So since they've been talking about the dynamic run estimator with pitching over on fangraphs (most notably in this article ).  I decided that I'd take a look at trying something like that with batting.  Bill James developed Offensive Winning Percentage, which was developed much in the same vein as the Win% used for pitchers. 

From The Book wiki:

Offensive Winning Percentage (OWP) is a Bill James statistic that measures the rate of offensive performance. A player's OWP is the winning percentage that the Pythagorean Theorem would project for a team that scored runs at the rate the player created them, but allowed a league average number of runs.

The formula for OWP is:

OWP = (RC/Out)^x/((RC/Out)^x + Lg(RC/Out)^x)

where RC is Runs Created and x is the Pythagorean exponent used (usually 2).

Note: I used Pythagenpat to find the exponent x

Later in that article it's noted the James set replacement level at .350.  So now we have something to work with.  Of course, I did this for the Brewers since I have all the data necessary readily available.

PLAYER	POS	mPA	wOBA	OBP	wRC	Outs	wRC/Out	LGwRC/Out	OWP	PA/27	OffWAR	FRAA/650	posadj/650	DefWAR	TotalWAR
Rivera ,Mike	C	150	0.329	0.332	17.55	100.2	0.18	0.18	0.488	40.42	0.51	0	11.61	0.27	0.78
Kendall, Jason	C	550	0.295	0.323	45.65	372.35	0.12	0.17	0.321	39.88	-0.4	7	11.61	1.57	1.17
Nelson ,Brad	1B	50	0.338	0.345	6.3	32.75	0.19	0.18	0.534	41.22	0.22	-5	-11.61	-0.13	0.1
Fielder, Prince	1B	650	0.382	0.377	110.5	404.95	0.27	0.19	0.686	43.34	5.04	-8	-11.61	-1.96	3.08
Weeks, Rickie	2B	600	0.343	0.357	78.6	385.8	0.2	0.18	0.562	41.99	3.03	-9	2.32	-0.62	2.41
Hall, Bill	3B	500	0.325	0.318	56.5	341	0.17	0.18	0.460	39.59	1.39	-1	2.32	0.1	1.49
Lamb, Mike	3B	200	0.319	0.330	21.4	134	0.16	0.18	0.444	40.3	0.47	-12	2.32	-0.3	0.17
Hardy, J.J.	SS	625	0.344	0.336	82.5	415	0.2	0.18	0.547	40.66	3.03	1	6.96	0.77	3.79
Braun, Ryan	LF	625	0.384	0.352	107.5	405	0.27	0.19	0.670	41.67	4.8	2	-6.96	-0.48	4.32
Cameron, Mike	CF	575	0.333	0.328	69.58	386.4	0.18	0.18	0.500	40.18	2.15	3	2.32	0.47	2.62
Hart, Corey	RF	600	0.345	0.329	79.8	402.6	0.2	0.18	0.545	40.24	2.91	2	-6.96	-0.46	2.45
Gwynn, Tony	OF	150	0.306	0.325	14.1	101.25	0.14	0.17	0.379	40	0.11	-6	-2.32	-0.19	-0.08
Duffy, Chris	OF	150	0.306	0.320	14.1	102	0.14	0.17	0.375	39.71	0.09	9	-2.32	0.15	0.25
Replacement	C	7	0.304	0.304	0.64	4.87	0.13	0.17	0.350	38.77	0	0	0	0	0
Replacement	1B	8	0.304	0.304	0.73	5.57	0.13	0.17	0.350	38.77	0	0	0	0	0
Replacement	2B	100	0.304	0.304	9.16	69.64	0.13	0.17	0.350	38.77	0	0	0	0	0
Replacement	3B	7	0.304	0.304	0.64	4.87	0.13	0.17	0.350	38.77	0	0	0	0	0
Replacement	SS	75	0.304	0.304	6.87	52.23	0.13	0.17	0.350	38.77	0	0	0	0	0
Replacement	LF	7	0.304	0.304	0.64	4.87	0.13	0.17	0.350	38.77	0	0	0	0	0
Replacement	CF	7	0.304	0.304	0.64	4.87	0.13	0.17	0.350	38.77	0	0	0	0	0
Replacement	RF	8	0.304	0.304	0.73	5.57	0.13	0.17	0.350	38.77	0	0	0	0	0
Totals	-	5849	0.336	0.326	724.14	3942.23	0.18	0.18	0.509	40.06	23.22			-0.8	22.55
			lgR/G		9.43
			pythexp		2.28

Alright, so now let's compare these values with what we get with a, uh, static run estimator.

PLAYER	sOffWar	dOffWAR
Rivera ,Mike	0.67	0.51
Kendall, Jason	-0.05	-0.4
Nelson ,Brad	0.74	0.22
Fielder, Prince	4.59	5.04
Weeks, Rickie	2.16	3.03
Hall, Bill	1.19	1.39
Lamb, Mike	0.45	0.47
Hardy, J.J.	2.41	3.03
Braun, Ryan	4.44	4.8
Cameron, Mike	1.66	2.15
Hart, Corey	2.49	2.91
Gwynn, Tony	0.2	0.11
Duffy, Chris	0.19	0.09
			R^2=.9729

 

So we appear to get a pretty decent correlation here, with some players getting higher due to the dynamic part of the estimator and others getting lower. What does everybody else think of this method? Is it worth thinking about batting wins about replacement in dynamic terms? And this also brings about the question of whether or not we should use dynamic runs for fielding as well. Anyway, I'm hoping we can get a decent discussion about this, so that's my two cents.