Original sin: unfair righty/lefty imbalance.

It predates non-uniform playing areas.  It predates the invention and/or discovery of the curve ball.  It's allowing some batters to stand closer to the bases than other batters.  Even the diamond itself is rendered non-symmetrical.  Its delusion of symmetry is further enhanced by the presence of two batter's boxes, one on each side of the plate.  But that delusion is an illusion.

When I was very young and saw some baseball on television my kiddie brain assumed that when the batter began to run the bases the batter would run towards the base closest to the box from which the ball was hit.  If the box was on the left side of the plate, the batter would towards the base to the left.  From the righty box, to the righty base.  In fact if the bases had been referred to as left, center and right (as the outfield positions are) then this entire travesty might not have occurred.

Maybe it was some early attempt at being touchy-feely and a departure from a medieval association of lefties with the devil.  Whatever it was, it was a mistake.  It messed up baseball in a fundamental way.  Later distortions only built on this faulty foundation.

There were two ways this could have been addressed:
1. Only have one batter's box.
2. Have batters run to the nearest base and not lock in direction.

Wow, that number two would be impossible.  Blah, blah, blah.  You know, the usual baseball knee jerk reaction to anything that's even a little different. And this change, especially at the beginning, would have been very different.  But what about base runners?  If you can win a million dollars by thinking of a way to handle that within ten seconds, do you think you could do it?

I would simply change the base location of the runners to reflect the next batter's intended direction of base running.  If a batter were to use the box on the left with a runner already on right base, then the runner would be directed by the umpire to occupy left base and run the bases clockwise.  Fielders could adapt accordingly so that true lefties, i.e., those who throw with their left hand, would not be restricted to playing first base and the outfield.

Lefties need not apply. Or why are there two batter's boxes? Monday, March 17, 2014

We're so stuck in our thinking that we don't even consider just how odd it is that baseball is so asymmetrical.  Aside from the utter absurdity of the non-uniform playing areas, why the heck are there two batter's boxes? ...

And if there are going to be two, why doesn't the righty batter run to "third" base? ..

Only about 42% of lefty batters throw lefty.

Most lefty batters are opportunists, taking advantage of two things:

1. 72% of pitches are thrown by righties, which is good for a lefty batter, bad for a righty batter.

2. Lefty batters are closer to all the bases, not just first base.
__________________________________

Let's try some anecdotal evidence.

Careers, From 1903 to 2015, (requiring batting_avg>=.340 and At least 5000 plate appearances), sorted by greatest Batting Average

Rk	Player	BA	PA	From	To	Age	G	AB	R	H	2B	3B	HR	RBI	BB	IBB	SO	HBP	SH	SF	GDP	SB	CS	OBP	SLG	OPS	Pos	Tm
1	Ty Cobb	.366	13084	1905	1928	18-41	3034	11434	2244	4189	724	295	117	1933	1249		681	94	291			897	212	.433	.512	.945	*89/H73145	DET-PHA
2	Rogers Hornsby	.358	9480	1915	1937	19-41	2259	8173	1579	2930	541	169	301	1584	1038		679	48	216		3	135	64	.434	.577	1.010	*465H/3978	STL-NYG-BSN-CHC-SLB
3	Shoeless Joe Jackson	.356	5695	1908	1920	20-32	1332	4981	873	1772	307	168	54	785	519		234	59	131			202	81	.423	.517	.940	978/3H	PHA-CLE-CHW
4	Tris Speaker	.345	11992	1907	1928	19-40	2792	10195	1882	3514	792	222	117	1531	1381		394	103	309			436	157	.428	.500	.928	*8/H3971	BOS-CLE-WSH-PHA
5	Ted Williams	.344	9788	1939	1960	20-41	2292	7706	1798	2654	525	71	521	1839	2021	86	709	39	5	20	197	24	17	.482	.634	1.116	*79H/1	BOS
6	Babe Ruth	.342	10622	1914	1935	19-40	2504	8399	2174	2873	506	136	714	2214	2062		1330	43	113		2	123	117	.474	.690	1.164	971/H83	BOS-NYY-BSN
7	Harry Heilmann	.342	8964	1914	1932	19-37	2146	7787	1291	2660	542	151	183	1540	856		550	40	277			113	64	.410	.520	.930	*93/H847	DET-CIN
8	Bill Terry	.341	7108	1923	1936	24-37	1720	6428	1120	2193	373	112	154	1078	537		449	9	137		38	56	6	.393	.506	.899	*3H/97	NYG
9	Lou Gehrig	.340	9663	1923	1939	20-36	2164	8001	1888	2721	534	163	493	1995	1508		790	45	106		2	102	100	.447	.632	1.080	*3/H976	NYY
10	George Sisler	.340	9012	1915	1930	22-37	2054	8267	1284	2812	425	164	102	1178	472		327	48	226			375	127	.379	.468	.847	*3/H197845	SLB-WSH-BSN

