Here is a chart showing per game Red Sox attendance figures from 2011 through 1901, starting at the left in 2011 and going to the right down (literally and graphically) to 1901, using data found on Baseball-Reference:
A few things to notice: attendance spiked by 93,000, just over 1,000 fans per game, in 1912 when the Sox moved from the Huntington Avenue Baseball Grounds to Fenway Park. But, the team’s record went from 78-75 to 105-47 from 1911 to 1912. Attendance bottomed at 2,366 per game in 1932, the last year of four that the Sox played in Fenway and in Braves Field, and had a 43-111 record. The bottom for a Fenway-only year is 2,945 per game in 1923, for a 61-91 team. In 1986, attendance jumped to 26,514, but was still below attendance levels in every year since; the post-’86 low is 27,747 in 1994.
Attendance soared from 7,741 per game in 1945 to 18,166 per game in ’46, after never getting to even 10,000 from 1901 through 1945. It similarly doubled from 1966 (10,014 per game for 811,172 total, the last year below 1 million) to 1967, 21,331 per game for 1,727,832 total.