Decision Making In Football

Football Math
Does Decision-Making Trump All Other Skills & Characteristics?

"L'architetto"
Andrea Pirlo

"It's a simple game," an old coach once told me, "made complicated by the idiots who play it."

I suspect he was speaking about me, directly, but one can see his point across the whole of the game (I hope...)

Given that human performance has it's limits, speed, size, strength and so on are capped by the physics of the human frame, is it any surprise to say that the brain offers the greatest source of potential?  Given that the four men pictured in this post are all 5' 10" or shorter (5' 6" - Britton; 5' 9" - Modric; 5' 7" - Xavi) and none are possessed of the freakish athleticism of say a Bale or a Ronaldo, it would seem we're on to something.  Granted, there is a minimum standard of athleticism, and technical skill, but it's evident that the greats are distinguished by their choices as much as the execution of those options.

I wondered how difficult, really, is the decision-making component of this game?  11 players, one ball, one goal...



Then, watching the LMSC U12B, I ran a repeat of a test I did last fall with my U12G side, and connected this first thought with this information, and fleshed out the actual number of choices against the time of possession a team enjoys.

The game I watched recently featured a 10 minute period where the ball was in play for 6 minutes and some change, that 6 minutes almost perfectly split between the two sides, repeating the results of numerous college matches and my test with my own U12 girls last fall.  It's the law of 33s.  In an amatuer match, the ball is out of play for 33% of the game time; in one team's possession (live, on the field) for 33% and in the other team's possession for 33%.  While I can't say this is an absolute law, I have yet to come across an exception.

Simultaneously, I counted one LMSC player's touches during that 10 minutes and while he was subbed out after the first 6, he was still looking for his second touch.  In an 8v8 game.  How much better did his decision-making get in that game?  How many decisions did he make?

How can we even begin to know?

To start, it's pretty easy.  A player gets the ball.  How many options exist?

Each player has 13 options (11-a-side): pass to one of ten teammates; dribble with the ball; shoot at goal; turn the ball over- some more appealing than others!  I'm ruling out choosing to do nothing as sooner or later the ball has to move.

Cold Hard Facts:

If we take a simple 4 player, 3-pass move, assuming that the three players doing the passing can both consider and decline to turn the ball over, shoot or dribble, and follow these instructions (if my math is way off, be gentle...I barely got out of high school due to math, and specifically chose Kenyon because Psychology counted as fulfillment of my Math/Science reqs) :

"El Maestro"
Xavi Hernandez

Permutations with RepetitionWhen you have n things to choose from ... you have n choices each time!When choosing r of them, the permutations are:n × n × ... (r times)(In other words, there are n possibilities for the first choice, THEN there are n possibilites for the second choice, and so on, multplying each time.)Which is easier to write down using an exponent of r:n × n × ... (r times) = n^rExample: there are 10 numbers to choose from (0,1,..9) and you choose 3 of them:10 × 10 × ... (3 times) = 10³ = 1,000 permutations So, the formula is simply:

nr

where n is the number of things to choose from, and you choose r of them (Repetition allowed, order matters)

formula advice courtesy of math is fun; any errors are my own!  

We find ourselves with a fairly straightforward 13 options to the third power for our soccer scenario.
A total of 2,197 choices from which to pick, altogether.  Of course, that's  just math.  It doesn't account for the movements of the defender(s) or variations in tactics, preferences in advancing versus backpassing, field size, weather conditions, systems of play, style of play, position, communication, time and score - not all of these conditional factors are helpful!  They may add stress and reduce the clarity with which a player can assess and select options.and on and on.  But it does indicate how many decisions must be made in a heartbeat among three players who all must move and think in respect to each other.

The "Welsh Xavi"
Leon Britton

Consider that in 8v8 (U12 and down) there are 10 options for each player; the same scenario has less than half the possible number of choices to be made.  (10X10X10 = 1000)  But in 6 minutes of real game time, a midfielder in the LMSC U12B game got only 1 touch...so he dealt with far fewer choices and that only once.

Of course, there are times when shooting, for example, just isn't sensible.  A central defender receiving a goal kick 20 yards from her own goal; a throw in (if for no other reason than it's an indirect restart, so scoring is highly unlikely) and so on.  So a player with an understanding of the laws of the game, physics, their own strength and the like will be able to eliminate a great many choices nearly instantly.  Experience will eliminate many options along the way.  However, the game isn't played by the numbers alone.  Players have to be able and willing to take the risk on an improbable (but not impossible) pass, shot or other attacking movement.  Think of all the times you hear a player or coach yell "Simple" or "Play simple."  The four men pictured here would agree...but then, all four can play passes that few others would even conceive of.  Simplicity is beauty, sure, but having guts and aggression makes for winners.  Genius lies in balancing the two.

Managing the thousands of choices is crucial, having the confidence and cleverness to buck the odds when it's a good time to do so is the difference.  And so far the discussion has only been regarding the player with the ball...what might we say of the decisions a player must make to see that he gets the ball in the first place?

Luka Modric

Lastly, a team that prefers keeping the ball must be that much more savvy.  A team that plays direct needn't worry so much about decision-making as there just isn't as much to do.  If a teammate is closer to the goal than you, give him the ball.  Possession-based approaches don't always work on the same (but reasonable) logic.  If a back or two and some central midfielders just connect some passes with the aim of getting those players on the ball facing the opponent's goal, they allow their other teammates to move into advanced positions and increase the likelihood of creating 2v.1 situations, or having multiple targets to serve the ball to in the penalty area, after having connected that handful of passes.  There are many other advantages to this approach, but for now it's simply enough to say that great decision-makers allow possession football to exist.




A Video Treat For Those Who Read All This Rambling:

A legend of the infamous '94 Colombian National Team, "El Pibe," Carlos Valderrama.  In the pantheon of designers of the game.