Earnings per Share - EPS Reconciliation (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Numerator:
Net income	$ 238.5	$ 207.1	$ 116.3
Less: Allocation to participating securities	(8.1)	(6.1)	(3.5)
Net income allocated to common stockholders	230.4	201.0	112.8
Net income allocated to common stockholders	$ 230.4	$ 201.0	$ 112.8
Denominator:
Common shares outstanding (in shares)	19,957,333	19,570,403	19,130,643
Dilutive potential common shares outstanding:
Share-based awards (in shares)	662,007	497,137	547,525
Diluted shares outstanding (in shares)	20,619,340	20,067,540	19,678,168
Earnings per share:
Basic (in dollar per share)	$ 11.55	$ 10.27	$ 5.90
Diluted (in dollar per share)	$ 11.18	$ 10.01	$ 5.74
Common Stock Split
Denominator:
Common shares outstanding (in shares)	29,936,000	29,355,605	28,695,965
Dilutive potential common shares outstanding:
Share-based awards (in shares)	993,011	745,706	821,288
Diluted shares outstanding (in shares)	30,929,011	30,101,311	29,517,253
Earnings per share:
Basic (in dollar per share)	$ 7.71	$ 6.85	$ 3.93
Diluted (in dollar per share)	$ 7.45	$ 6.67	$ 3.82