The 1974 American League probably came the closet. The Orioles had the best record at 91-71 (.562), the Angels the worst of 68-94 (.420), and a whole lot of clustering around .500, especially out west. The 1983 NL was almost identical, with the Dodgers through the Mets occupying almost the exact same numbers, and the 1968 NL was also pretty clustered, especially beyond the Cardinals.
That 1968 NL “race” might be a pretty good indication of how the league table format, versus the divisional format, really fails the business in September once the one and only pennant race is already wrapped up: from an average attendance of 19,182 the week of June 19-25, patronage cratered to an average of 7,775 for the week of September 18-24.
The 1909 National League probably had the highest STDEV. The third place Giants were 18.5 games behind, fourth-place Reds were 33.5 behind, and three different teams were 55+ games behind, with the Doves (yes, the Doves) bringing up the rear at 65.5 games behind the first place Pirates, who nevertheless still needed seven games to dispatch the Tigers in that Series.