Stock-Based Compensation - Fair Value Assumptions (Details) - Performance-based restricted stock - $ / shares	12 Months Ended
Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Expected volatility, minimum (percentage)	41.00%	26.10%	21.20%
Expected volatility, maximum (percentage)	89.00%	67.00%	54.80%
Risk-free interest rate (percentage)	0.81%	0.23%	1.61%
Dividend yield	0.00%	0.00%	0.00%
Minimum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Grant-date stock price (in dollars per share)	$ 21.40	$ 14.07	$ 15.62
Maximum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Grant-date stock price (in dollars per share)	$ 142.99	$ 4,318.03	$ 3,595.17

The estimated dividend rate (a percentage of the share price) to be paid (expected dividends) to holders of the underlying shares over the option's term.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (f)(2)(iii)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

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- Definition

The estimated measure of the maximum percentage by which a share price is expected to fluctuate during a period. Volatility also may be defined as a probability-weighted measure of the dispersion of returns about the mean. The volatility of a share price is the standard deviation of the continuously compounded rates of return on the share over a specified period. That is the same as the standard deviation of the differences in the natural logarithms of the stock prices plus dividends, if any, over the period.

+ References

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- Definition

The estimated measure of the minimum percentage by which a share price is expected to fluctuate during a period. Volatility also may be defined as a probability-weighted measure of the dispersion of returns about the mean. The volatility of a share price is the standard deviation of the continuously compounded rates of return on the share over a specified period. That is the same as the standard deviation of the differences in the natural logarithms of the stock prices plus dividends, if any, over the period.

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- Definition

The risk-free interest rate assumption that is used in valuing an option on its own shares.

+ 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 (f)(2)(iv)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

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- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

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- Definition

Price of a single share of a number of saleable stocks of a company.

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