Most lefty batters may be opportunists. 1903-2012 and 2015 data, including Bryce Harper.

Qualified for 2015 league batting title baseball-reference.com:

Bats RH, Throws LH: ZERO batters found

Bats LH, Throws RH: 33 found and listed below.

Bats/Throws: Executive Summary Friday, March 1, 2013

1903-2012 righties:
63% PA
73% Innings

2012 righties:
60.42% PA
70.10% Innings

For 836 batters with at least 5,000 PA since 1901:
- 99.6% of righty batters throw righty
- only 42.2% of lefty batters throw lefty; this suggests that some lefty batters may be opportunists
- 54.9% bat right, throw right (RR) ...

There is virtually no such thing as switch pitching...

It seems pretty clear that changing how one throws is extremely rare but that right handed players can learn to bat lefty, either exclusively or as switch hitters.
__________________________

For 2015, Bats LH, Throws RH, (requiring Qualified for league batting title), sorted by greatest Batting Average

Bryce Harper

Rk	Player	BA	Year	Age	Tm	Lg	G	PA	AB	R	H	2B	3B	HR	RBI	BB	IBB	SO	HBP	SH	SF	GDP	SB	CS	OBP	SLG	OPS	Pos
1	Bryce Harper	.334	2015	22	WSN	NL	102	432	347	74	116	25	1	29	69	81	11	87	3	0	1	8	4	4	.463	.663	1.126	*9/8D
2	Dee Gordon	.329	2015	27	MIA	NL	94	421	401	49	132	17	5	1	28	13	2	64	1	4	2	5	34	14	.350	.404	.754	*4
3	Jason Kipnis	.326	2015	28	CLE	AL	101	468	405	66	132	31	6	6	39	47	4	69	8	2	6	2	11	7	.401	.477	.878	*4/D
4	Prince Fielder	.324	2015	31	TEX	AL	106	463	411	53	133	22	0	16	63	40	11	53	8	0	4	12	0	0	.391	.494	.885	*D3/H
5	Joe Panik	.309	2015	24	SFG	NL	97	423	375	56	116	25	2	7	35	37	0	42	4	3	4	7	3	2	.374	.443	.816	*4/H
6	Joey Votto	.309	2015	31	CIN	NL	105	462	372	59	115	22	2	19	51	86	6	81	3	0	1	8	6	2	.442	.532	.974	*3/H
7	Ben Revere	.295	2015	27	TOT	ML	103	416	390	53	115	13	6	1	27	20	0	37	1	4	1	4	24	5	.330	.367	.697	*789/H
8	Odubel Herrera	.286	2015	23	PHI	NL	97	339	318	41	91	22	3	5	29	12	0	77	3	5	1	5	9	4	.317	.421	.739	*8H
9	Josh Reddick	.281	2015	28	OAK	AL	100	391	359	45	101	17	3	13	58	29	0	39	0	0	2	5	5	1	.333	.454	.787	*9/H8
10	Daniel Murphy	.278	2015	30	NYM	NL	85	348	320	28	89	20	0	8	38	24	10	26	2	0	2	10	1	2	.330	.416	.746	*45/HD3
11	Mike Moustakas	.277	2015	26	KCR	AL	98	416	372	47	103	18	1	10	39	26	0	47	11	3	4	10	1	2	.339	.411	.750	*5/H
12	Brock Holt	.275	2015	27	BOS	AL	89	344	305	35	84	17	4	2	26	33	0	72	2	3	1	4	5	1	.349	.377	.726	4957/63H8
13	Christian Yelich	.270	2015	23	MIA	NL	90	373	337	37	91	14	1	6	28	34	0	79	2	0	0	7	12	2	.340	.371	.711	*78/H
