BASE STATES

A look at how base-state effects the batter-pitcher match-up.
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PITCHERS 

Base State	PA	FIP*	BABIP	K%	BB%	HR%	GB%	FB%	HR/FB	PPA	IBB%
"---”	1045868	4.36	0.294	17.9	7.6	2.8	43	36.9	10.7	3.84	0.01
“1--”	342077	4.27	0.311	15.9	6.9	2.8	41.6	37.8	10.4	3.84	0.01
"-2-”	167165	4.53	0.293	16.9	10.3	2.2	44.4	35.9	9.5	4.03	3.71
“12-”	135831	4.21	0.290	17.5	7.7	2.6	42.7	37.5	10.2	3.77	0.05
“--3”	55109	4.67	0.301	17	10.7	2.2	43.7	36.8	9.1	3.98	3.58
“1-3”	58709	4.34	0.307	15.9	7.7	2.5	43	37.2	9.5	3.78	0.55
“-23”	42529	4.42	0.297	16.6	9.4	1.9	44.5	36.5	8.9	4	10.88
“123”	48959	4.06	0.296	17.9	6.7	2.6	42.8	38	9.5	3.69	0

*where FIP here is the 'generic' version of the metric, using 3.2 as the constant, and 'PPA' is pitches per plate appearance.
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I was inspired to run this query after Tom Tango at The Book Blog mentioned that a pitcher is much more likely to walk a batter with a runner on 2nd rather than 1st. This is affirmed by the chart-- with the difference a little over 3%.  Similarly, pitchers attempt to avoid contact in the '--3' and '-23' base states when first base is also vacant and HR/FB drops as the pitcher is apparently living ouside-the-zone a touch more than usual.


This is naturally an advantage for the hitter as he sees a bump in his OBP and OPS therefore, but not so much with his SLG percentage:

BATTERS 

Base State	PA	wOBA*	BA	OBP	SLG	OPS
"---”	1045868	0.323	0.258	0.32	0.413	0.734
“1--”	342077	0.327	0.277	0.325	0.433	0.759
"-2-”	167165	0.311	0.252	0.36	0.394	0.754
“12-”	135831	0.312	0.254	0.314	0.405	0.718
“--3”	55109	0.323	0.277	0.373	0.429	0.802
“1-3”	58709	0.330	0.296	0.338	0.459	0.797
“-23”	42529	0.292	0.273	0.412	0.423	0.836
“123”	48959	0.319	0.281	0.316	0.445	0.761

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*where wOBA is also the 'generic' version of the metric and does not include IBB or SB/CS.

It's also worth noting that BABIP is at it's highest when the first basemen is holding the runner. BABIP jumps about 17 points from bases empty to a state of "1--", but GB-BABip, in particular, sees a 20 point surge once right side of the infield is opened up:

BABIP

Base State	GB_BABIP	FB_BABIP	LD_BABIP	wBABIP*
"---”	0.216	0.195	0.707	0.356
“1--”	0.236	0.199	0.721	0.369
"-2-”	0.210	0.195	0.701	0.346
“12-”	0.207	0.196	0.710	0.350
“--3”	0.221	0.192	0.728	0.352
“1-3”	0.226	0.189	0.747	0.360
“-23”	0.220	0.189	0.725	0.348
“123”	0.219	0.187	0.730	0.353

*wBABIP is (0.90*1B + 1.24*2B + 1.56*3B + 1.95*HR) / (AB - SO + SF), 
GB excludes bunts, FB includes "pop ups"

I'm uncertain why GB-BAbip would be lowest of all the base states during "12-", but I'm open to suggestions. The 1B may be behind the runner in most of these situations, and the SS/2B may play deeper with the double play an option, but none of this should be an advantage over the bases empty state.

FB-BABip seems to fall slightly as the bases fill up, especially with a runner on third, which leads me to wonder if this is the effect of a slight shift in positioning as the outfielders feel less inclined to prevent the extra base hit rather than the bloop single.

I'm also going to speculate that LD-BABip reaches it's peak with both the 1B and the 3B holding the runners in a state of "1-3". Unlike ground balls, line drives are pulled more often than not (WAG), and with the majority of hitters being right-handed, the hot corner would see more LD-BIP than a first baseman.