Comparison of runs-to-wins converters against actual data

By Tangotiger

All team data from 1919-2000 was "binned" into one of 25 bins (5 classes of RS+RA x 5 classes of RS-RA).

• Quality: within each bin, the teams were sorted by quality classes, RS-RA, from 1 (best) to 5 (worst)
• ENV: teams were sorted by run environment of RS+RA, and put in each class from 1 (low scoring environment) to 5 (high scoring environment)
• RS: Runs scored
• RA: Runs allowed
• Actual win%: their actual winning record
• Tango win%: their expected winning record based on the Tango Distribution (using .852 as the control value)
• ActualExp: custom exponent to match the actual win%
• TangoExp: custom exponent to match the Tango win%
• ClayExp: Pythagaport
• PatdavidExp: custom exponent = RPG ^ .28
• Actual Bestfit: best-fit x value in RPG ^ x to match the actual win%
• Tango Bestfit: best-fit x value in RPG ^ x to match the Tango win%

The closer the run differential is to zero, the higher the best-fit "x" value is to .29. The higher the run differential, the more the best-fit value approaches .27. Since as the run differential approaches zero, it doesn't matter what value you use (there's little difference in the exponent being 1.03 ^ .29 or 1.03 ^ .27), then I would lean towards minimizing the win% values from the extreme teams just as much as the middle teams. A best-fit value of .28 will do that.

 

Quality	ENV	RSG	RAG	Actual Win%	Tango win%	ActualExp	TangoExp	ClayExp	PatdavidExp (.28)	ActualBestFit	TangoBestFit
1	1	3.96	3.13	0.5906	0.5983	1.56	1.7	1.73	1.73	0.228	0.271
1	2	4.58	3.44	0.6245	0.6246	1.76	1.77	1.81	1.79	0.273	0.273
1	3	4.99	3.83	0.6214	0.6187	1.87	1.82	1.87	1.84	0.286	0.276
1	4	5.63	4.18	0.6373	0.6367	1.88	1.88	1.94	1.9	0.278	0.276
1	5	6.36	4.72	0.6384	0.6413	1.91	1.95	2.02	1.96	0.268	0.277
2	1	3.79	3.39	0.5499	0.5473	1.8	1.71	1.73	1.74	0.298	0.271
2	2	4.28	3.68	0.5671	0.5666	1.78	1.77	1.8	1.79	0.278	0.274
2	3	4.74	4.11	0.5678	0.5653	1.9	1.82	1.87	1.84	0.293	0.276
2	4	5.3	4.54	0.5754	0.5723	1.97	1.88	1.94	1.9	0.296	0.277
2	5	5.92	5.05	0.5724	0.5771	1.82	1.94	2.01	1.96	0.251	0.278
4	1	3.33	3.94	0.4275	0.4284	1.73	1.71	1.74	1.74	0.278	0.272
4	2	3.74	4.28	0.4378	0.4411	1.87	1.77	1.81	1.79	0.3	0.274
4	3	4.11	4.75	0.4328	0.4344	1.87	1.83	1.87	1.84	0.287	0.276
4	4	4.55	5.28	0.4257	0.4301	2	1.88	1.94	1.9	0.304	0.277
4	5	4.98	5.94	0.4191	0.4158	1.86	1.94	2.01	1.95	0.26	0.277
5	1	3.09	4.23	0.376	0.3686	1.61	1.72	1.75	1.75	0.24	0.271
5	2	3.48	4.55	0.3786	0.3834	1.85	1.77	1.81	1.79	0.294	0.274
5	3	3.75	5.12	0.3558	0.3617	1.9	1.82	1.87	1.84	0.295	0.275
5	4	4.21	5.7	0.3608	0.3613	1.89	1.89	1.94	1.9	0.279	0.277
5	5	4.68	6.39	0.3492	0.3527	1.99	1.95	2.02	1.96	0.287	0.277