Baseball Musings: Probabilistic Model of Range, 2005, Runs Created Against Fielders

February 19, 2006

Probabilistic Model of Range, 2005, Runs Created Against Fielders

A few days ago I made my first attempt to calculate runs saved by teams based on the Probabilistic Model of Range (PMR). I'm using a modified version of the runs created formula that appeared in The Bill James Handbook 2005. That formula is designed for batters. I've modified it in the following ways:

Count any time a fielder fails to get an out as a time on base. So if there is a failed fielder's choice, or the batter reaches on an error, it's a time on base. Since we're looking at defenses, this seems appropriate.
Total bases are based on the number of bases achieved by the batter when he earns a time on base. So a two base error in this system counts the same as a double. The weights used for the various types of hits are the same as in the Handbook.

So that makes the formula (Times On Base - GDP)* (Weighted Total Base)/(Balls in Play). I'd like to hear what you think about the formula, but I believe it's a good first approximation. It was easy to apply to teams; you're just looking at all balls in play, and the likelihood that a particular ball will end in a particular result. But I wasn't quite sure how to then apply it to individual fielders.

When I was looking just at the probability of catching the ball, I wanted to look at all balls in play. I was looking at the piece of team DER that belonged to a particular fielder. But here, I'm trying to predict runs, so I made the decision to only look at balls in play in which the fielder had a non-zero chance of making the play. If you will, I used the probabilities of various balls in play to define the zone for the fielder, and the results of those balls to define runs created against (RCA).

The results made me wish I had worked on this last year. They're conveying information much more clearly than simply looking at the probability of catching the ball. Let's look at the shortstops first:

Probabilistic Model of Range, 2005, Runs Created Against Shortstops, Original Model (minimum 400 fieldable balls in play)
Player	Fieldable Balls In Play	Actual Outs by Fielder	Predicted Outs by Fielder	RCA	Predicted RCA	RCA/27 Outs	Predicted RCA/27	Runs Saved/27 Outs
John McDonald	521	178	172.92	27.41	36.40	4.16	5.68	1.527
Adam Everett	1490	517	498.79	71.05	95.41	3.71	5.16	1.454
Omar Infante	529	191	173.53	30.93	37.40	4.37	5.82	1.446
Bobby Crosby	925	312	304.63	42.34	56.74	3.66	5.03	1.365
Rafael Furcal	1648	596	576.97	84.81	109.11	3.84	5.11	1.264
Clint Barmes	859	306	279.67	49.78	56.65	4.39	5.47	1.077
Yuniesky Betancourt	610	177	174.31	39.99	45.58	6.10	7.06	0.961
Juan Uribe	1729	537	557.52	82.57	103.72	4.15	5.02	0.872
Julio Lugo	1761	560	540.03	122.06	134.05	5.88	6.70	0.817
Jimmy Rollins	1625	510	519.18	89.33	106.01	4.73	5.51	0.784
David Eckstein	1737	615	617.90	97.98	114.19	4.30	4.99	0.688
Jack Wilson	1734	600	610.94	104.81	121.02	4.72	5.35	0.632
Orlando Cabrera	1613	469	481.07	87.65	99.85	5.05	5.60	0.558
Oscar M Robles	554	172	179.32	31.03	35.19	4.87	5.30	0.427
Russ M Adams	1511	401	437.66	91.76	106.33	6.18	6.56	0.381
Neifi Perez	1269	445	448.29	65.47	71.20	3.97	4.29	0.316
Wilson Valdez	516	155	153.97	27.33	28.84	4.76	5.06	0.297
Miguel Tejada	1846	572	590.91	122.90	132.45	5.80	6.05	0.251
Juan Castro	774	264	260.08	59.78	61.02	6.11	6.33	0.221
Jhonny Peralta	1603	509	549.61	94.74	106.72	5.03	5.24	0.218
Jason A Bartlett	769	281	270.60	47.53	47.88	4.57	4.78	0.211
J.J. Hardy	1085	346	359.91	66.62	71.75	5.20	5.38	0.184
Omar Vizquel	1620	538	558.31	86.16	91.63	4.32	4.43	0.107
Alex Gonzalez	1273	452	441.85	91.18	88.58	5.45	5.41	-0.033
Derek Jeter	1913	561	602.13	115.11	122.15	5.54	5.48	-0.063
Carlos Guillen	834	262	270.95	54.67	55.58	5.63	5.54	-0.095
Khalil Greene	1246	399	409.60	74.67	74.98	5.05	4.94	-0.110
Jose Reyes	1865	522	569.16	115.79	123.88	5.99	5.88	-0.113
Cesar Izturis	1175	366	386.49	74.27	76.18	5.48	5.32	-0.157
Royce Clayton	1528	473	502.95	99.61	98.82	5.69	5.30	-0.381
Bill Hall	609	196	205.22	47.93	46.59	6.60	6.13	-0.473
Edgar Renteria	1773	491	499.45	128.25	120.64	7.05	6.52	-0.531
Marco Scutaro	846	259	282.20	50.54	48.34	5.27	4.62	-0.644
Michael Young	1930	534	580.38	134.80	131.21	6.82	6.10	-0.711
Felipe Lopez	1467	459	493.34	95.85	89.31	5.64	4.89	-0.750
Cristian Guzman	1333	417	438.14	83.54	75.53	5.41	4.65	-0.754
Mike Morse	581	156	170.02	47.09	43.64	8.15	6.93	-1.220
Angel Berroa	1818	551	594.20	168.48	137.92	8.26	6.27	-1.989

