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Share-Based Compensation - Narrative (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2020
Sep. 30, 2019
Sep. 30, 2018
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Pre-tax share-based compensation expense $ 46.1 $ 43.1 $ 38.5
Income tax benefit related to share-based compensation expense 7.7 $ 6.9 $ 9.6
Unrecognized compensation cost related to share-based compensation awards, net of estimated forfeitures $ 51.2    
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) $ 35.80 $ 32.46 $ 35.29
Total intrinsic value of stock options exercised $ 151.6 $ 35.8 $ 71.0
Performance shares      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Vesting period 3 years    
Percent payout 77.00% 200.00% 187.00%
Payout percentage in December 2020 for performance period ending September 30, 2020 93.00%    
Maximum potential shares to be delivered in payment under performance share awards (in shares) 32,000    
Weighted average grant date fair value of awards granted (in dollars per share) $ 265.04 $ 155.04 $ 219.04
Total fair value of shares vested $ 5.6 $ 25.8 $ 26.5
Shares granted in the period (in shares) 36,000    
Performance shares | Minimum      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Percent payout 0.00%    
Performance shares | Maximum      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Percent payout 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) $ 200.36 $ 170.75 $ 188.41
Total fair value of shares vested $ 8.7 $ 7.8 $ 7.2
Shares granted in the period (in shares) 71,000    
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 5 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) $ 171.51 $ 182.39 $ 183.76
Shares granted in the period (in shares) 6,900    
2020 Long Term Incentive Plan      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Shares authorized (up to) (in shares) 13,000,000.0    
Shares available for grant (in shares) 12,900,000    
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