Towards a Unified Theory of Wargaming Complexity

Put on your thinking man’s cap, because today we’re talking math.

Earlier this week, Delta Vector (you know Delta, he runs the excellent Delta Vector blog) posted the latest installment of his in-depth analysis of wargame design, this one on the perfect number of units.   The entire series is well worth your time, as he devotes each post to a detailed look at different ways of managing wargames with copious examples from around the genre.  In this installment he comes to the conclusion that the right number of units is between 5 and 12.  
This particular post hit home, because on the exact same day that Delta posted his analysis, your humble blogger posted a summary of One Hour Wargames in which he came to almost the exact same conclusion.  Ain’t that a kick in the serendipity pants.
One maneuver unit each makes for a dull game indeed.
Reading through Delta’s analysis, it occurred to me that he made a couple of simplifying assumptions that might not hold true for everyone.  As a further refinement of his idea, it struck me that the number of units (U) is just one variable.  The other three would be how complex (C) the rules are, how much time (T) you have , and how nimble (N) your brain feels that day.  
For games of a given length, you can have more units, but you’re going to need smarter (read: faster playing) players, or simpler rules.  Likewise, for games of a given complexity, the more units in play, the longer the game will last.  
Let’s set U as our constant. You can compare DBA to its big battle brother DBM. They use the same basic rules, but the latter triples the number of stands in the game and turns a one hour game into a full afternoon affair.  I’ve seen guys who have the rules down pat that can burn through a full game of DBM just as fast as I muddle through a stripped down game of DBA, proving that fast brains can mitigate the rules complexity.  Or consider Advanced Squad Leader – my turns take a lot longer to get through than most of my regular opponents.  Not necessarily because they are smarter than me, but because I seldom play the game and have to spend a lot more time on each turn.  Also, because they are in fact smarter than me.
At any rate, since we are approaching this from a game design standpoint, our equation would look like this:
C = U * N * T
This isn’t particularly earth shaking, it is an analysis that we all run in our back brains whenever we choose which game to grab for pushing lead around a table.  When you really sit down to design a game (or analyze a game’s ruleset) however, then it’s something you need to spend a few more brain cells on.  If you bolt on another subsystem for the rules you’re tinkering with, you’ve got to understand that the subsystem will lead to longer or more complicated games, and you might want to consider scaling back the numbers of units in the game.