Many years ago, Bill James posed a question about shortstops; how many runs does one save with his glove? At the time, someone claimed Ozzie Smith saved 100 runs with his defense. Bill estimated at that time, the difference between the best and worst shortstop in the league was about 25 runs. As you can see here, among regular shortstops, Adam Evertt saved the most runs in 2005, about 24 below expectations. Angel Berroa, the worst regular in the majors, cost the Royals about 31 runs. That puts the difference at 55. Looking at the data, Berroa was an out lier. He was the rare shortstop who contributed nothing offensively while killing the team with his defense. He never should have played a full season at shortstop. Compared to Cristian Guzman, Everett saved about 35 runs, which fits in nicely with Bill's estimate. The magnitude of the numbers looks right to me.

The second feature to look at concerns Derek Jeter and Jose Reyes. There's been discussion as the model developed of how to handle ball in play could be handled by a particular fielder, but are caught by someone else. Runs created against appears to handle this situation quite well. Both Jeter and Reyes allowed fewer runs than the model predicts, despite turning many fewer outs than expected. Why? Others are turning the shortstop misses into outs. What happens, then, is that when calculating RCA, Derek and Jose don't get hurt in the numerator of the equation; they just get bumped up in the denominator.

However, when you look at them in terms of runs per game (27 outs), things change. The outs they don't get matter. They're so many outs behind where they should be, they're actually allowing more runs per game than expected. In other words, the cost of an out by one of these shortstops is high in terms of runs allowed. That I find to be a very cool result, that we can see both team and individual contributions to defense in one line.

The other thing we can see is who plays in tough ballparks. Let's demonstrate this with leftfielders:

