Every year a lot of people face the question “how many teams can we grow this year”. It is a complex question but for fun let’s throw a little theory at it. If someone throws out an arbitrary number as a growth target is the number pulled out of the hat or is it predictable.
Question: How fast can FIRST and VEX (plus others) grow ? What are the probable program growth limit ?
The answer may lie in some mathematical theory that describes unconstrained social networks. The reason it is an “unconstrained social network” is because participation is essentially by behavioral choice, not government or institutional mandate. Even if participation is mandated, performance will still follow the curve.
In your own experience you know some team members are ‘higher producers’ or more participatory than other members. If you could quantify ‘participation or productivity’ and then plot productivity versus number of students you would get a chart that looks like the following.
The same plot describes a million other things, such as company financial ranking versus number of companies (plot the S&P 500), Zipf’s law of city-town distribution, popularity of girl scout cookies versus recipe, soft drink sales versus variety, all kinds of things in the physical and biological universe, the list goes on and on.
This is the basis of the “Pareto Principle (also known as the 80-20 rule, the law of the vital few, and the principle of factor sparsity) and can help you manage those things that really make a difference to your results.
So for fun I’d like to throw around some numbers – quick estimation without pulling out a slide rule. Here in Georgia there are roughly 380 public high schools but for this exercise I’ll round it off to 400.
I’m guessing maybe 40 of them will become FRC teams.
Roughly halving the cost of the program maybe quadruples the 40 number so that produces 160 FTC/VRC teams.
One more round 4 * 160 = 640 FLL teams.
So you get something looking like 40/160/640 for a FRC/ (FTC/VEX) / FLL spread. Is the model approximately correct ? Is it correlatable to other data ? For example if you looked at the states in a region for number of football teams versus highly competitive football teams. BOA marching bands versus total marching bands.
It is a neat exercise that might be useful in being a predictor in the number of teams produced in a region. To use an economist’s terms, exceeding those boundary’s would incur a higher marginal cost per team startup. I am NOT arguing that we should not pursue a team in every school but that we should have a good grip on how we approach team growth.
Some interesting stats:
California 34M population
145 teams = 4.3 FRC teams / M
145 teams / 2079 schools = 0.07 FRC teams / school
Michigan 10M+ population
132 teams = 13.2 FRC teams / M
132 teams / 752 schools = 0.18 FRC teams / school
Georgia 9M+ population
28 teams = 3.1 FRC teams / M
28 teams / 356 schools = 0.08 FRC teams / school
Having said all that it seems achieving > 50% participation of high schools in FRC/FTC/VEX is very doable and in the not too distant future. Most of the growth (in raw numbers) would be in FTC/VEX.
For the truly mathematical inquisitive you can start reading here: