In typical practices of estimating cartel damages, an outcome variable such as winning bid price is regressed on a cartel dummy variable and multiple control variables. When the number of bidders in a bid is influenced by collusion, two approaches can be employed. One approach is to exclude the bidder number variable in the regression analysis. The other approach is to use predicted numbers of bidders for the collusive bids obtained, based on the observed relationship in the non-collusive bids. We show that these two approaches are equivalent in estimating the effects of collusion.