Share-Based Compensation - Stock Option Plan (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
Share-Based Payment Arrangement [Abstract]
Share-based compensation arrangement by share-based payment award, number of shares authorized (in shares)	3,000,000
Stock options authorized (in shares)	1,387,697	1,569,798
Weighted average grant date fair value, granted (in dollar per share)	$ 22.82	$ 19.83	$ 0.00
Employee service share-based compensation, non vested awards, total compensation cost not yet recognized, stock options	$ 10.6
Employee service share-based compensation, non vested awards, total compensation cost not yet recognized, period for recognition	4 years 10 months 2 days
Share-based compensation arrangement by share-based payment award, options, exercises in period, total intrinsic value	$ 39.0	$ 11.7	$ 4.2

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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.

+ References

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-Publisher FASB
-Name Accounting Standards Codification
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- Definition

Amount of cost to be recognized for option under share-based payment arrangement.

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- Definition

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

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The difference between the maximum number of shares (or other type of equity) authorized for issuance under the plan (including the effects of amendments and adjustments), and the sum of: 1) the number of shares (or other type of equity) already issued upon exercise of options or other equity-based awards under the plan; and 2) shares (or other type of equity) reserved for issuance on granting of outstanding awards, net of cancellations and forfeitures, if applicable.

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Amount of accumulated difference between fair value of underlying shares on dates of exercise and exercise price on options exercised (or share units converted) into shares.

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The weighted average grant-date fair value of options granted during the reporting period as calculated by applying the disclosed option pricing methodology.

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