Adjusted Range Factor

Who was the most valuable defensive player in 2013 during the regular season?

Andrelton Simmons, with Pedro Florimon a close 2^nd; next question.  But can we quantify that?  I think that we can, and I think it can be done in an objective manner.  I think it can be done relying entirely on the statistics, without resorting to relying on anybody’s judgment.  Further I think that we can go into history and find out who was the best fielder of all time (Nap Lajoie, according to the stats I have, Bill James be damned) and what kind of a fielder was Babe Ruth really?  (Much much much better than you have been lead to believe)

I have read that there is good statistical proof that good defense keeps balls that are in play (Base Hits that are not home runs and outs that are not strike outs) from being hits and not pitching.  That is, there is proof that it is not a skill that appears constant from year to year for pitchers.  (The exception is apparently knuckleballers.)  I have also read that a good stat for total team defense is outs/balls in play:

Defensive Outs (DO) = IP*3-K

Balls in Play (BIP) = H-HR+IP*3-K +E

Team Defensive Rating = (DO)/(BIP)

The team that led the league in that statistic in 2013 was the Cincinnati Reds.  They converted .723 of batted balls into outs.  The worst team was The Colorado Rockies, who converted in-play balls into outs .684 percent of the time.  The league average was .701.  There are, however, 27 outs in a game, and Cincinnati and Colorado both managed get 27 batters out in most of their games.  One would expect, however, that if Colorado’s shortstop and Cincinnati’s shortstop got to 4.16 balls a game (the league average) Cincinnati’s had the better shortstop, but by how much?  Cincinnati’s shortstop’s range factor should be multiplied by 1.031 (=.723/.701) and Colorado’s shortstop’s range should be multiplied by .976 (=.684/.701) giving Colorado’s shortstop a range rating of 4.06 and Cincinnati’s shortstop 4.29.  If each shortstop played in an otherwise average defense, each would be expected to reach that many balls per game.  (Assists + Putouts – Errors) 

Strikeouts are a 2^nd factor that must be adjusted for.  This season Detroit struck out the most batters with .234 percent of the batters they faced and so did not strike out .766 percent of the batters that they faced.  Minnesota (last place) struck out .158 percent of the batters that they faced and failed to strikeout .842 percent of the batters that they faced.  The league average was .800.  Minnesota fielders had to make more plays than they would have if they were behind a pitching staff that struck out more batters; their stats are a bit padded (.800/.842 = .950) and Detroit did not get as many chances as they might have otherwise – (.800/.762 = 1.050)  The number I actually go with, however is 1-(K)/(H+IP83) because I have a complete set of that data, and do not have complete data for batters faced by pitchers.

A Third factor is the ball park that a team plays in.  When I conceived of the idea that a ball park needs to be adjusted for, I conceived of it as the Colorado adjustment.  The field at Colorado is the highest in square footage in the league, and in spite of that, more homeruns are hit there than in any other park due to the low air density, blah blah blah, if you are reading this you are likely familiar with the problem.  It occurred to me that if the fielders have more square footage to cover then it must be harder to stop hits in the park as well and the statistics bore this out.  In an average year teams playing at Coors Field make about .96 as the (approximately) same teams on the road.  What did not occur to me, however, is that there might be stadiums that had a higher Outs per Ball in play than others.  Stadiums with large foul territories do, in fact show such an effect.  I feel confident that, in order, the stadiums with the largest foul territories in baseball history are “The Polo Grounds”, “Braves Field” in Boston, “Qualcom Stadium” and the old “Yankee Stadium”, and I feel so confident of that that I will not fact check it.

A fourth and final factor to adjust for is total infield vs. outfield chances.  If a pitching staff consisted of Justin Masterson, A.J. Burnett, Doug Fister and Rick Porcello, all with GB/FB ratios of 1.28 or above, then the outfield is going to look pretty bad and the infield is going to have their stats padded.  It could, however, be that the infield is good and the outfield is bad.  I go with a middle of the road adjustment for this.  I divide Outfield Putouts by Putouts minus Strikeouts (OFPO/(PO-K) for teams and the league to gauge the amount of balls that go to the infield vs. balls that go to the outfield and compare it to the league average.  By this rating Oakland had the highest rating (meaning more balls went to the outfield) of ..382 and Pittsburg had the lowest rating of ..227.  As I said, I go half way with this adjustments, so Oakland’s infielders have an adjustment of (.382/.3285+1)/2 =1.081 and their outfielders have an adjustment of (.3285/.382+1)/2=.960

