Metcalfe’s Law states that the value of a computer network is proportional to the square of the number of nodes on the network.
For example, going from two computers connected to a network to three, a 50% increase in nodes, increases the value of the network by 125%.
How the math works: The two node network has a value of 4 units (2×2). The three node network has a value of 9 units (3×3).
So, the three node network is more than twice as valuable (9 units vs 4 units) as the two node network.
The key point of the law is that the value of the network grows proportionally faster than the number of nodes.
This law can be applied to any network, including a soccer team.
When a team of 11 players is on offense, each player can be thought of as a node on a network to move the ball through IF that player can keep the ball with the team, consistently.
At elite levels, usually, all players on each team are effective nodes, so Metcalfe’s Law isn’t all that helpful there.
But with youth teams, it’s common to have varying numbers of players that can keep the ball with the team reliably (better than 60% of the time) at game speed (i.e. before the other team closes them down or closes down their passing options).
In my experience, the number of players on a team that are effective nodes on offense is a key differentiator in how good a team is and at what level it can compete.
It also can predict time of possession.
As a coach, one thing I sized up as the competition warmed up was how many players could cleanly trap and pass.
I put teams into one of four buckets
- Level 1 is a team where all players can move the ball and keep it with the team consistently (50-70% of the time). These teams can compete at elite levels. Metcalfe’s law here says the value of the network is 121 units (11 x 11), as all 11 players are effective network nodes.
- Level 2 has 8 (+/-1) players who are proficient nodes. Their Metcalfe’s Law value is around 64 (8 x 8), about half value of a Level 1 team.
- Level 3 has about about 6 players as proficient nodes, or a value of about 36.
- Level 4 has 4 or fewer of players as proficient nodes. This is typically a beginner level team. Metcalfe’s Law here says the value of the network is about 16 (4 x 4), where only 4 players are effective network nodes,
I used Metcalfe’s Law to predict time of possession by comparing the values of the network for each level of team.
In a Level 1 vs. Level 2 match-up, for example, I would expect the Level 1 team to have the ball 1.8x more than the Level 2 team (L1 value of 121 divided by L2 value of 64). That factors out to about 65% possession for the Level 1 team vs. 35% for the Level 2 team.
Here’s how that approach predicts time of possession for match-ups between teams at different levels (shown is the time of possession for better team):
- Level 1 v 4: 1 will have ball 94% of time
- Level 1 v 3: 77%
- Level 1 v 2: 65%
- Level 2 v 3: 70%
- Level 2 v 4: 88%
- Level 3 v 4: 70%
If teams are on the same level, possession will be close to 50/50.
In my experience, these estimates fit well.
It makes sense. With each successive player who becomes a reliable node in the offensive network, the ways a team can keep the ball goes up by even more.
So, what does this mean?
As a player, one of the most valuable ways to improve your team’s offensive effectiveness is to improve your turnover ratio.