Hot dogs are an integral part of the experience of a American Family Field baseball game. The hot dogs, or frankfurters, that are sold at the stadium are called Fastball Franks. During the regular season, a total of $81$ games are played at American Family Field, each one bringing around $37$ thousand fans. Some games bring more fans than others: attendance depends on many factors, from the weather to the reputation of the opposing team. Demand for hot dogs depends not only on attendance, but also on many other factors, such as temperature or the time of the day when the game takes place.

Although it is not a simple task, estimating the demand for hot dogs during each one of the $81$ games of a season is very important for concessions at American Family Field. On the one hand, underestimating the demand would mean $$ besides unsatisfied and hungry fans $$ lost profit: the cost of a lost sale is estimated at $$3.$ On the other hand, overestimating the demand would mean an excess of unsold hot dogs at the end of the game: the cost of an unsold hot dog, including ingredients, energy and labor, is estimated at $$2.$

Annie Adams is the representantive of the concessions at American Family Field. A year ago, she hired three consulting firms for preparing mathematical models, one by each firm, to predict the demand for hot dogs during each game of the season based on multiple factors that are known as late as just two days before the game: air temperature, rain, the opposing team, time of day for the game, injured players who would be absent$,$ and dozens of other factors.

After a year of frantic data crunching, the consultants have presented their final models to Ms$.$ Adams. You have been hired as an independent expert to evaluate the quality of the forecasts produced by their proposed models. Due to intellectual property issues, you are not allowed to see the actual models, only the forecasts they produced. They are, for your purposes, to be treated as black boxes.

As input data, you have been given the forecast that each model yielded for hot dogs demand in each game in the two most recent seasons. You have also been given by the concessions a detailed record of the actual demand for hot dogs in each of the $81$ games of these two seasons. Your task now is to help Annie Adams evaluate and compare the quality of these competing forecasting approaches.

Please enter all your numerical answers with at least $4$ significant figures.