Here are the defenses rank ordered with the final adjustments that I make:

yearID	teamID	OIP	fAdj	Kadj	Park	OFO/O	IFA	OFA
2013	ARI	0.7062	1.0072	0.9910	1.0072	0.3064	0.9576	1.0073
2013	ATL	0.7084	1.0103	1.0063	0.9990	0.3161	0.9985	1.0271
2013	BAL	0.7121	1.0155	0.9870	1.0021	0.3210	0.9887	1.0058
2013	BOS	0.7040	1.0040	1.0179	0.9947	0.3413	1.0474	1.0178
2013	CHA	0.6961	0.9928	1.0049	1.0107	0.3331	0.9940	0.9837
2013	CHN	0.7130	1.0169	0.9956	0.9907	0.3430	1.0445	1.0109
2013	CIN	0.7227	1.0307	1.0191	1.0022	0.3315	1.0528	1.0457
2013	CLE	0.6926	0.9877	1.0406	1.0020	0.3232	1.0175	1.0298
2013	COL	0.6840	0.9755	0.9630	0.9879	0.2904	0.8957	0.9779
2013	DET	0.6921	0.9870	1.0479	0.9928	0.3355	1.0528	1.0364
2013	HOU	0.6901	0.9842	0.9663	1.0049	0.3263	0.9432	0.9479
2013	KCA	0.7076	1.0093	0.9993	1.0005	0.3573	1.0522	0.9864
2013	LAA	0.6908	0.9853	0.9914	1.0007	0.3464	1.0025	0.9631
2013	LAN	0.7007	0.9994	1.0194	1.0073	0.2907	0.9531	1.0399
2013	MIA	0.7046	1.0049	0.9905	0.9978	0.3400	1.0149	0.9890
2013	MIL	0.7050	1.0055	0.9805	0.9993	0.3356	0.9972	0.9814
2013	MIN	0.6917	0.9866	0.9442	0.9961	0.3241	0.9290	0.9383
2013	NYA	0.6976	0.9949	1.0007	0.9893	0.3493	1.0382	0.9908
2013	NYN	0.6998	0.9981	0.9921	1.0220	0.3285	0.9687	0.9688
2013	OAK	0.7137	1.0179	0.9945	1.0096	0.3820	1.0842	0.9627
2013	PHI	0.6859	0.9782	0.9941	1.0108	0.3255	0.9576	0.9643
2013	PIT	0.7076	1.0092	1.0110	1.0074	0.2771	0.9334	1.0516
2013	SDN	0.7054	1.0060	0.9885	1.0181	0.3212	0.9659	0.9821
2013	SEA	0.6917	0.9865	1.0118	0.9963	0.3318	1.0068	0.9993
2013	SFN	0.6969	0.9940	1.0095	1.0148	0.3461	1.0152	0.9759
2013	SLN	0.7016	1.0007	1.0081	1.0090	0.3127	0.9757	1.0115
2013	TBA	0.7164	1.0218	1.0225	1.0111	0.3228	1.0244	1.0378
2013	TEX	0.7034	1.0032	1.0197	0.9950	0.3430	1.0507	1.0171
2013	TOR	0.6972	0.9944	0.9949	0.9977	0.3335	0.9991	0.9879
2013	WAS	0.6995	0.9977	1.0059	0.9863	0.3222	1.0077	1.0224
	Avg	0.7012	1.0000	1.0000	1.0000	0.3285	1.0000	1.0000

OIP – Outs per Ball in Play

Fadj – Fielding adjustment

Kadj – Strike out Adjustment

GB – OFO/O – Out field Put Outs divided by Putouts – Strikeouts

IFA = Fadj*Kadj/Park*(OFO/AvgOFO+1)/2

OFA = Fadj*Kadj/Park*( AvgOFO /OFO+1)/2

And here are your rightful 2013 Gold Glove Winners (Voter Results may Vary)

	American		National
C	Yan Gomes		Russell Martin
1B	Adam Rosales		Joey Votto
2B	Eric Sogard		Brandon Phillips
3B	Manny Machado		Nolan Arenado
SS	Stephen Drew		Andrelton Simmons
LF	Andy Dirks		Denard Span
CF	Chris Young		Carlos Gomez
RF	Shane Victoino		Juan Lagares

ARF – Adjusted Range Factor

Notes: I did not necessarily give my Golden Glove vote to the player with the highest Range Factor, but instead to the player with the highest defensive runs saved.  How I calculate this will be another blog post.

One of the values of using this method is that it is almost completely objective.  It still relies on the opinion of the official scorer as to what is an error in its calculations.  The other value is that there are enough stats to make such evaluations back to 1955 and enough stats to make some pretty good guesses back to 1871.  Estimating the amount of Innings played is slightly fraught and prone to some error, but the errors for full time players are apt to be fairly small.  I have made such guesses back to 1871.  Since I mention it earlier:

1923 Gold Glove Winners: (According to me)

	American	National
C	Muddy Ruel	Zack Taylor
1B	Joe Judge	Charlie Grimm
2B	Aaron Ward	Jimmy Johnston
3B	Rube Lutzke	Pie Traynor
SS	Dave Bancroft	Rabbit Maranville
LF	Baby Doll Jacobson	Jack Smith
CF	Johnny Mostil	Jigger Statz
RF	Babe Ruth	Max Carey

Note: These totals are based on estimated Innings played.  This will also require a Blog Post.