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Share-Based Compensation - Narrative (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Pre-tax share-based compensation expense $ 51.7 $ 46.1 $ 43.1
Income tax benefit related to share-based compensation expense 8.6 $ 7.7 $ 6.9
Unrecognized compensation cost related to share-based compensation awards, net of estimated forfeitures $ 69.0    
Weighted average period for recognition of total unrecognized compensation cost 2 years    
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) $ 55.50 $ 35.80 $ 32.46
Total intrinsic value of stock options exercised $ 108.4 $ 151.6 $ 35.8
Performance shares      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Vesting period 3 years    
Percent payout 93.00% 77.00% 200.00%
Payout percentage in December 2020 for performance period ending September 30, 2020 144.00%    
Maximum potential shares to be delivered in payment under performance share awards (in shares) 68,000    
Weighted average grant date fair value of awards granted (in dollars per share) $ 298.10 $ 265.04 $ 155.04
Total fair value of shares vested $ 7.4 $ 5.6 $ 25.8
Shares granted in the period (in shares) 44,000    
Performance shares | Minimum      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Percent payout 50.00% 0.00% 0.00%
Performance shares | Maximum      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Percent payout 200.00% 200.00% 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) $ 265.32 $ 200.36 $ 170.75
Total fair value of shares vested $ 10.4 $ 8.7 $ 7.8
Shares granted in the period (in shares) 254,000    
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) $ 228.80 $ 171.51 $ 182.39
Shares granted in the period (in shares) 5,600    
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  
Shares available for grant (in shares) 11,400,000    
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