Provided by Baseball-Reference.com: View Play Index Tool Used
Generated 7/13/2015.

Of the top ten, only Hornsby and Heilmann bat righty.

Of the lefty batters these were true lefties, i.e., they also threw lefty: Speaker, Ruth, Terry, Gehrig and Sisler.  However, the remaining lefties were opportunists who threw righty: Cobb, Jackson and Williams (three of the top five).

Ty Cobb and Joe Jackson

Here are the top opportunists (bat left, throw right):

Careers, From 1903 to 2015, Bats LH, Throws RH, (requiring batting_avg>=.320 and At least 5000 plate appearances), sorted by greatest Batting Average

Rk	Player	BA	PA	From	To	Age	G	AB	R	H	2B	3B	HR	RBI	BB	IBB	SO	HBP	SH	SF	GDP	SB	CS	OBP	SLG	OPS	Pos	Tm
1	Ty Cobb	.366	13084	1905	1928	18-41	3034	11434	2244	4189	724	295	117	1933	1249		681	94	291			897	212	.433	.512	.945	*89/H73145	DET-PHA
2	Shoeless Joe Jackson	.356	5695	1908	1920	20-32	1332	4981	873	1772	307	168	54	785	519		234	59	131			202	81	.423	.517	.940	978/3H	PHA-CLE-CHW
3	Ted Williams	.344	9788	1939	1960	20-41	2292	7706	1798	2654	525	71	521	1839	2021	86	709	39	5	20	197	24	17	.482	.634	1.116	*79H/1	BOS
4	Eddie Collins	.333	12044	1906	1930	19-43	2825	9949	1821	3315	438	187	47	1300	1499		468	77	512			741	195	.424	.429	.853	*4/H69875	PHA-CHW
5	Wade Boggs	.328	10740	1982	1999	24-41	2440	9180	1513	3010	578	61	118	1014	1412	180	745	23	29	96	236	24	35	.415	.443	.858	*5DH/317	BOS-NYY-TBD
6	Rod Carew	.328	10550	1967	1985	21-39	2469	9315	1424	3053	445	112	92	1015	1018	144	1028	25	128	64	216	353	187	.393	.429	.822	34H/D657	MIN-CAL
7	Earle Combs	.325	6513	1924	1935	25-36	1456	5746	1186	1866	309	154	58	633	670		278	17	74			98	71	.397	.462	.859	*87/H9	NYY
8	Sam Rice	.322	10251	1915	1934	25-44	2405	9269	1514	2987	498	184	34	1077	708		275	56	213			351	143	.374	.427	.801	*98H/71	WSH-CLE
9	Ross Youngs	.322	5336	1917	1926	20-29	1211	4627	812	1491	236	93	42	592	550		390	37	119			153	83	.399	.441	.839	*9/4H87	NYG
10	Chuck Klein	.320	7170	1928	1944	23-39	1753	6486	1168	2076	398	74	300	1201	601		521	12	69		55	79		.379	.543	.922	*97H/83	CHC-PIT-PHI
11	Charlie Gehringer	.320	10244	1924	1942	21-39	2323	8860	1775	2839	574	146	184	1427	1186		372	50	141		27	181	90	.404	.480	.884	*4H/35	DET
12	Mickey Cochrane	.320	6207	1925	1937	22-34	1482	5169	1041	1652	333	64	119	830	857		217	29	151			64	45	.419	.478	.897	*2/H7	PHA-DET

Provided by Baseball-Reference.com: View Play Index Tool Used
Generated 7/13/2015.

