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Stock-based Compensation - Schedule of Compensation Cost for Share-based Payment (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2018
Sep. 30, 2017
Sep. 30, 2016
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Document Fiscal Year Focus 2018    
Before tax stock-based compensation expense $ 10,258 $ 8,159 $ 7,959
Tax benefit (2,622) (2,917) (2,832)
After tax stock-based compensation expense 7,636 5,242 5,127
Stock Options      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Before tax stock-based compensation expense 225 274 534
Stock options      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Before tax stock-based compensation expense $ 10,033 $ 7,885 $ 7,425