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← Why the Better Team Loses

Why the Better Team Loses

Three short lessons on luck in low-scoring games: goals by chance, single matches against seasons, and what a league table really shows.

Spark & Whetstone · sparkwhetstone.org/learn/why-the-better-team-loses · CC BY-NC-SA 4.0. Answers are at the end, so you can try each question first.

Lesson 1. Goals by chance

Goals are rare, so a simple model treats them as random events with an average rate, a Poisson distribution. A team averaging 1.6 goals scores exactly one goal more often than any other number, about a third of its matches, and none about a fifth.

In such a low-scoring game, a single lucky or unlucky goal changes the result.

Question. Team A averages 2 goals a game, team B 1. In the simple model, which result is most likely for A?

  1. A wins most of the time but not always
  2. They are equally likely to win, because one game is too short to tell
  3. A always wins

Say it back. In your own words: why does luck matter more in low-scoring games?

Lesson 2. One match against a season

A single match is one roll of loaded dice. A season is many rolls, and the better team’s edge shows more clearly as the matches add up.

Even so, in a short league the best team often does not finish top. Simulate a four-team league with each team playing six matches, and the strongest team tops it less than half the time.

Question. Two leagues use the same teams. One plays 6 matches each, the other 38. In which is the best team more likely to finish first?

  1. The 6-match league
  2. They are the same, because the teams are the same in both leagues
  3. The 38-match league

Say it back. In your own words: why is a season fairer than a single match?

Lesson 3. What a league table shows

A table gives 3 points for a win and 1 for a draw, then sorts by points and breaks ties by goal difference. It records results, not strength.

Two teams on the same points can be very different in strength; a team that scores more and concedes less but draws a lot can sit below one that scraped narrow wins.

Question. Team X has 4 wins and 2 losses; team Y has 3 wins and 3 draws. Who has more points?

  1. Team Y
  2. They are level
  3. Team X, with more wins

Say it back. In your own words: why does a league table show results rather than strength?

At the table: Dice soccer

Players: Two to four, ages 7 and up. You'll need: Two dice per player, paper.

  1. A "strong" team scores a goal on a roll of 4, 5 or 6; a "weak" team only on a 6. Each team rolls twice per match.
  2. Play a short league of three matches, then a long one of twelve, keeping a table.
  3. Before you start, guess how often the weak team will win a single match.
  4. Compare the short and long leagues: in which did the strong team come out on top more clearly?

Answers

  1. A wins most of the time but not always — A is favoured, but with random goals around low averages, draws and B wins still happen often — in this model A wins about 61% of games.
  2. The 38-match league — With 38 matches the luck in each game averages out more, so the stronger team’s edge shows more reliably.
  3. They are level — X: 4 × 3 = 12. Y: 3 × 3 + 3 × 1 = 12. They are level, so goal difference decides who is above.