It sounds like you are proposing the development of a corkage model. That is kind of like taking a sledgehammer to crack a nut, but ok.
Actually, by your logic, they should charge the weighted average of the markups of all the bottles sold, since that's a much closer estimate of the revenue lost over time, possible further weighted by day of the week, on the assumption that average price per bottle sold increases at a predictable rate from Monday to Saturday.
We should first figure out how we would apply weights to the markups of bottles sold. Do you propose applying different weights to the margins of the most frequently sold bottles, most expensive bottles, bottles with the highest margins, lowest margins and so on? Keep in mind that restaurants normally experience a decline in margin percentage as the price (to them) of a bottle of wine increases. Regarding further weighting by day of the week, how would you propose reconciling weighting the difference between average price/bottle and, would you take into account the average number of bottles sold from Monday to Saturday?
Indeed, they might even multiply that figure by some fraction>1, given the propensity of bottle-bringers to be higher-end consumers and thus the loss per bottle being somewhat greater when corkage fees are substituted for restaurant markups.
Margin is margin. Again, most fine restaurants experience a drop (sometimes significant, sometimes less so) in margin percentage as consumers move up the price curve on a restaurants wine list. If your model focused on high-end consumers under the belief that they will buy expensive wines, then the corkage would have to be based on a lower margin than the margin gained on lower priced wine.
Perhaps there's a correlation as well between entree price or total food expenditures and wine expenditures that might be explored, allowing fees to calculated by table at the end of each meal, although this would give the savvy customer a chance to game the system by ordering cheaper food in order to get the lower corkage and may also have the unintended consequences of encouraging the kind of people who tip poorly as well and probably should be introduced only secretly, if at all.
I would assume that most people on this board are not trying to game any systems and also typically order the food on the menu that suits them instead of ALWAYS ordering the chicken. But since you raised the question, do you think the correlation is an inverse correlation, and also would it be linear? Do you assume that those consumers that do exercise corkage also spend less on their meal because they are cheap overall, or would you assume that they exercise corkage so they can spend more on their meal? If you are really looking for model accuracy, perhaps we could introduce a separate model that could help predict total expenditures which could then be used as a factor in the optimal corkage algorithm. Your last point on tipping is also very interesting. I think anyone would be hard pressed to prove a positive relationship exists between consumers who exercise corkage and consumers who are cheap when it comes to the gratuity, especially as you originally asserted that the bottle-bringers are usually higher-end consumers.
Of course, then you'd have to correct for the propensity of a person bringing a bottle of Bordeaux to stay home or go elsewhere as the corkage charge rises or falls, and correct again for the probability that their seat would have been filled by another, non-corkage customer anyway, to determine if low fees should prove to be a net revenue -- and, given high hospitality industry fixed costs -- even a net profit enhancer or merely a loss-leader expected to pay off over time.
Here we risk introducing noise into our model as I dont really think it makes any difference since the number of consumers exercising corkage in restaurants is a small percentage of total diners. I think the better question is how much of an incentive is it for a restaurant to offer a low, law-abiding corkage fee in order to realize an expected food and beverage margin.
If only there was an engineer with an interest in wine on this board to help us create an apt and accurate statistical model.
There are too many variables and spurious assumptions to get into any sort of meaningful modeling. Rules of thumb are useful and generally simpler when they focus on the things that matter. It is not necessary to boil the ocean when the practical issue is that restaurants cant legally charge a corkage in excess of $25 in DC. And in this case, what matters for a business is margin.
