Stock-Based Compensation - Schedule of Equity-Based Compensation Plans (Details) - $ / shares	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017
Equity-based compensation plans
Number of Securities to be Issued Upon Exercise of Outstanding Options or Vesting of Performance Share Awards (in shares)	1,731,277
Weighted-Average Exercise Price of Outstanding Options (in dollars per share)	$ 74.38	$ 62.62	$ 57.03	$ 45.14
Number of Securities Remaining Available for Future Issuance Under Equity Compensation Plans (in shares)	4,039,917
Equity compensation plans approved by security holders [Member]
Equity-based compensation plans
Number of Securities to be Issued Upon Exercise of Outstanding Options or Vesting of Performance Share Awards (in shares)	1,731,277
Weighted-Average Exercise Price of Outstanding Options (in dollars per share)	$ 74.38
Number of Securities Remaining Available for Future Issuance Under Equity Compensation Plans (in shares)	4,039,917
Equity Compensation Plans Not Approved By Security Holders [Member]
Equity-based compensation plans
Number of Securities to be Issued Upon Exercise of Outstanding Options or Vesting of Performance Share Awards (in shares)	0
Weighted-Average Exercise Price of Outstanding Options (in dollars per share)	$ 0
Number of Securities Remaining Available for Future Issuance Under Equity Compensation Plans (in shares)	0