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Stock-Based Compensation Plans - Schedule of Performance Award Activity (Details) - Nonvested Stock Units - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Number of Shares      
Grant date fair values of shares vested $ 11.2 $ 6.5 $ 4.6
Granted, weighted average grant date fair value (in usd per share) $ 35.32 $ 22.33 $ 22.17