March 21, 2007
Probabilistic Model of GDPs
Something that's been on my mind is using ideas from the Proabilistic Model of Range on a very specific issue, double plays. The idea is to look at a particular set of balls in play, ground balls with a man on first and less than two outs, and see what fielders do well. What might make this very interesting, however, is that we can not only look at who starts the double play, but who is the pivot man, and who finishes the job. I'm imagining we can look at shortstop/second baseman combinations and see if the probabilities go up or down with a change in personnel, or with who is fielding vs. who is pivoting.
As always, your thoughts are welcome. Here's a couple of tables to start us off. The first shows how often each of the infield positions starts a double play.
Probability of a Fielding Position Starting a GDP, Groundballs Only, Man on First, Less Than Two Out, 2006
| Position | GDP | Total | Pct |
| 1 | 274 | 11076 | 0.025 |
| 2 | 4 | 11076 | 0.00036 |
| 3 | 234 | 11076 | 0.021 |
| 4 | 1099 | 11076 | 0.099 |
| 5 | 802 | 11076 | 0.072 |
| 6 | 1484 | 11076 | 0.134 |
Pretty much what you'd expect, although I'm impressed that third basemen start as many as they do. This next chart divides the infield into eighteen pie slices, five degrees wide. Zero represents the third base line, 17 the first base line. The probability given is the probability of a ball being turned into a double play on that vector.
Probability of a GDP on a Ball Hit on the Vector, Groundballs Only, Man on First, Less Than Two Out, 2006
| Vector | GDP | Total | Probability |
| 0 | 17 | 177 | 0.096 |
| 1 | 112 | 334 | 0.335 |
| 2 | 369 | 869 | 0.425 |
| 3 | 243 | 987 | 0.246 |
| 4 | 213 | 803 | 0.265 |
| 5 | 370 | 711 | 0.520 |
| 6 | 533 | 842 | 0.633 |
| 7 | 335 | 626 | 0.535 |
| 8 | 119 | 452 | 0.263 |
| 9 | 264 | 643 | 0.411 |
| 10 | 212 | 464 | 0.457 |
| 11 | 394 | 660 | 0.597 |
| 12 | 331 | 647 | 0.512 |
| 13 | 129 | 636 | 0.203 |
| 14 | 52 | 765 | 0.068 |
| 15 | 109 | 761 | 0.143 |
| 16 | 85 | 414 | 0.205 |
| 17 | 10 | 102 | 0.098 |
You can see from this that second baseman cheat more toward the bag than shortstops. Vector 8 represents the five degrees to the shortstop side of the bag. Vector 9 represents the five degrees to the second base side of the bag. As you can see, a lot more GDP's are started on the second base side. That makes sense, of course, as there are more right-handed hitters, and against a righty, a shortstop can't cheat as much. And while the lines are great places to hit the ball to avoid a double play, the absolute best place is the hole between second and first. I guess there is something to the idea of hitting behind the runner!
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Note to hitters: Don't hit the ball to zone 11!
Seriously though, interesting stuff David. What I would worry about with comparing different double play combos is sample size. For instance, on the Phillies, Chase Utley and Jimmy Rollins were rarely out of the starting lineup last year, so whoever their subs were are going to have extremely small samples.