February 15, 2006
Probabilistic Model of Range, 2005, Team Runs Saved
So far with the range calculations I've been interested in the probability of getting to a batted ball. I'm going to change gears a bit and try to look at runs saved instead. The methodolgy is the same in principle; predict how many runs should be expected given the balls in play, and compare that to how many were actually allowed.
Of course, both these numbers are difficult to calculate. What I'm going to do is use a version of the Bill James runs created formula that appears in The Bill James Handbook 2005. The formula I'm usings is (Times On - GDP)*(Weighted Total Bases)/Balls in Play. I'm not making an adjustment for sac hits or sac flys. I am however, counting all non-out balls in play as a time on base. I'm also counting all non-out balls in play in the total base calculation. In this case, if a player reaches on a 1-base error or a failed fielder's choice, that's the same as a single. If they reach on a three-base error, that's the same as a triple. Since we're measuring range, errors should hurt the teams that commit them.
So I add up all the actual results on balls in play against a team, and calculate actual runs created against (RCA). I also add up all the predictions for the ball (the chance of a single, double, triple, home run, GDP or out) and use that to predict the number of expected runs. Here's the table showing which defenses saved the most runs by this calculation (the traditional calculation is here):
Probabilistic Model of Range, 2005, Runs and Predicted Runs, Original Model Including Parks
Team | InPlay | RCA | Predicted RCA | RCA per 27 Outs | Predicted RCA/27 | Runs Saved per 27 Outs |
Astros | 4204 | 424.18 | 510.24 | 3.71 | 4.63 | 0.9163 |
Athletics | 4286 | 395.81 | 482.57 | 3.34 | 4.23 | 0.8872 |
Cardinals | 4414 | 428.09 | 514.59 | 3.52 | 4.40 | 0.8816 |
Indians | 4385 | 420.76 | 508.22 | 3.50 | 4.37 | 0.8669 |
White Sox | 4457 | 420.22 | 503.66 | 3.42 | 4.25 | 0.8290 |
Phillies | 4211 | 442.77 | 517.76 | 3.89 | 4.71 | 0.8170 |
Braves | 4559 | 488.44 | 569.82 | 3.99 | 4.80 | 0.8048 |
Blue Jays | 4511 | 464.49 | 543.76 | 3.81 | 4.59 | 0.7811 |
Twins | 4545 | 458.47 | 532.69 | 3.71 | 4.44 | 0.7269 |
Pirates | 4467 | 480.44 | 538.91 | 3.98 | 4.58 | 0.5962 |
Angels | 4383 | 465.62 | 519.73 | 3.95 | 4.51 | 0.5613 |
Red Sox | 4575 | 552.63 | 605.03 | 4.59 | 5.13 | 0.5363 |
Orioles | 4377 | 473.93 | 526.22 | 4.05 | 4.59 | 0.5344 |
Tigers | 4527 | 478.16 | 532.86 | 3.91 | 4.44 | 0.5286 |
Diamondbacks | 4571 | 547.20 | 594.48 | 4.53 | 5.02 | 0.4885 |
Giants | 4520 | 491.96 | 542.16 | 4.06 | 4.55 | 0.4875 |
Mariners | 4546 | 472.36 | 521.65 | 3.86 | 4.33 | 0.4708 |
Devil Rays | 4560 | 557.49 | 602.93 | 4.68 | 5.14 | 0.4515 |
Cubs | 4117 | 434.25 | 475.70 | 3.92 | 4.36 | 0.4344 |
Brewers | 4252 | 467.77 | 499.93 | 4.12 | 4.45 | 0.3310 |
Rangers | 4697 | 559.00 | 590.74 | 4.54 | 4.84 | 0.2981 |
Mets | 4424 | 460.25 | 488.90 | 3.86 | 4.15 | 0.2877 |
Rockies | 4537 | 583.74 | 611.55 | 4.97 | 5.24 | 0.2767 |
Dodgers | 4392 | 467.44 | 487.51 | 3.95 | 4.15 | 0.2003 |
Marlins | 4367 | 526.65 | 532.17 | 4.56 | 4.64 | 0.0812 |
Nationals | 4538 | 482.25 | 486.34 | 3.96 | 4.00 | 0.0335 |
Padres | 4423 | 513.08 | 514.33 | 4.38 | 4.39 | 0.0119 |
Yankees | 4483 | 509.11 | 497.02 | 4.28 | 4.16 | -0.1157 |
Royals | 4611 | 612.92 | 591.70 | 5.16 | 4.94 | -0.2189 |
Reds | 4650 | 586.40 | 553.75 | 4.84 | 4.53 | -0.3164 |
Again, with the line drives fluctuating so much year to year, I'd be more concerned about the order than the magnitude of the runs saved. But Houston and Oakland are impressive teams.
The next trick is to make this work for players. I'm trying to figure out how to split the run elements between fielders who have a chance at catching a given ball. Any suggestions would be welcome.
Correction: Fixed the year of The Bill James Handbook.
The Braves seem to stand out from the other top teams with a high Predicted RCA. What would that indicate, a staff with high strikeouts (lower balls in play), a team that gave up an above-average number of EBH, committed a high number of errors?
Also, is Caught Stealing included in the calculation along with GIDP? It would seem a team with a good catcher would reduce baserunners and save you some runs.
A high predicted RCA would mean that balls put in play against a pitching staff were likely to result in more runs. Caught stealing is not included, since we're dealing with range here, not throwing arms.
"A high predicted RCA would mean that balls put in play against a pitching staff were likely to result in more runs."
So this means that the high predicted CRA for teams like the Red Sox would be a reflection of their home ballpark and BABIP? It seems to me that a ball put in play in Fenway has more chances to lead to a run than in most places (small foul territory, the Monster).
Would it be possible to run a "smoothed visiting team" version of this item to get a handle on park effects? Thanks.