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Stock-Based Compensation - Schedule of Stock Option Activity (Details) - $ / shares
 12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Options      
Options outstanding, beginning of year (in shares) 1,083,402 1,328,390 1,268,984
Options granted (in shares)   301,025 372,450
Options forfeited (in shares) (8,065) (40,965) (24,175)
Options expired (in shares) (3,999) (5,869) (8,721)
Options exercised (in shares) (599,662) (499,179) (280,148)
Options outstanding, end of year (in shares) 471,676 1,083,402 1,328,390
Options exercisable, end of year (in shares) 251,049 537,241 709,826
Weighted-Average Exercise Price      
Options outstanding, beginning of year (in dollars per share) $ 74.38 $ 62.62 $ 57.03
Options granted (in dollars per share)   90.28 66.09
Options forfeited (in dollars per share) 81.40 79.00 72.88
Options expired (in dollars per share) 86.59 84.25 76.92
Options exercised (in dollars per share) 71.38 52.18 40.62
Options outstanding, end of year (in dollars per share) 77.96 74.38 62.62
Options exercisable, end of year (in dollars per share) $ 74.73 $ 68.16 $ 55.11