1. His career hit average
2. His 2016 hit average
3. A hit average based on his current 2016 hit average adjusted for his Marcel projection hit average

The first two are straight forward. For his career, Bradley’s hit average is .210, a bit low. This season, it stands at .302, which is very good. So to figure the Marcel regressed hit average, I figure how many PA he has left (assuming he gets 4 PA in all remaining Red Sox games), and figure out what his average for the season would be if he hits at his Marcel rate the rest of the way. Right now, that number is .233. (As a sanity check, that’s in line with the regressed projections at FanGraphs.)

That works out to a very large range for the probability of Bradley tying DiMaggio. Using his career number, it’s an extremely unlikely 6.09E-07. For the regressed average, it’s a slightly less unlikely 4.51E-06, so a factor of ten better. For his season average, it’s a somewhat doable 3.86E-04 or about 1 in 2600. The great thing about streaks, however, is that the longer they go on, the lower the probability of completing them to a certain distance. If we get a few more data points, I’ll graph the results to show the advance.

from baseballmusings.com http://ift.tt/1TSN8Vj