What team combined high relative strikeouts with high relative runs scored more than any other?

Maybe the 1927 Yankees. They score 35% more runs than average while having 45% more strikeouts than average. So they had 1.35 runs for every run the average team scored and the strikeout ratio was 1.45.

 

Their harmonic mean would be 2*1.35*1.45/(1.35 + 1.45) = 1.40

 

That is the highest I found for all teams from 1920-2020 (the 27 Yanks were 3rd in relative strikeouts and 9th in relative runs over this time period). Data came from the Lee Sinins Complete Baseball Encyclopedia.

 

Here is the top 10:

 

Team	YEAR	Rel R	Rel SO	Harmonic
Yankees	1927	1.35	1.45	1.40
Yankees	1928	1.38	1.24	1.31
Cubs	1931	1.26	1.33	1.29
Yankees	1920	1.16	1.42	1.28
Yankees	1926	1.20	1.36	1.27
A's	1933	1.26	1.28	1.27
Yankees	1921	1.22	1.30	1.26
Yankees	1930	1.43	1.13	1.26
Yankees	1936	1.35	1.17	1.25
Cubs	1929	1.21	1.29	1.25

How does Ohtani's all-round batting-pitching season compare to some other great seasons?

A SABR friend, Tom Thayer, raised this issue. So I calculated the harmonic mean of batting WAR (BWAR) and pitching WAR (PWAR) for a few different players (some of whom were suggested by Jessica Brand, Emory Brinkman and Adam Darowski).

 

Harmonic = (2*BWAR*PWAR)/(BWAR  + PWAR)

 

It is like the Bill James Speed Score that uses HRs ans SBs. 

The table below has the "Batting-Pitching Score" for each guy as Harmonic. For the guys whose teams played fewer than 162 games, I gave  them a pro-rated score (see Per 162). Ohtani compares very well. Anyone ahead of him was more than 90 years ago.

This is not a top 10 or leader list. I can't think of anyone else since 1945 who might do well. But if anyone has any suggestions, please let me know.

 

Player	Year	BWAR	PWAR	Harmonic	Team G	Per 162
Whitney	1883	2.1	11.4	3.55	98	5.86
Caruthers	1886	3.9	7.6	5.15	139	6.01
Foutz	1886	1.3	9.7	2.29	139	2.67
Terry	1890	1.4	4.9	2.18	129	2.73
Stivetts	1891	1.4	7.7	2.37	139	2.76
Ruth	1918	4.7	2.3	3.09	126	3.97
Ruth	1919	9.1	0.8	1.47	138	1.73
Rogan	1925	1.9	7.4	3.02	84	5.83
Dihigo	1929	3.2	1.6	2.13	62	5.57
Ferrell	1935	2.4	8.2	3.71	154	3.91
Ohtani	2021	4.9	4.1	4.46	162	4.46