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Stock-Based Compensation - Narrative (Details) - USD ($) $ in Millions |  |  | 12 Months Ended |
--- | --- | --- | --- | ---
Jul. 08, 2022 | Jan. 01, 2022 | Sep. 30, 2022 | Sep. 30, 2021 | Sep. 30, 2020 | Mar. 18, 2021
Employee Stock Option |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Intrinsic value of options exercised |  |  | $ 27.6 | $ 66.9 | $ 44.1 |
Stock-based compensation expense |  |  | 10.8 | 12.4 | 9.7 |
Unrecognized pre-tax compensation expense |  |  | $ 12.0 |  |  |
Weighted average period to recognize pre-tax compensation expense |  |  | 1 year 6 months |  |  |
Restricted Stock Units (RSUs) |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Stock-based compensation expense |  |  | $ 113.6 | $ 64.2 | $ 33.7 |
Weighted average period to recognize pre-tax compensation expense |  |  | 2 years 4 months 24 days |  |  |
Granted (in shares) |  |  | 1,396,170 |  |  |
Share-based payment award (in shares) |  |  | 4,069,431 | 3,831,850 |  |
Unrecognized pre-tax compensation expense |  |  | $ 140.7 |  |  |
Restricted Stock Units (RSUs) | Chief Executive Officer |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Share-based payment award (in shares) | 99,521 |  |  |  |  |
Restricted Stock Units, Market-Based | Chief Executive Officer |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Granted (in shares) |  | 800,000 |  |  |  |
Equity award value | $ 38.4 |  |  |  |  |
Performance-Based Restricted Stock Units | Chief Executive Officer |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Share-based payment award (in shares) | 149,282 |  |  |  |  |
2004 Plan |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Shares reserve for issuance (in shares) |  |  | 175,083 |  |  |
2004 Plan | Restricted Stock Units (RSUs) |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Share-based payment award (in shares) |  |  | 0 |  |  |
2013 Plan |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Shares reserve for issuance (in shares) |  |  | 4,072,137 |  |  |
Number of shares forfeited (in shares) |  |  | 131,897 |  |  |
2013 Plan | Restricted Stock Units (RSUs) |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Share-based payment award (in shares) |  |  | 3,145,886 |  |  |
2021 Plan |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Number of shares authorized (in shares) |  |  | 7,190,077 |  |  | 8,000,000
2021 Plan | Restricted Stock Units (RSUs) |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Share-based payment award (in shares) |  |  | 923,545 |  |  |
Outside Of Equity Compensation Plans | Employee Stock Option |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Shares reserve for issuance (in shares) |  |  | 778,425 |  |  |
Outside Of Equity Compensation Plans | Restricted Stock Units (RSUs) |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Shares reserve for issuance (in shares) |  |  | 838,625 |  |  |

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