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Stock-Based Compensation - Fair Value Assumptions (Details) - $ / shares
12 Months Ended
Sep. 30, 2020
Sep. 30, 2019
Sep. 30, 2018
Share-based Payment Arrangement [Abstract]      
Expected volatility, minimum 21.20% 21.00% 21.10%
Expected volatility, maximum 54.80% 57.10% 61.20%
Risk-free interest rate 1.61% 2.92% 1.81%
Dividend yield 0.00% 0.00% 0.00%
Grant-date stock price (in dollars per share) $ 15.62 $ 9.82 $ 20.50