Stock and Other Compensation Plans - Narrative (Details) - USD ($)	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Share-Based Payment Arrangement [Abstract]
Stock-based compensation cost	$ 25,400,000	$ 23,700,000	$ 22,200,000
Capitalized stock-based compensation cost	$ 14,700,000	13,500,000	11,500,000
Maximum shares authorized (in shares)	11,200,000
Shares available for future issuance (in shares)	400,000
Service period	3 years
Unrecognized compensation cost	$ 17,600,000
Cost recognition period	1 year 4 months 24 days
Fair value of restricted stock vested	$ 21,600,000	$ 22,800,000	$ 16,000,000.0
Minimum initial investment	1,250
Minimum cash payments	25
Maximum annual cash payments	$ 100,000