5.5: Cost Benefit Analysis

Now that the various ways to earn and deny points are understood, it’s time to rank these options in terms of how they contribute to the overall goal: winning matches. A rudimentary way of ranking these options would be to say the ones that provide the most points are the most valuable. However, it is not that simple. The task that earns the most points may be incredibly difficult, while a task that earns less points may be very simple to accomplish.  It is for this reason that a cost-benefit analysis must be performed. In a cost-benefit analysis, a comparison between the cost of an item and the benefit of the item takes place. In the case of a cost-benefit analysis within the Strategic Design of a competition robot, the “cost” is the level of difficulty of the given task, while the “benefit” is the number of points earned or denied by the same task. The goal is to identify the tasks which give the highest ratio of benefit to cost.

How does one determine the difficulty of performing a task? There are many factors to consider when assessing the difficulty of a task within a competition robotics game. Some of these include:

  • How long does it take to complete the task? The more time spent, the more difficult the task.
  • How much distance needs to be traveled to complete the task? This is similar to the previous item, since distance is proportional to time
  • Many tasks within competition robotics require lifting and placing objects, thus the weight of the object is a factor. Lifting a ping pong ball is not as difficult as lifting a bowling ball. The heavier the object, the more difficult the task.
  • Similar to weight is the height of the where the object is being placed. The higher the placement height, the more difficult the task.
  • The precision required for the task. For example, parking a robot in a 12”x12” space compared to parking a robot in a 24”x24” space. The more precision required, the harder the task.
  • Does the task require a specific mechanism to complete? Tasks that can be done in conjunction with other tasks involve less difficulty, since you can essentially do two tasks at once (or two tasks with the same robot feature.) This is why denying an opponent a point is often seen as not very difficult. While it may be difficult to defend an opponent during a match, it can typically be done without adding extra functionality to the robot; simply blocking the opposing robot’s path can suffice. Thus, it is an easy feature to add to a robot.

Here’s a simple exercise on how to perform a basic cost-benefit analysis based on what has been taught so far. The following exercise is a good way of taking the analysis from the previous steps and organizing it in such a way that choosing the optimal  strategy becomes a much easier task.

  1. From the "analyzing the game" portion of the unit, take the list of all the different possible robot tasks, whether they are to score points, or to prevent the opponent from scoring.
  2. Assign a rank on a scale of 1-100 for each task, indicating the benefit   towards winning a match. (100 being the most beneficial, 1 being the least.)  Using a relative scale from 1-100 as opposed to the pure point values allows for a more uniform comparison between tasks, since some tasks will not have a clearly defined point value.
  3. Assign a rank on a scale of 1-10 for each task, indicating how difficult each task will be to complete.  (100 being the most difficult, 1 being the easiest.) When evaluating difficulty, consider both how difficult it would be to execute the task during a match, as well as how difficult it would be to build a robot to complete the task.
  4. Take the ratio of benefit to difficulty for each task.  The task with the highest ratio is the most optimal according to your analysis.

At this point, revisit the list of items. Do the most optimal tasks based on the analysis agree with personal assessments of the tasks? If not, it is important to determine why. A very common reason is usually that the initial rankings and assessments of cost-benefit were done incorrectly. However, sometimes the most optimal strategies are not intuitive. That is why this type of analysis is so crucial.

How does one avoid making incorrect assessments of cost and benefit? One of the most common errors that can take place in these types of assessments is the underestimation of the level of difficulty to complete tasks. As such, tasks which are harder can often be overvalued. This is very dangerous at it leads to overcomplicated robots that do not perform well. It is important to always be realistic and reasonable when evaluating the level of difficulty of any task.