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Stock-based Compensation - Fair Value Assumptions (Details) - $ / shares
12 Months Ended
Sep. 30, 2018
Sep. 30, 2017
Sep. 30, 2016
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]      
Expected volatility (minimum) 21.10% 32.60% 29.90%
Expected volatility (maximum) 61.20% 66.00% 151.20%
Risk-free interest rate 1.81% 1.30% 1.21%
Dividend yield 0.00% 0.00% 0.00%
Grant-date stock price $ 20.50 $ 12.51 $ 14.24