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Share-Based Compensation - Narrative (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Pre-tax share-based compensation expense $ 43.1 $ 38.5 $ 38.5
Income tax benefit related to share-based compensation expense, Total 6.9 $ 9.6 $ 12.3
Unrecognized compensation cost related to share-based compensation awards, net of estimated forfeitures, Total $ 43.1    
Weighted average period for recognition of total unrecognized compensation cost 1 year 10 months 24 days    
Stock options      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Expiration period 10 years    
Vesting period 3 years    
Per share weighted average fair value of stock options granted (in dollars per share) $ 32.46 $ 35.29 $ 25.70
Total intrinsic value of stock options exercised $ 35.8 $ 71.0 $ 141.1
Performance shares      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Vesting period 3 years    
Payout percentage 200.00% 187.00% 10.00%
Payout percentage in December 2016 for performance period ending September 30, 2016 77.00%    
Maximum potential shares to be delivered in payment under performance share awards (in shares) 28,000    
Weighted average grant date fair value of awards granted (in dollars per share) $ 155.04 $ 219.04 $ 174.37
Total fair value of shares vested $ 25.8 $ 26.5 $ 0.9
Shares granted in the period (in shares) 57,000    
Performance shares | Minimum      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Payout percentage 0.00%    
Performance shares | Maximum      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Payout percentage 200.00%    
Restricted stock and restricted stock units      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Weighted average grant date fair value of awards granted (in dollars per share) $ 170.75 $ 188.41 $ 138.32
Total fair value of shares vested $ 7.8 $ 7.2 $ 7.6
Shares granted in the period (in shares) 48,000    
Restricted stock and restricted stock units | Minimum      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Vesting period 1 year    
Restricted stock and restricted stock units | Maximum      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Vesting period 4 years    
Unrestricted stock      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Weighted average grant date fair value of awards granted (in dollars per share) $ 182.39 $ 183.76 $ 129.68
Shares granted in the period (in shares) 6,000    
2012 Long Term Incentive Plan      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Shares authorized (up to) (in shares) 11,800,000    
Shares available for grant (in shares) 3,400,000    
2003 Directors Stock Incentive Plan      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Shares authorized (up to) (in shares) 500,000    
Shares available for grant (in shares) 200,000