Stock-based Compensation - Additional Information (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 [Line Items]
Vesting period, minimum	3 years
Number of shares of common stock that may be issued (in shares)	1,000,000
Restricted Stock Awards [Abstract]
Dividend yield percent	0.00%	0.00%	0.00%
Stock Option Awards [Abstract]
Total unrecognized compensation costs	$ 10.9
Weighted average period for recognition of unrecognized compensation costs	1 year 9 months 18 days
Restricted Stock Awards
Restricted Stock Awards [Abstract]
Vested restricted stock withheld for tax withholding obligations (in shares)	28,731	34,922	35,514
Vested restricted stock withheld for tax withholding obligations, weighted average price (in dollars per share)	$ 79.23	$ 81.65	$ 63.83
Fair value, restricted stock	$ 7.6	$ 10.5	$ 8.9
Actual tax benefit realized	$ 2.9	$ 4.0	$ 3.3
Restricted Stock Awards \| Performance Vesting
Restricted Stock Awards [Abstract]
Granted (in shares)	99,260
Granted, weighted average grant date fair value (in dollars per share)	$ 80.72
Expiration date	Sep. 30, 2022
Restricted Stock Awards \| Time Vesting
Restricted Stock Awards [Abstract]
Granted (in shares)	49,340
Granted, weighted average grant date fair value (in dollars per share)	$ 77.14
Restricted Stock Awards \| Executive Officers and Key Employees \| Performance Vesting
Restricted Stock Awards [Abstract]
Granted, weighted average grant date fair value (in dollars per share)		$ 79.88	$ 58.45
Maximum amount of shares pursuant to restricted stock awards	200.00%
Number of shares issued for maximum performance payout (in shares)	527,820
Number of shares elected to be defer at target payout (in shares)	80,760
Restricted Stock Awards \| Executive Officers and Key Employees \| Time Vesting
Restricted Stock Awards [Abstract]
Granted (in shares)	37,580
Granted, weighted average grant date fair value (in dollars per share)	$ 76.66	76.60	63.05
Restricted Stock Awards \| Non Employee Directors \| Time Vesting
Restricted Stock Awards [Abstract]
Granted (in shares)	11,760
Granted, weighted average grant date fair value (in dollars per share)	$ 78.69	$ 63.20	$ 63.45

Disclosure of the aggregate tax benefit realized from the exercise of equity instruments during the annual period.

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Share-based Compensation Arrangement by Share-based Payment Award, Maximum Target Award, Percentage

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Share based compensation arrangement by share based payment award number of shares elected to be defer at target payout.

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Share-based Compensation Arrangement by Share-based Payment Award, Number Of Shares To Be Issued At Maximum Performance Target

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This element represents the number of vested shares withheld pursuant to elections by employees to satisfy tax withholding obligations.

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The weighted-average price of vested compensation awards withheld to satisfy tax withholding obligations.

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Amount of cost not yet recognized for nonvested award under share-based payment arrangement.

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Weighted-average period over which cost not yet recognized is expected to be recognized for award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

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Period over which grantee's right to exercise award under share-based payment arrangement is no longer contingent on satisfaction of service or performance condition, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. Includes, but is not limited to, combination of market, performance or service condition.

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The number of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

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The weighted average fair value at grant date for nonvested equity-based awards issued during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

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Fair value of share-based awards for which the grantee gained the right by satisfying service and performance requirements, to receive or retain shares or units, other instruments, or cash.

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Date the equity-based award expires, in CCYY-MM-DD format.

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The estimated dividend rate (a percentage of the share price) to be paid (expected dividends) to holders of the underlying shares over the option's term.

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Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

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Number of shares authorized for issuance under share-based payment arrangement.

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