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Stock-Based Compensation - Schedule of Stock-Based Compensation Expense (Income) (Details) - USD ($) $ in Millions | 3 Months Ended | 12 Months Ended
--- | --- | ---
Dec. 31, 2021 | Dec. 31, 2022 | Sep. 30, 2021 | Sep. 30, 2020
Equity-based compensation plans |  |  |  |
Stock-based compensation expense | $ 4.9 | $ 28.7 | $ 29.8 | $ 30.2
Income tax benefit recognized for stock-based compensation | (0.8) | (4.2) | (4.4) | (3.6)
Stock-based compensation cost, net of tax | 4.1 | 24.5 | 25.4 | 26.6
Stock options |  |  |  |
Equity-based compensation plans |  |  |  |
Stock-based compensation expense | 0.2 | 0.3 | 1.8 | 6.8
Nonvested Stock Awards [Member] |  |  |  |
Equity-based compensation plans |  |  |  |
Stock-based compensation expense | 3.5 | 25.7 | 19.3 | 15.8
Income tax benefit recognized for stock-based compensation | 3.1 | 2.5 | 2.0 | 3.1
Performance Shares [Member] |  |  |  |
Equity-based compensation plans |  |  |  |
Stock-based compensation expense | 0.5 | 2.6 | 6.1 | 6.7
Stock Appreciation Rights (SARs) |  |  |  |
Equity-based compensation plans |  |  |  |
Stock-based compensation expense | 0.3 | (0.8) | 1.1 | 0.2
Restricted Stock Units (RSUs) |  |  |  |
Equity-based compensation plans |  |  |  |
Stock-based compensation expense | $ 0.4 | $ 0.9 | $ 1.5 | $ 0.7

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- Definition Amount of expense for award under share-based payment arrangement. Excludes amount capitalized. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (h)(1)(i) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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