I think they're all in the Hall of Fame.

How about true lefties (both bat and throw lefty)?

Careers, From 1903 to 2015, Bats LH, Throws LH, (requiring batting_avg>=.320 and At least 5000 plate appearances), sorted by greatest Batting Average

Rk	Player	BA	PA	From	To	Age	G	AB	R	H	2B	3B	HR	RBI	BB	IBB	SO	HBP	SH	SF	GDP	SB	CS	OBP	SLG	OPS	Pos	Tm
1	Tris Speaker	.345	11992	1907	1928	19-40	2792	10195	1882	3514	792	222	117	1531	1381		394	103	309			436	157	.428	.500	.928	*8/H3971	BOS-CLE-WSH-PHA
2	Babe Ruth	.342	10622	1914	1935	19-40	2504	8399	2174	2873	506	136	714	2214	2062		1330	43	113		2	123	117	.474	.690	1.164	971/H83	BOS-NYY-BSN
3	Bill Terry	.341	7108	1923	1936	24-37	1720	6428	1120	2193	373	112	154	1078	537		449	9	137		38	56	6	.393	.506	.899	*3H/97	NYG
4	Lou Gehrig	.340	9663	1923	1939	20-36	2164	8001	1888	2721	534	163	493	1995	1508		790	45	106		2	102	100	.447	.632	1.080	*3/H976	NYY
5	George Sisler	.340	9012	1915	1930	22-37	2054	8267	1284	2812	425	164	102	1178	472		327	48	226			375	127	.379	.468	.847	*3/H197845	SLB-WSH-BSN
6	Tony Gwynn	.338	10232	1982	2001	22-41	2440	9288	1383	3141	543	85	135	1138	790	203	434	24	45	85	259	319	125	.388	.459	.847	*98H/7D	SDP
7	Paul Waner	.333	10766	1926	1945	23-42	2550	9459	1627	3152	605	191	113	1309	1091		376	38	174		127	104	0	.404	.473	.878	*9H/378	PIT-BSN-BRO-NYY
8	Stan Musial	.331	12717	1941	1963	20-42	3026	10972	1949	3630	725	177	475	1951	1599	127	696	53	35	53	243	78	31	.417	.559	.976	3798H/1	STL
9	Heinie Manush	.330	8419	1923	1939	21-37	2009	7654	1288	2524	491	160	110	1183	506		345	70	186		11	113	59	.377	.479	.856	*78H9/3	DET-SLB-WSH-BOS-BRO-PIT
10	Babe Herman	.324	6228	1926	1945	23-42	1553	5603	882	1818	399	110	181	997	520		553	11	92		43	94	0	.383	.532	.915	*937H	BRO-CIN-CHC-PIT-DET
11	Edd Roush	.323	8148	1913	1931	20-38	1967	7363	1099	2376	339	182	68	981	484		260	53	256			268	92	.369	.446	.815	*8H/7394	CHW-IND-NEW-NYG-CIN

Provided by Baseball-Reference.com: View Play Index Tool Used
Generated 7/13/2015.

Finally, how about those who bat right but throw left?  In other words, natural lefties who chose to bat from the disadvantaged righty batter's box.

Careers, From 1903 to 2015, Bats RH, Throws LH, (requiring batting_avg>=.220 and At least 5000 plate appearances), sorted by greatest Batting Average

Rk	Player	BA	PA	From	To	Age	G	AB	R	H	2B	3B	HR	RBI	BB	IBB	SO	HBP	SH	SF	GDP	SB	CS	OBP	SLG	OPS	Pos	Tm
1	Hal Chase	.291	7938	1905	1919	22-36	1919	7417	980	2158	322	124	57	941	276		660	30	216			363	37	.319	.391	.710	*3/487H6915	NYY-CHW-BUF-CIN-NYG
2	Rickey Henderson	.279	13346	1979	2003	20-44	3081	10961	2295	3055	510	66	297	1115	2190	61	1694	98	30	67	172	1406	335	.401	.419	.820	*78HD/9	OAK-NYY-TOR-ANA-SDP-NYM-SEA-BOS-LAD

Provided by Baseball-Reference.com: View Play Index Tool Used
Generated 7/13/2015.

Need I say more?