Probabilistic Model of Range, 2005, Runs Created Against Leftfielders, Original Model (minimum 200 fieldable balls in play)
Player	Fieldable Balls In Play	Actual Outs by Fielder	Predicted Outs by Fielder	RCA	Predicted RCA	RCA/27 Outs	Predicted RCA/27	Runs Saved/27 Outs
Chris A Burke	272	120	101.65	26.59	41.11	5.98	10.92	4.935
Coco Crisp	617	294	261.44	66.21	96.11	6.08	9.93	3.846
Reed Johnson	282	134	112.67	34.77	41.96	7.01	10.05	3.049
Bobby Kielty	242	99	96.77	21.15	30.47	5.77	8.50	2.733
Carl Crawford	717	341	309.93	58.46	84.48	4.63	7.36	2.731
Matt T Holliday	558	236	214.67	72.13	87.09	8.25	10.95	2.701
Pedro Feliz	300	138	131.98	29.23	40.98	5.72	8.38	2.663
Jay Payton	245	107	94.67	24.01	30.14	6.06	8.60	2.537
Eric Byrnes	433	209	185.38	34.82	43.41	4.50	6.32	1.824
Carlos Lee	708	307	289.83	90.47	104.77	7.96	9.76	1.803
Kevin Mench	521	231	213.63	51.08	61.35	5.97	7.75	1.784
Moises Alou	284	132	123.81	25.23	31.83	5.16	6.94	1.781
Scott Podsednik	557	260	240.02	55.04	66.05	5.72	7.43	1.715
Craig Monroe	255	99	102.25	35.00	42.14	9.54	11.13	1.582
Raul Ibanez	255	106	103.57	22.14	27.17	5.64	7.08	1.443
Kelly A Johnson	356	166	154.90	42.52	47.68	6.92	8.31	1.394
Rondell White	270	119	118.43	30.45	36.12	6.91	8.24	1.327
Luis Gonzalez	619	270	246.42	95.06	97.93	9.51	10.73	1.225
Randy Winn	497	226	209.19	47.81	53.67	5.71	6.93	1.215
Cliff Floyd	654	283	267.59	76.59	82.93	7.31	8.37	1.061
Hideki Matsui	520	218	204.33	65.97	69.62	8.17	9.20	1.029
Adam Dunn	616	246	243.81	88.16	95.94	9.68	10.62	0.948
Frank Catalanotto	389	163	160.10	49.82	54.50	8.25	9.19	0.939
Jason Bay	625	266	257.22	83.97	89.04	8.52	9.35	0.824
Todd Hollandsworth	251	103	101.45	36.08	37.60	9.46	10.01	0.549
Shannon Stewart	555	249	237.55	74.67	75.06	8.10	8.53	0.434
Garret Anderson	531	201	208.94	59.21	61.67	7.95	7.97	0.016
Pat Burrell	627	236	247.60	82.06	85.00	9.39	9.27	-0.118
David Dellucci	228	84	90.32	29.17	30.85	9.38	9.22	-0.152
Marlon Byrd	210	100	102.84	21.98	21.78	5.93	5.72	-0.215
Terrence Long	423	166	163.61	76.66	73.49	12.47	12.13	-0.342
Reggie Sanders	268	108	105.77	47.56	43.95	11.89	11.22	-0.671
Ryan Klesko	504	204	202.51	76.35	69.22	10.11	9.23	-0.877
Miguel Cabrera	495	188	208.43	72.91	72.74	10.47	9.42	-1.049
Manny Ramirez	689	243	254.92	125.73	118.56	13.97	12.56	-1.412
Larry Bigbie	232	98	96.20	34.67	28.06	9.55	7.87	-1.677

You can pick out the stadiums where fielding is difficult. Look at Manny Ramirez, Matt Holliday, Luis Gonzalez and Terrance Long. They're all in left fields that generate a lot of runs. And look at Coco Crisp in left, saving 30 runs. Some of that has to translate to center at Fenway.

As always, I'm anxious to hear your criticisms of the model.

Update: I was just reading and responding to an e-mail from Studes at The Hardball Times (see comment below) and I need to clarify something. When I'm talking about runs saved by a fielder (Predicted RCA - RCA), I shouldn't be so liberal in attributing those runs to the fielder. As the Jeter/Reyes comment above shows, those numbers are influenced by teammates. You should think of the runs saved as being attributed to "the fielder and his surrounding teammates."

Update: In order to make things a bit clearer, I've noted in the headings to the tables that the Out columns are outs that are attributed to the fielder, whether actual or predicted.

Posted by David Pinto at 01:56 PM | Probabilistic Model of Range | TrackBack (0)

Comments

Maybe it's just the engineer in me, but what Uncertainties are you coming up with in the data?

Other note, Bigbie at the bottom aye? Something seems odd about that to me. Are you using any sort of park factors?

Fantastic work,as always.

Posted by: Mike Lafser at February 19, 2006 02:07 PM

Hey David,

I think you're really onto something here, but I'm kind of confused by your approach and the tables.

When applying run values to situations like this (player's performance against an average with the same number of batted balls), I agree that you have to include both the run impact of the hits allowed/disallowed vs. average, AND the run value of the outs caught/not caught vs. average.

