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Stock-Based Compensation - Schedule of Stock-Based Compensation Expense (Income) (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Equity-based compensation plans      
Stock-based compensation expense $ 29.8 $ 30.2 $ 30.0
Income tax benefit recognized for stock-based compensation (4.4) (3.6) (4.9)
Stock-based compensation cost, net of tax 25.4 26.6 25.1
Stock options      
Equity-based compensation plans      
Stock-based compensation expense 1.8 6.8 6.9
Nonvested Stock Awards [Member]      
Equity-based compensation plans      
Stock-based compensation expense 19.3 15.8 15.0
Income tax benefit recognized for stock-based compensation (2.0) (3.1) (2.1)
Performance Shares [Member]      
Equity-based compensation plans      
Stock-based compensation expense 6.1 6.7 7.1
Stock Appreciation Rights (SARs)      
Equity-based compensation plans      
Stock-based compensation expense 1.1 0.2 0.4
Restricted Stock Units (RSUs)      
Equity-based compensation plans      
Stock-based compensation expense $ 1.5 $ 0.7 $ 0.6