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