Earnings per Share - EPS Reconciliation (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
Numerator:
Net income	$ 207.1	$ 116.3	$ 169.6
Less: Allocation to participating securities	(6.1)	(3.5)	(4.0)
Net income allocated to common stockholders	$ 201.0	$ 112.8	$ 165.6
Denominator:
Common shares outstanding (in shares)	19,570,403	19,130,643	18,824,328
Dilutive potential common shares outstanding:
Share-based awards (in shares)	497,137	547,525	356,151
Diluted shares outstanding (in shares)	20,067,540	19,678,168	19,180,479