So I think you comparison of Everett and Berroa is incomplete (again, if I understand what you did). Given your approach, the "runs per nine outs" is the only really good number to use. Personally, I would use a "run value" for outs in my original calcuation (making the "per 27 outs" column unnecessary).

I completely don't understand your comment re: Jeter and Reyes; I guess I don't understand your methodology for attributing balls to fielders. Are you saying that the "zone" in question for shortstops differs by team? How do you know that balls they didn't get to were fielded by others?

Finally, I don't understand the ballpark point in your last table. How do you know that the ballpark is affecting these players vs. their own talent?

Sorry for all the questions.

Posted by: studes at February 19, 2006 03:47 PM

this is great, thanks for getting this wonderful stuff up. I had suggested something along these lines a comment to a pmr post, but this is very well thought out and exactly why I think looking at balls that aren't outs is much more useful than looking at the ones that are. Thank you.

Posted by: andy at February 19, 2006 05:46 PM

david honey,

any system which has astros adam everett and chris burke at the top of the ratings sounds great to me...

Posted by: lisa gray at February 19, 2006 08:04 PM

Post a comment

Baseball Info Solutions The publisher of the Bill James Handbook and a great source of stats.

ESPN.com's baseball page.

STATS, Inc. You'll find great baseball books and fantasy games here.

Baseball Direct Scoreboard This is powered by STATS, Inc. Good box scores, and good situational stats.

Baseball Reference.com It's like having Total Baseball and the Big Mac online!

Baseball Trade Rumors Thoughts on wheeling and dealing.

Baseball Prospectus.com Wonderful commentary and analysis.

Baseball Primer Baseball for the Thinking Fan.

The Hardball Times Baseball. Insight. Daily.

Minor League Spilts Database Up-to-date minor league statistics, broken down by situation.

Inside The Book A blog by the authors of The Book.

Baseboogle A search engine for baseball research sites.

Win Shares From Major League Baseball Graphs.

The Transaction Guy A baseball transactions blog.

Japan Baseball Daily An English language site for Japanese baseball news and stats.

Doug's Business of Baseball Weblog A blog with a focus on the economics of the game.

Why I Like Baseball A Yankee fan writes about her favorite team.

Skilton's Baseball Links Links to numerous baseball sources.

Dan Lewis A blog about all sports.

Birds in the Belfry A site about the Orioles. Articles and research.

Only Baseball Matters A baseball blog by a John J. Perricone.

Jocksalot Lots of sports links.

Al's Ramblings A Brewer's blog.

Futility Infielder Jay Jaffe's baseball site. More than just a blog.

Mike's Baseball Rants Mike Carminati's baseball blog.

Aaron's Baseball Blog A general interest baseball blog.

Boy of Summer Travis Nelson on baseball.

Baseball Crank Dan McLaughlin's blog on baseball, the war and politics.

Bambino's Curse Edward Cossette's blog about the Red Sox.

Oakland Athletics Blog David Levens writes about the A's.

Ducksnorts Articles and Blog by Geoff.

Boston Sports Media Bruce Allen's roundup of the Boston Sports Media.

The Diamond Angle An online baseball magazine.

The Cub Reporter A Chicago Cubs blog.

Bronx Banter A baseball blog by Al Belth.

At Home Plate Articles by Jonathan Leshanski.

Dodger Thoughts Jon Weisman on the Dodgers.

The Clark & Addison Chronicle A Chicago Cubs web log.

Baseball Writing Joe Zibell's essays on baseball.

The Eddie Kranepool Society A Mets blog.

Mariners Weblog The Seattle Post-Intelligencer's weblog written by Shannon Fears

PortlandSoxFan.com A Red Sox blog from Portland, CT.

The Detroit Tigers Weblog Two Tigers fans and their take on the Motor City team.

A Rookie's Life The blog of Cleveland Indians' rookie Jody Gerut.

The Baseball Desert An Englishman living in France writes about the American game.

ChiSox Daily Mike Lubuda writes about the White Sox.

Shallow Center A blog mostly about the Phillies.

