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Share-Based Compensation - Narrative (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2018
Sep. 30, 2017
Sep. 30, 2016
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Pre-tax share-based compensation expense $ 38.5 $ 38.5 $ 40.5
Income tax benefit related to share-based compensation expense, Total 9.6 $ 12.3 $ 12.9
Unrecognized compensation cost related to share-based compensation awards, net of estimated forfeitures, Total $ 41.1    
Weighted average period for recognition of total unrecognized compensation cost 1 year 9 months 8 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) $ 35.29 $ 25.70 $ 21.28
Total intrinsic value of stock options exercised $ 71.0 $ 141.1 $ 21.9
Performance shares      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Vesting period 3 years    
Payout percentage 187.00% 10.00% 93.00%
Payout percentage in December 2016 for performance period ending September 30, 2016 200.00%    
Maximum potential shares to be delivered in payment under performance share awards (in shares) 145,000    
Weighted average grant date fair value of awards granted (in dollars per share) $ 219.04 $ 174.37 $ 87.64
Total fair value of shares vested $ 26.5 $ 0.9 $ 7.1
Shares granted in the period (in shares) 40,000    
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) $ 188.41 $ 138.32 $ 105.38
Total fair value of shares vested $ 7.2 $ 7.6 $ 7.0
Shares granted in the period (in shares) 47,000    
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) $ 183.76 $ 129.68 $ 98.79
Shares granted in the period (in shares) 7,000    
2012 Long Term Incentive Plan      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Shares authorized (in shares) 11,800,000    
Shares available for grant (in shares) 4,500,000    
2003 Directors Stock Incentive Plan      
Share-based Compensation Arrangement by Share-based Payment Award, Additional General Disclosures [Abstract]      
Shares authorized (in shares) 500,000    
Shares available for grant (in shares) 200,000