They won 4 straight world series. So you might be wondering why I don't write about the 1949-53 Yankees, who won 5 in a row. Those latter Yankees seem pretty dominiating. But I don't think in any 4 year period any team has done what those earlier Yankees did. The 1936-39 team had winning percentages of .667, .662, .651 and .702. Their only losing month in the 4 years was Sept. 1938 when they went 13-14.
First, they lead their league in ERA, HRs, Runs, fewest runs allowed and SLG in all 4 years. And, if I recall correctly, their run differential of 411 in 1939 is the highest of all time (967-556). The following table only amplifies their regular season dominance (the lines are in order of the years starting with 1936).
They spent 530 days in first place. That was about 80% of the time. The Indians were a half game ahead of the Yankees on July 12, 1938. But neither team had played 77 games yet. So no team besides the Yankees was in first place during the 2nd half of any of these 4 seasons. Where I have "Games left to play on clinch date," I simply added wins and losses and then subtracted from 154. I did not try to take ties or actual games left into account. So it is an approximation. But the lowest total was 12. That was the closest "race."
UPDATE: (April 16) I also figured out what the closest any team got to the Yankees was in each year between Sept. 1 and the date they clinched. Here are those games behind numbers in order of the years: 16-9-13-11.5. So between Sept. 1, 1936 and the date they clinched, the fewest games behind for the 2nd place team was 16. And in all 4 years, the closest any team came to them between Sept. 1 and the clinch date was 9 games, in 1937.
Then notice that no team ever finished closer than 9.5 games with the average games ahead being 14.75. Also notice that going into Sept., the closest anyone got was 11 games. In 1938, they went from being a half game behind on July 12 to being up 14 games up by Aug 31. In about 7 weeks, they gained 14 games.
You might be wondering if they kept up this dominance in the World Series. After all, they were playing the best the National League could throw at them. The table below summarizes what happened.
Notice that their edges in SLG and OBP are much larger than their edge in AVG (maybe they had a sabermetrician working for them back then). OBP just used walks, hits and atbats. They had 23 more walks while having huge leads in HRs and TB. Their winning pct against the NL champs was .842 while never losing more than 2 games in any one series. Their Pythagorean winning pct was .825 (runs scored squared divided by the sum of runs scored squared + runs allowed squared).
From other research, I have found that winning pct is about 1.21*(OPS differential) + .500. OPS is OBP + SLG. The Yankees had a .760 OPS while their opponents had .590. That would give the Yankees a pct of .706, not as dominat as what actually happened but still pretty impressive considering the competition.