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Share-Based Compensation (Details) - USD ($)	12 Months Ended
Share-Based Compensation (Details) - USD ($)	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Share-Based Compensation
Share-Based Payment Arrangement, Expensed and Capitalized, Amount	$ 180,000
Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant	1,033,413
Performance-Accelerated Restricted Share (PARS) Awards
Share-Based Compensation
Pretax compensation expense	$ 7,600,000	$ 6,100,000	$ 5,600,000
Vesting period	5 years
Compensation Plan for Non-Employee Directors
Share-Based Compensation
Pretax compensation expense	$ 1,300,000	1,200,000	1,300,000
Total share-based compensation cost	1,300,000
Total income tax benefit recognized		1,500,000	1,400,000
Total unrecognized compensation cost related to share-based compensation arrangements	$ 9,000,000.0
Weighted average period	1 year 7 months 6 days
Compensation Plan for Non-Employee Directors \| Selling, general and administrative expenses
Share-Based Compensation
Total share-based compensation cost	$ 8,900,000	$ 7,300,000	$ 6,900,000
RSU
Share-Based Compensation
Vesting period	3 years 6 months