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Stock-Based Compensation - Fair Value Assumptions (Details) - $ / shares
12 Months Ended
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Share-based Payment Arrangement [Abstract]      
Expected volatility (minimum) 21.00% 21.10% 32.60%
Expected volatility (maximum) 57.10% 61.20% 66.00%
Risk-free interest rate 2.92% 1.81% 1.30%
Dividend yield 0.00% 0.00% 0.00%
Grant-date stock price (in dollars per share) $ 9.82 $ 20.50 $ 12.51