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Stock-Based Compensation - Valuation Assumptions (Details)
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Performance Shares      
Stock Based Compensation Activity [Line Items]      
Risk-free interest rate 0.99% 0.20% 1.60%
Expected volatility of the Company’s stock 30.00% 30.90% 21.80%
Employee Stock Option      
Stock Based Compensation Activity [Line Items]      
Expected life of option (years) 6 years 6 years 6 months 6 years 6 months
Risk-free interest rate 1.35% 0.60% 1.67%
Expected volatility of the Company’s stock 27.80% 27.60% 22.40%
Expected dividend yield on the Company’s stock 1.71% 2.28% 2.49%