Stock-Based Compensation - Schedule of Stock Option Activity (Details) - $ / shares	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Options
Options outstanding, beginning of year (in shares)	1,328,390	1,268,984	1,531,691
Options granted (in shares)	301,025	372,450	261,900
Options forfeited (in shares)	(40,965)	(24,175)	(43,270)
Options expired (in shares)	(5,869)	(8,721)	(1)
Options exercised (in shares)	(499,179)	(280,148)	(481,336)
Options outstanding, end of year (in shares)	1,083,402	1,328,390	1,268,984
Options exercisable, end of year (in shares)	537,241	709,826	650,143
Weighted-Average Exercise Price
Options outstanding, beginning of year (in dollars per share)	$ 62.62	$ 57.03	$ 45.14
Options granted (in dollars per share)	90.28	66.09	86.59
Options forfeited (in dollars per share)	79.00	72.88	66.49
Options expired (in dollars per share)	84.25	76.92	41.52
Options exercised (in dollars per share)	52.18	40.62	34.41
Options outstanding, end of year (in dollars per share)	74.38	62.62	57.03
Options exercisable, end of year (in dollars per share)	$ 68.16	$ 55.11	$ 45.92