Fair Value Measurements - Schedule of Assets and Liabilities Measured at Fair Value on a Recurring Basis (Details) - USD ($) $ in Millions	Sep. 30, 2021	Sep. 30, 2020
Sponsored funds and separate accounts [Member]
Assets [Abstract]
Investments, at fair value	$ 368.3	$ 303.4
Investment related to long-term incentive plans [Member]
Assets [Abstract]
Investments, at fair value	160.0	146.6
Other equity and debt investments [Member]
Assets [Abstract]
Investments, at fair value	60.0	54.8
Fair Value, Recurring [Member]
Assets [Abstract]
Contingent consideration asset	19.4	39.7
Total Assets Measured at Fair Value	607.7	544.5
Liability [Abstract]
Contingent consideration liabilities	42.4	25.3
Fair Value, Recurring [Member] | Level 1 [Member]
Assets [Abstract]
Contingent consideration asset	0.0	0.0
Total Assets Measured at Fair Value	404.6	323.9
Liability [Abstract]
Contingent consideration liabilities	0.0	0.0
Fair Value, Recurring [Member] | Level 2 [Member]
Assets [Abstract]
Contingent consideration asset	0.0	0.0
Total Assets Measured at Fair Value	31.7	42.4
Liability [Abstract]
Contingent consideration liabilities	0.0	0.0
Fair Value, Recurring [Member] | Level 3 [Member]
Assets [Abstract]
Contingent consideration asset	19.4	39.7
Total Assets Measured at Fair Value	44.0	57.1
Liability [Abstract]
Contingent consideration liabilities	42.4	25.3
Fair Value, Recurring [Member] | NAV as a Practical Expedient [Member]
Assets [Abstract]
Total Assets Measured at Fair Value	127.4	121.1
Fair Value, Recurring [Member] | Sponsored funds and separate accounts [Member]
Assets [Abstract]
Investments, at fair value	368.3	303.4
Fair Value, Recurring [Member] | Sponsored funds and separate accounts [Member] | Level 1 [Member]
Assets [Abstract]
Investments, at fair value	241.3	176.3
Fair Value, Recurring [Member] | Sponsored funds and separate accounts [Member] | Level 2 [Member]
Assets [Abstract]
Investments, at fair value	18.4	40.9
Fair Value, Recurring [Member] | Sponsored funds and separate accounts [Member] | Level 3 [Member]
Assets [Abstract]
Investments, at fair value	24.6	17.4
Fair Value, Recurring [Member] | Sponsored funds and separate accounts [Member] | NAV as a Practical Expedient [Member]
Assets [Abstract]
Investments, at fair value	84.0	68.8
Fair Value, Recurring [Member] | Investment related to long-term incentive plans [Member]
Assets [Abstract]
Investments, at fair value	160.0	146.6
Fair Value, Recurring [Member] | Investment related to long-term incentive plans [Member] | Level 1 [Member]
Assets [Abstract]
Investments, at fair value	160.0	145.5
Fair Value, Recurring [Member] | Investment related to long-term incentive plans [Member] | Level 2 [Member]
Assets [Abstract]
Investments, at fair value	0.0	0.0
Fair Value, Recurring [Member] | Investment related to long-term incentive plans [Member] | Level 3 [Member]
Assets [Abstract]
Investments, at fair value	0.0	0.0
Fair Value, Recurring [Member] | Investment related to long-term incentive plans [Member] | NAV as a Practical Expedient [Member]
Assets [Abstract]
Investments, at fair value	0.0	1.1
Fair Value, Recurring [Member] | Other equity and debt investments [Member]
Assets [Abstract]
Investments, at fair value	60.0	54.8
Fair Value, Recurring [Member] | Other equity and debt investments [Member] | Level 1 [Member]
Assets [Abstract]
Investments, at fair value	3.3	2.1
Fair Value, Recurring [Member] | Other equity and debt investments [Member] | Level 2 [Member]
Assets [Abstract]
Investments, at fair value	13.3	1.5
Fair Value, Recurring [Member] | Other equity and debt investments [Member] | Level 3 [Member]
Assets [Abstract]
Investments, at fair value	0.0	0.0
Fair Value, Recurring [Member] | Other equity and debt investments [Member] | NAV as a Practical Expedient [Member]
Assets [Abstract]
Investments, at fair value	$ 43.4	$ 51.2