When Do 10 Runs Not Equal a Win? Baseball Databank Data Dump 2.2

by Matt Klaassen on Feb 16, 2011 2:30 PM EST in Sabermetric Primers

I tried to start this baseball-databank data dump series for myself last season, but it didn't take. I'm hoping to have better luck this season with shorter, and, uh, "dumpier" posts. So, for your breathless perusal (drum roll please)... historical runs-per-win conversions!

As common sense would tell you (and as you might infer from a basic of baseball history combined with the plot above), the more offense-oriented the run environment, the more runs it take to lead to a "win." I won't get into all the details here, as it's done well elsewhere (for example, at the Saber Library). There are different runs-per-win estimators ranging from from simply league runs allowed per game times two to PythagenPat. For the graph above and the data below, I've used two estimators: Tom Tango's relatively simple (lgRA*1.5)+3, and Patriot's more sophisticated PythagenPat: (lgRPG^(1-z)) * 2, where z is between 0.27 and 0.29 (last season I used 0.287, but Patriot has since told me that 0.28 has been found to "work" the best, historically). PythagenPat is considered to be the most accurate, but as you can see above, Tango's simple conversion tracks it extremely closely, with a bigger difference at in more "extreme" environments.

But is 10 runs still a win? Taking baseball as a whole, yes, as you'll see. Even if I separate the 2010 leagues, the NL (where runs are more scarce) runs-to-wins overall conversion is still closer to 10 than to 9. Let's take a look at "modern times" (1947 to the present).

Both estimators see the last season a win was closer to nine runs than 10 was 1992. However, 2010 was closest since that season, at about 9.6 runs per win according to both estimators. It wouldn't take much of a drop to put it closer to nine than 10. In any case, to get a sense for how much of a difference between 9.6 and 10 runs per win makes, take a player who is 50 runs above average offensively. In a 10 rpw environment, that's worth ive wins. In a 9.6 rpw environment, that's worth 5.2 wins. I suppose it depends on how much accuracy you're after... Enough talk, here is the table (thrilling, isn't it?):

Runs per Win, 1871-2010
*Season*	*RPG*	*TangoRPW*	*PatRPW*
2010	4.4284	9.64255	9.617611029
2009	4.6629	9.99428	9.981617827
2008	4.6881	10.03215	10.02049645
2007	4.8335	10.25025	10.24330591
2006	4.9099	10.3648	10.35957058
2005	4.6476	9.97134	9.958039724
2004	4.8482	10.27234	10.26576675
2003	4.7722	10.15826	10.14955663
2002	4.6609	9.99133	9.978588219
2001	4.8234	10.23506	10.22784829
2000	5.197	10.79544	10.79222813
1999	5.1426	10.71391	10.71084462
1998	4.8213	10.23202	10.22475288
1997	4.8064	10.20958	10.20190305
1996	5.0661	10.59908	10.59579697
1995	4.8842	10.32624	10.32048931
1994	4.9593	10.43894	10.43455099
1993	4.6356	9.95346	9.939643803
1992	4.1256	9.18836	9.139453187
1991	4.3194	9.47913	9.446649243
1990	4.2933	9.43991	9.405442001
1989	4.1534	9.23008	9.183776802
1988	4.1526	9.22895	9.182576395
1987	4.7624	10.14366	10.13464762
1986	4.4302	9.64531	9.620479487
1985	4.3534	9.53013	9.500131794
1984	4.2777	9.41654	9.380856641
1983	4.3328	9.49926	9.467772054
1982	4.303	9.45448	9.420763484
1981	3.9977	8.99659	8.934643423
1980	4.2914	9.43706	9.402442737
1979	4.4937	9.74057	9.719583169
1978	4.1406	9.21091	9.163423382
1977	4.4841	9.72621	9.704666477
1976	3.9921	8.9882	8.925640812
1975	4.2234	9.33517	9.295055739
1974	4.1329	9.19939	9.151176325
1973	4.2256	9.33843	9.298496753
1972	3.6877	8.53151	8.430114661
1971	3.9019	8.85283	8.779901481
1970	4.3582	9.53726	9.507593059
1969	4.0885	9.13273	9.080224319
1968	3.42	8.12998	7.98489122
1967	3.7654	8.64806	8.557632809
1966	3.9974	8.99607	8.934087117
1965	3.9926	8.98893	8.926421947
1964	4.0536	9.08044	9.024420389
1963	3.9519	8.92778	8.86070202
1962	4.4871	9.73068	9.70931397
1961	4.5761	9.86421	9.847615261
1960	4.3226	9.48389	9.451649614
1959	4.4197	9.62956	9.604061418
1958	4.3176	9.47642	9.443812655
1957	4.284	9.42606	9.390875979
1956	4.4933	9.73992	9.718900369
1955	4.526	9.78895	9.769753577
1954	4.4039	9.60581	9.579272037
1953	4.6675	10.00123	9.988749833
1952	4.1944	9.29161	9.24899382
1951	4.5664	9.84959	9.832512944
1950	4.9205	10.38078	10.37575626
1949	4.6644	9.99666	9.984058775
1948	4.642	9.96298	9.949431313
1947	4.4217	9.63262	9.607252457
1946	4.0455	9.06829	9.011436281
1945	4.2057	9.30856	9.266920677
1944	4.1788	9.26817	9.224167423
1943	3.8844	8.82661	8.751553706
1942	4.0982	9.14732	9.095777231
1941	4.5277	9.79156	9.772458909
1940	4.7221	10.08314	10.07275964
1939	4.8946	10.34193	10.33640145
1938	4.9724	10.45861	10.45440785
1937	4.9582	10.4373	10.43290055
1936	5.2509	10.87634	10.87275745
1935	4.9479	10.42191	10.41735229
1934	4.9715	10.4573	10.45309002
1933	4.5127	9.76901	9.749085092
1932	4.9238	10.38566	10.38068666
1931	4.8674	10.30107	10.29495503
1930	5.6354	11.45309	11.4402923
1929	5.2526	10.87884	10.87524025
1928	4.7485	10.12274	10.11327367
1927	4.8024	10.20356	10.19576453
1926	4.7034	10.05516	10.04409445
1925	5.1894	10.78404	10.78086417
1924	4.7937	10.19057	10.18252189
1923	4.8389	10.2584	10.25159603
1922	4.9042	10.35625	10.35091208
1921	4.8766	10.31489	10.30897333
1920	4.3535	9.53018	9.500190213
1919	3.8842	8.82628	8.751197837
1918	3.6111	8.41664	8.303691707
1917	3.577	8.36553	8.247201123
1916	3.5522	8.32832	8.205985691
1915	3.839	8.75846	8.67773386
1914	3.9001	8.85017	8.777028191
1913	4.0691	9.10366	9.049217854
1912	4.5802	9.87032	9.853922514
1911	4.5523	9.82839	9.810588717
1910	3.8585	8.78778	8.709530656
1909	3.5682	8.35223	8.23248619
1908	3.3991	8.09865	7.949753065
1907	3.5945	8.39175	8.276208905
1906	3.6832	8.52476	8.422707096
1905	3.9483	8.9225	8.855020902
1904	3.8072	8.71085	8.626015118
1903	4.5396	9.80945	9.790987214
1902	4.5168	9.77514	9.755439462
1901	5.0976	10.64642	10.64328835
1900	5.3851	11.07767	11.07214784
1899	5.4791	11.21859	11.21088496
1898	5.1497	10.72448	10.72140392
1897	6.1339	12.20081	12.16019681
1896	6.2487	12.37309	12.32371431
1895	6.8593	13.28892	13.17929756
1894	7.6555	14.48323	14.26369485
1893	6.696	13.04394	12.95259388
1892	5.2458	10.86867	10.86512532
1891	5.8506	11.77591	11.75320437
1890	6.1883	12.28251	12.23784665
1889	6.1458	12.21868	12.17719232
1888	4.9631	10.44468	10.44035115
1887	6.5734	12.86007	12.78143191
1886	5.6707	11.50599	11.49179173
1885	5.3197	10.9796	10.97519937
1884	5.568	11.35201	11.34162992
1883	5.857	11.78552	11.76247384
1882	5.4041	11.10612	11.10020934
1881	5.1499	10.72481	10.7217299
1880	4.7616	10.14245	10.13341609
1879	5.2926	10.93885	10.93481193
1878	5.1552	10.73285	10.72976579
1877	5.6649	11.49738	11.48341183
1876	5.8147	11.72211	11.7012852
1875	6.1537	12.23061	12.18854209
1874	7.4844	14.22663	14.03348219
1873	8.9883	16.48243	16.01101468
1872	9.284	16.92598	16.38854802
1871	10.636	18.954	18.07390475