14	Kyle Seager	.269	2015	27	SEA	AL	109	456	417	55	112	24	0	16	44	35	5	58	2	0	2	14	4	3	.327	.441	.768	*5
15	Kolten Wong	.268	2015	24	STL	NL	106	445	403	55	108	20	2	11	46	26	2	67	13	0	3	7	11	8	.330	.409	.740	*4/H
16	Robinson Cano	.268	2015	32	SEA	AL	104	450	418	53	112	27	1	12	50	26	3	74	3	0	3	11	2	4	.313	.423	.737	*4/DH
17	Matt Carpenter	.266	2015	29	STL	NL	103	444	379	64	101	29	1	15	56	58	4	87	4	0	3	3	3	2	.367	.467	.834	*5/4H3
18	Joe Mauer	.264	2015	32	MIN	AL	107	443	398	44	105	20	2	6	46	40	11	73	1	0	4	15	1	1	.330	.369	.699	*3D/H
19	Brandon Crawford	.263	2015	28	SFG	NL	105	415	376	54	99	20	4	19	70	27	4	87	8	0	4	10	4	4	.323	.489	.812	*6/H
20	Pablo Sandoval	.261	2015	28	BOS	AL	97	379	353	32	92	16	1	9	35	20	1	54	5	0	1	12	0	0	.309	.388	.697	*5/H
21	Stephen Vogt	.260	2015	30	OAK	AL	102	391	339	46	88	15	2	15	60	43	5	73	2	0	7	8	0	1	.340	.448	.789	*23H/D
22	Didi Gregorius	.259	2015	25	NYY	AL	101	373	340	37	88	13	1	5	32	20	0	56	6	3	4	3	4	2	.308	.347	.655	*6/H
23	Curtis Granderson	.257	2015	34	NYM	NL	109	465	405	59	104	21	1	17	41	55	3	109	3	0	2	2	9	4	.348	.440	.788	*9/H8
24	Brian McCann	.251	2015	31	NYY	AL	89	350	311	44	78	12	1	18	65	28	2	65	6	0	5	5	0	0	.320	.469	.789	*2H/3D
25	Chris Coghlan	.250	2015	30	CHC	NL	104	350	308	37	77	18	1	11	25	39	6	59	2	1	0	3	10	2	.338	.422	.760	*7H/4359
Rk	Player	BA	Year	Age	Tm	Lg	G	PA	AB	R	H	2B	3B	HR	RBI	BB	IBB	SO	HBP	SH	SF	GDP	SB	CS	OBP	SLG	OPS	Pos
26	Jace Peterson	.250	2015	25	ATL	NL	104	432	380	42	95	19	3	5	48	41	3	85	3	5	3	1	9	9	.326	.355	.681	*4/H
27	Chris Davis	.248	2015	29	BAL	AL	106	437	383	57	95	18	0	28	79	47	2	137	2	0	5	4	0	1	.330	.514	.844	*39D
28	Lucas Duda	.247	2015	29	NYM	NL	106	445	381	57	94	26	0	21	53	49	3	115	12	0	3	9	0	1	.348	.480	.829	*3/H
29	Brad Miller	.245	2015	25	SEA	AL	102	363	318	31	78	16	3	9	35	36	0	73	2	2	5	6	11	1	.321	.399	.721	*6/DH7498
30	Kevin Kiermaier	.244	2015	25	TBR	AL	105	372	353	41	86	20	11	4	21	14	0	72	2	2	1	3	11	2	.276	.397	.672	*8H/9
31	Pedro Alvarez	.235	2015	28	PIT	NL	99	346	311	41	73	15	0	15	53	30	7	87	2	0	3	3	2	0	.303	.428	.731	*3H/D
32	Brandon Moss	.213	2015	31	TOT	ML	102	402	362	37	77	18	1	15	51	34	2	112	3	0	3	10	0	0	.284	.392	.676	*93/HD
33	Luis Valbuena	.213	2015	29	HOU	AL	92	379	338	50	72	11	0	21	43	34	0	82	5	0	2	10	1	0	.293	.432	.725	*5/3

Provided by Baseball-Reference.com: View Play Index Tool Used
Generated 8/8/2015.

Original sin: unfair righty/lefty imbalance. Monday, July 13, 2015