The House that Dewey Built Jeff Kuhn writes about the Red Sox.

SethSpeaks.net A blog by a Twins fan.

Frank's Field of Dreams News about Asian players in the United States.

Jay's Giants Blog William Jay blogging about the Giants.

Baseball Savant Cutting edge baseball news and analysis updated everyday from all aspects of the greatest show on dirt!

Athletics Nation Blogging about the A's.

Red Reporter JD Arney writes about the Reds.

Dominican Players Raul Tavares writes about players from his home country.

The Pearly Gates An Anaheim Angels Blog.

Red Sox Haven Randy Booth on baseball.

Tigers Weblog The Detroit News weblog on the Tigers, written by Tom Gage.

Management by Baseball Jeff Angus writes on how business can learn from baseball.

The View From the Bleachers A Chicago Cubs blog.

Cubs Now! Brian Hipp on the Cubs.

Honest Wagner A Pittsburgh Pirates weblog.

All-Baseball.com A collection of excellent baseball weblogs.

Soxaholix A comic strip blog about the Red Sox.

Most Valuable Network Blogging all 30 teams.

Baseball, Etcetera Andrew Godfrey's baseball blog.

Most Valuable Network, Astros Lisa Gray and others write about the Astros.

fenwayfanatics.com A Boston Red Sox blog.

Balls, Sticks & Stuff A sports blog with an emphasis on baseball.

Phillies Nation Brian Michael writes about the Phillies.

Batgirl Less stats, more sass.

Sabernomics Economic thinking about baseball.

Fire Brand of the American League A blog about the Red Sox.

Ivy Chat Chicago Cubs and other rants.

Baseball Evolution A group website writing about baseball.

The Cubdom.com Byron Clarke blogs about the Cubs.

Red Sox Stats Sabermetric numbers for the Red Sox system.

DRays Bay A blog devoted to the Tampa Bay Devil Rays.

Baseball Analysts Rich Lederer and Bryan Smith combine their baseball expertise into a single site.

Over the Monster A Red Sox blog by Randy Booth.

Viva el Birdos Ghosts of the St. Louis Cardinals past, present, and future.

Black Sox Blog A look at the current and historical teams of the South Side of Chicago.

Redleg Nation A group blog about the Cincinnati Reds.

Barry's Journal Barry Bonds' web log.

Hardball Dollars Keeping track of major league salaries.

Clem's Baseball and it's "Green Cathedrals" The resource for baseball stadiums on the web.

The Baseball Zealot Looking at the game of baseball from all sides of the spectrum .

Was Watching Laconic commentary from a Yankeeland zealot.

Bleed Cubbie Blue A Chicago Cubs blog.

Beaneball A's baseball from the heart of New York City.

The Writers A collection of sports writers express their opinions.

Yard Work What the Baseball Tonight crew would write if it could.

United States of Baseball Peter Handrinos' baseball columns.

Beer Leaguer Alternative veiwpoints on the Philadelphia Phillies.

Red Sox Connection Links to everything Red Sox.

Baseball Pilgrimages Stories of visits to baseball parks.

Fangraphs Multi-year charts of player stats.

Roto Authority Unique fantasy baseball information.

Yanksfan vs. Soxfan A Yankees fan and a Red Sox fan battle it out in the blogosphere.

Sawxblog.com A Red Sox fan writes about the home town team.

Oriole Magic An MVN blog about the Orioles.

The Baltimore Chop Joseph Jackson on the Orioles.

Lookout Landing A Seattle Mariners blog.

Sons of Bart Brush A blog about the Harvard baseball team.

Base Blogging A resource for sports and baseball bloggers.

Three True Outcomes A group blog by on major league baseball.

Cardinals Diaspora A blog for Cardinals fans living away from St. Louis.

Where Have You Gone, Andy Van Slyke? A Pittsburgh fan chronicles life in the Grand Canyon.

Brew Crew Ball A blog about the Milwaukee Brewers.

Getting Paid to Watch Posts by a former trainer for the NY Mets.

The Gas House Gang An historical St. Louis Cardinals Blog.

6-4-2 An Angels/Dodgers double play blog.