Tweet Comment 17 comments | 3 recs |

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Comments

I love these posts so much

by Lucas Apostoleris on Feb 16, 2011 2:38 PM EST reply actions

Great stuff, Matt.

Baseball is my preferred sport. It should be yours, too.
I'm a columnist for Beyond the Box Score, an SB Nation blog.
Oh, I'm on Twitter, too.

by Satchel Price on Feb 16, 2011 2:39 PM EST via mobile reply actions

Wow. 1871: 18 runs = 1 win.

Kind of wish they had TV back then.

A DRaysBay writer from Cubs Stats and Twitter @BradleyWoodrum

by BWoodrum on Feb 16, 2011 2:46 PM EST reply actions

I suspect the awful fielding would've turned you off.

by garik16 on Feb 16, 2011 3:32 PM EST up reply actions 3 recs

rec'd

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by PWHjort on Feb 16, 2011 4:22 PM EST up reply actions

Wow. Very cool.

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by Kyle Boddy on Feb 16, 2011 4:05 PM EST reply actions

basic question

What do we mean by runs per win here? Is it the impact of 10 (or whatever) runs on a set number of games? IOW, is this the number of runs it takes to convert a loss to a win for 162 games? Or is it incremental? If you add ten (or whatever) runs to the total number of runs (or ten less to runs allowed), and add an additional game, it becomes a win?

by studes on Feb 16, 2011 4:19 PM EST reply actions

I know the answer... just a minute... WOULD YOU STOP GRILLING ME?!?!?!?!

Honestly, though (assuming you aren’t trying to expose me for the charlatan I so obviously am), I’m a bit confused about this, too. I think it’s supposed to be how many more runs a team would need to win one more game (on average) over a set number of games. What I’m a bit fuzzy on (and I think this is your question, studes) is how that changes/is adjusted for 162 or 154 games or whatever.

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by Matt Klaassen on Feb 16, 2011 9:45 PM EST up reply actions

Although the RPW is the common form, it might be easier to think about in terms of the reciprocal, which you could call wins per run. It’s the slope of the W% function with respect to run differential. By differentiating, it’s the instantaneous slope—at the exact point in question (run ratio of 1).

Over any number of games, run differential divided by RPW will approximately be equal to marginal wins (over .500). The tricky part is that as run differential improves, it takes more marginal runs each time to produce a marginal win. That is the reason for having a win estimator like Pythagenpat rather than just using a fixed RPW, and it’s something that this formula doesn’t capture—it only gives you the instantaneous change at R = RA.

by Walksaber on Feb 16, 2011 11:22 PM EST up reply actions

Which formula

(RPG^)2?

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by Matt Klaassen on Feb 17, 2011 12:24 AM EST up reply actions

sorry, I mean

(RPG ^ (1-z)) x 2?

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by Matt Klaassen on Feb 17, 2011 12:24 AM EST up reply actions

Yes, that one, or any of them (Tango, Palmer, any others out there). They all measure the number of runs per win at that point.

In reality, it takes more runs to buy the second win, more still to buy the third win, etc. Of course, the fixed RPW formula will give results that match Pythagenpat well for real teams, since they don’t exhibit extreme run differentials.

by Walksaber on Feb 17, 2011 5:48 PM EST up reply actions