Stock-Based Compensation - Restricted Stock Unit Activity - Tabular Disclosure (Details) - Restricted Stock Units (RSUs) - $ / shares	12 Months Ended
Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Number of Shares [Roll Forward]
Outstanding at beginning of period (in shares)	538,238
Restricted stocks granted (in shares)	590,066	249,685	349,930
Vested (in shares)	(267,834)
Forfeited (in shares)	(141,516)
Outstanding at end of period (in shares)	718,954	538,238
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Additional Disclosures [Abstract]
Outstanding at beginning of period (in dollars per share)	$ 71.99
Granted (in dollars per share)	57.22
Vested (in dollars per share)	55.86
Forfeited (in dollars per share)	72.04
Outstanding at end of period (in dollars per share)	$ 67.40	$ 71.99

No definition available.

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- Definition

The number of equity-based payment instruments, excluding stock (or unit) options, that were forfeited during the reporting period.

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Weighted average fair value as of the grant date of equity-based award plans other than stock (unit) option plans that were not exercised or put into effect as a result of the occurrence of a terminating event.

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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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- Definition

The number of non-vested equity-based payment instruments, excluding stock (or unit) options, that validly exist and are outstanding as of the balance sheet date.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(i)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(ii)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

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- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

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No definition available.

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- Definition

Per share or unit weighted-average fair value of nonvested award under share-based payment arrangement. Excludes share and unit options.

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The number of equity-based payment instruments, excluding stock (or unit) options, that vested during the reporting period.

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The weighted average fair value as of grant date pertaining to an equity-based award plan other than a stock (or unit) option plan for which the grantee gained the right during the reporting period, by satisfying service and performance requirements, to receive or retain shares or units, other instruments, or cash in accordance with the terms of the arrangement.

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