Rare Events

So I have been watching some World Cup this week.

Yeah, honestly I have.

Anyway, the games have been fun, exciting, and all of that. But there is a fundamental problem with this sport:

The measurement of the better team within a game (or the score) is not accurate with the action we see.

In other words, it is way too hard to score a goal.

Now I have actually done this as a side project years ago, using funny things like math and probability to illustrate my point. But I don’t want to get into the weeds on this, so I’ll just talk about what I mean in a general sense.

Think about it this way:

  • Both teams have 10 chances to score in a game

  • Team A is better than Team B

  • Team A has twice of good of a chance of scoring than Team B

OK, now if the chance of score for Team A is 80%, than means Team B’s chance is 40%. Usually the score will be 8-4. Sometimes 9-3, maybe even 6-5, but Team A wins almost all the time.

Let’s chance things around a bit. Team A has a 2% chance, Team B at 1%. The typical score will be 0-0. Team A may score 1, maybe even Team B if lucky, but we can agree that more often than not the game will end in a tie.

Now let’s modify the chances once more. Team A has a 10% chance, Team B at 5%. The typical score will be 1-0, but there is a much greater chance of a tie game than scenario 1. A 1-1 game or a 0-0 game is not that rare.

The final scenario is most like a real soccer game. Most of the time, the better team wins. However you can see when the probably of a goal increases, the more likely the better team wins. When you lower that probability, ties and upsets increase.

I have an issue with this. I feel the team who plays better should have more to show than some clumsy 1-0 win.

Let’s add one more thing to the equation: the tie-breaker.

Penalty kicks do take skill. The better PK team is much more likely to win based on the probability of converting one. But I would argue that this is a skill that is very distinct to the 120 minute game we just witnessed. PK’s come up so rarely in a game (average less than 1 a game), it is not a skill that is valued on the pitch. Yet at the end of regulation, all of the sudden it is the only skill that matters. This is NOT the equivalent of shooting free throws to decide a tie in basketball; free throws are something that appear often within the game and is a skill all players have to learn. Yet no one in their right mind would say the NBA should change their overtime policy to this. PK’s are a different; only certain players ever use this within the regulation game. And when this tie-breaker becomes important, at least 5 guys on each side have to be adept at this.

Over half the Round of 16 games have been decided by PKs. So this tie-breaker is not trivial at all. In fact due to some of my basic logic I showed above, half the games ending in a tie is no anomaly. Even when the superior team has a 2x more likely chance of scoring, many times the setto is ended in a way that is not emphasized during the gameplay.

Anyway, the next time you talk to your hipster friend about soccer and they argue that ‘soccer is so awesome, Americans are just stupid; all they want is scoring’, think about the reasoning presented here about why soccer needs more scoring. Your hipster friend may not understand math, but maybe it will shut him up for a bit.