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Earnings Per Common Share
 9 Months Ended
Sep. 30, 2021
Earnings Per Share [Abstract]  
Earnings Per Common Share Earnings Per Common Share
The following table sets forth the computation of basic and diluted earnings per common share:
Three Months EndedNine Months Ended
September 30,September 30,
 2021202020212020
Numerator:
Net income (loss)$421,415 $488,682 $1,615,787 $866,397 
Amounts attributable to noncontrolling interests(1,473)(69,643)(82,203)(4,420)
Net income (loss) available to Arch419,942 419,039 1,533,584 861,977 
Preferred dividends(16,090)(10,403)(38,159)(31,209)
Loss on redemption of preferred shares(15,101)— (15,101)— 
Net income (loss) available to Arch common shareholders$388,751 $408,636 $1,480,324 $830,768 
Denominator:
Weighted average common shares and common share equivalents outstanding — basic389,274,220 402,850,485 395,899,591 403,081,266 
Effect of dilutive common share equivalents:
Nonvested restricted shares2,131,915 1,580,791 1,877,930 1,690,447 
Stock options (1)6,497,212 4,763,381 6,482,964 5,543,184 
Weighted average common shares and common share equivalents outstanding — diluted397,903,347 409,194,657 404,260,485 410,314,897 
Earnings per common share:
Basic$1.00 $1.01 $3.74 $2.06 
Diluted$0.98 $1.00 $3.66 $2.02 
(1)    Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For the 2021 third quarter and 2020 third quarter, the number of stock options excluded were 1,948,006 and 4,713,241, respectively. For the nine months ended September 30, 2021 and 2020 period, the number of stock options excluded were 2,397,507 and 2,361,413, respectively.