A Simple Mathematical Representation of Top Performers

Steve Jobs has a quote along the lines that he built Apple by seeking A players. When it comes to top performers, A players really like working with one another, shooing away B and C players. I think people know that intuitively. Here is a simple way to see it mathematically.

Suppose:

  • 2 A players who can each shoot a basketball 100% of the time
  • 2 B players who can each shoot a basketball 50% of the time

From here, we can form 4 different teams, and see the mathematical result:

  • A + A = shoots a basketball 100% of the time
  • A + B = shoots a basketball 50% of the time
  • B + A = shoots a basketball 50% of the time
  • B + B = shoots a basketball 25% of the time

As you can see, A players outperform B players, and that it is *unwise* to mix A players with B players as that would weaken the team. But that is not all. People work together for long batches of time, be it years or even decades with one another. So the performance, over the long run, become exacerbated between A players and B players and anything between them.

Let us take a look at all 4 teams and their scores after 20, 40, 60 games where each point is 3.

20 games:

  • AA
    • 100% * 3 points * 20 games = 60 points
  • AB
    • 50% * 3 points * 20 games = 30 points
  • BA
    • 50% * 3 points * 20 games = 30 points
  • BB
    • 25% * 3 points * 20 games = 15 points

40 games:

  • AA
    • 100% * 3 points * 40 games = 120 points
  • AB
    • 50% * 3 points * 40 games = 60 points
  • BA
    • 50% * 3 points * 40 games = 60 points
  • BB
    • 25% * 3 points * 40 games = 30 points

60 games:

  • AA
    • 100% * 3 points * 60 games = 180 points
  • AB
    • 50% * 3 points * 60 games = 90 points
  • BA
    • 50% * 3 points * 60 games = 90 points
  • BB
    • 25% * 3 points * 60 games = 45 points

Notice how the more games are played, the more exaggerated the score. That is why it is important to keep A players with A players as the gap between any weaker team would be significantly large over the long term.

Accrete the highest A players you can get, and if you have to have B players, keep them separate from A players or face a drag in performance.1

Footnote

  1. Naturally, real life is not as simple as the frameworks above reveal. Reality is closer to A players being the main operators while B players cover the gaps A players missed. ↩︎