El Guapo's Ghost Rambles on about the Red Sox Baseball and the Red Sox.

Baseball Etc

Tiger Tales A Detroit Tigers web log.

The Baseball Card Blog A blog about baseball cards.

Sox1Fan A Red Sox blog.

Out of Left Field Another Red Sox blog.

New York Yankees Update A Yankees blog with lots of photos.

Liberty Ball A current and historical Phillies blog.

Crawfish Boxes A Houston Astros blog.

MLB Rumors Clearinghouse News from around the majors.

Roar From 34 A group blog about the Orioles.

Blogging Baseball All-time baseball highlights and real-time commentary.

Rubber Arm A group blog about major league baseball.

Fenway Nation More news about the Red Sox.

Rays of Light A Devil Rays blog.

Fantasy Baseball Chronicle Information for fantasy players.

American Legends A sports blog.

Duffy's Cliff An interactive Red Sox site, featuring a lexicon of the Red Sox.

Oriole Post - The World of Baseball and Beyond An Orioles blog.

DRays Bay A Devil Rays blog.

Mets Heads A blog about the New York Mets.

The Soul of Baseball Joe Posnanski promotes his book on Buck O'Neil and blogs about baseball.

My Baseball Bias A blog about East Coast baseball.

Sports Business Radio Articles and talk about the business of sports.

The Game of Baseball A blog about Major League Baseball.

Baseball Hot Corner Opinionated observations for the thinking fan.

FantasyDope.com Fantasy baseball news.

Peter's Red Sox Forever A Red Sox blog.

Sox Nest Commentary on the Red Sox.

The Big Oz A Florida Marlins blog.

Baseball Reflections Where old school baseball meets sabermetrics.

The Sommer Frieze A Yankees blog.

Fenway Nation A Red Sox fan site.

In-Between Hops A Milwaukee Brewers blog.

Right Field Bleachers Another Milwaukee Brewers blog.

On Baseball and the Reds Another Cincinnati Reds blog.

Crooked Pitch A fantasy baseball blog.

Bless You Boys A Detroit Tigers blog.

Cubs f/x Pitch f/x and the Chicago Cubs.

The Hot Corner

Eephus Pitch Tossing pure junk about New York baseball since 2006.

It Is High, It Is Far, It Is Caught A tribute to John Sterling.

Baseball GB Baseball from a British perspective.

Nick and Nick's Twins Blog A couple of Nicks write on the Twins.

SkyKing162 Baseball with a hint of lime.

Center Field A Red Sox blog.

Empyreal Environs Writing about the Red Sox.

Trophy League Planet Aggregating the baseball blogosphere.

Cardinals Best News Links Aggregating St. Louis Cardinals news.

Zell's Pinstripe Blog A Yankees Blog.

HSAC Blog Official Musings of the Harvard College Sports Analysis Collective.

The Baseball Fix A general baseball blog.

MLB Roundup A baseball video blog.

Fantasy Dope Fantasy Baseball News.

The Cubs Brickyard Hilarious fake news.

Spitting Seeds A blog about Major League baseball.

Infield Chatter A blog covering all aspects of baseball.

The Bronx View A blog and podcast about the Yankees.

Jorge Says No A blog about the Yankees.

Ivy League to MLB Shawn Haviland blogs about his efforts to rise through the Oakland Athletics system.

This Purist Bleeds Pinstripes Blog of a girl who somehow has found a way to balance being a baseball purist with being a New York Yankees fan.

Baseball from Wrigley A Chicago Cubs blog.

Sliding into Home A Yankees blog.

Boras Blog Blogging about Scott Boras.

Injury Tool Fantasy Pitch F/X offers complete information on injuries.

Instapundit Politics and the law. This site inspired me to start blogging.

Rookie Cards Baseball Card grading.

Wild Treasure Treasure hunts through the blogosphere.

San Diego Ticket Finder San Diego Ticket Information.

Prize Sports.net Baseball Collectibles.

Fantasy Sports R Us The #1 Fantasy Baseball Leagues site on the web.

RotoRank - Fantasy Baseball Draft Guides Customized For Any Fantasy Baseball League.