Income Taxes - Expense (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Income Tax Disclosure [Abstract]
Current federal tax expense (benefit)	$ 73.1	$ 49.1	$ 28.0
Current state and local tax expense (benefit)	17.8	10.9	5.2
Current foreign tax expense (benefit)	0.7	0.9	0.4
Current income tax expense (benefit), total	91.6	60.9	33.6
Deferred federal income tax expense (benefit)	(7.1)	(4.9)	(3.4)
Deferred state and local income tax expense (benefit)	(1.6)	(1.1)	(0.6)
Deferred foreign income tax expense (benefit)	0.0	0.0	0.0
Deferred income taxes, total	(8.7)	(6.0)	(4.0)
Income tax expense, total	$ 82.9	$ 54.9	$ 29.6