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Stock-Based Compensation - Additional Information (Details) - USD ($) $ / shares in Units, $ in Millions | 1 Months Ended | 12 Months Ended |
--- | --- | --- | ---
Oct. 31, 2020 | Sep. 30, 2020 | Sep. 30, 2019 | Sep. 30, 2018 | Sep. 30, 2017
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |  |
Common stock reserved for issuance stock awards (in shares) |  | 5,771,194 |  |  |
Income tax benefit recognized for stock-based compensation |  | $ 3.6 | $ 4.9 | $ 5.8 |
Stock options |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |  |
Tenure of award (in years) |  | 3 years |  |  |
Share-based compensation arrangement by share-based payment award, vesting period |  | 10 years |  |  |
Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercises in Period, Intrinsic Value |  | $ 18.5 | 10.2 | 23.2 |
Employee Service Share-based Compensation, Tax Benefit from Exercise of Stock Options |  | 4.3 | $ 2.4 | $ 6.3 |
Unrecognized compensation expense |  | $ 2.6 |  |  |
Weighted-average period for unrecognized compensation expense to be recognized (in years) |  | 1 year 10 months 24 days |  |  |
Weighted-average per share fair values for stock option granted (in dollars per share) |  | $ 26.16 | $ 20.00 | $ 26.84 |
Nonvested Stock Awards [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |  |
Unrecognized compensation expense |  | $ 8.4 |  |  |
Weighted-average period for unrecognized compensation expense to be recognized (in years) |  | 1 year 10 months 24 days |  |  |
Fair value of shares vested |  | $ 18.6 | $ 12.3 | $ 13.2 |
Income tax benefit recognized for stock-based compensation |  | $ 3.1 | $ 2.1 | $ 3.0 |
Weighted-average fair value, nonvested performance shares |  | $ 79.44 | $ 72.66 | $ 69.15 | $ 55.22
Granted (in shares) |  | 183,725 | 278,175 | 163,225 |
Performance Shares [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |  |
Share-based compensation arrangement by share-based payment award, vesting period |  | 3 years |  |  |
Unrecognized compensation expense |  | $ 6.7 |  |  |
Weighted-average period for unrecognized compensation expense to be recognized (in years) |  | 1 year 9 months 18 days |  |  |
Share-based compensation arrangement by share-based payment award, vesting description |  | Performance share awards generally vest over a three-year service period following the grant date. Performance shares vest under two separate measurement criteria. The first type vest only if the Company’s total shareholder return (TSR) over the three year term of the awards compares favorably to that of a comparator group of companies. The second type vest only if the Company’s return on invested capital (ROIC) over the vesting period compares favorably to that of a comparator group of companies. |  |  |
Performance Shares [Member] | Subsequent Event |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |  |
Stock Issued During Period, Shares, Share-based Compensation, Net of Forfeitures | 68,125 |  |  |  |
Performance Shares [Member] | Shareholder Return [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |  |
Weighted-average fair value, nonvested performance shares |  | $ 137.74 | $ 85.89 | $ 112.30 |
Nonvested Performance Share Awards [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |  |
Fair value of shares vested |  | $ 6.9 | $ 5.8 | $ 7.6 |
Income tax benefit recognized for stock-based compensation |  | $ 0.2 | $ 1.4 | $ 2.1 |
Period over which shareholder return compares favorably to that of a competitor group of companies for purposes of calculating executive performance shares earned (in years) |  | 3 years |  |  |
Potential payouts, low end of range (as a percent) |  | 0.00% |  |  |
Potential payouts, high end of range (as a percent) |  | 200.00% |  |  |
Weighted-average fair value, nonvested performance shares |  | $ 89.54 | $ 84.10 | $ 89.11 | $ 60.71
Granted (in shares) |  | 55,325 | 73,950 | 57,625 |
Nonvested Performance Share Awards [Member] | Shareholder Return [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percent |  | 111.00% | 126.00% | 200.00% |
Nonvested Performance Share Awards [Member] | Return on Invested Capital [Member] |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percent |  | 200.00% | 200.00% | 191.00% |
Stock Appreciation Rights (SARs) |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercises in Period, Intrinsic Value |  | $ 0.7 | $ 0.6 | $ 3.8 |
Granted (in shares) |  | 14,875 | 18,250 | 11,650 |
Restricted Stock Units (RSUs) |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |  |
Fair value of shares vested |  | $ 0.8 | $ 0.4 | $ 0.4 |
Granted (in shares) |  | 7,925 | 8,350 | 8,125 |

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