Not every question has a number answer
"How many goals will we score?" wants a number, like 2 or 3. But "Will we win?" is a different kind of question. It only has two answers: yes or no.
Nobody actually knows for sure, not even the coach! So instead of a flat "yes" or "no," we answer with "how sure are you?" The weather report does this too. It says "70% chance of rain," not "it will rain."
A percentage is a way of saying how much of something, out of 100. 100% means for sure. 0% means never. 50% means it could go either way.
Building a Confidence Machine
Computers can answer "how sure are you?" questions too. You give the computer one team's strength, and it turns that strength into a percentage: its chance of winning.
This kind of machine always draws a curvy answer. It starts down near 0%, and climbs up toward 100%, but it can never dip below 0% or shoot past 100%. Want to see the curve for yourself? Let's build one.
Play the Game The Confidence-O-Meter
Press the button, and watch 16 past matches turn into one curvy line. Then take the controls, and see what the machine predicts.
How to play
- Press "Train the Confidence Machine!" to see 16 past matches, and the curvy line drawn through them.
- Drag the Team Power slider. Then tap the Home button to flip it between Yes and No.
- Watch the dot ride the curve, and the percentage change.
- Find where the dot sits exactly on the dashed 50% line. That is the tipping point, where the guess flips.
The real formula
Grown-up mathematicians have a name for that curvy machine. They call it a sigmoid. Think of it as a squishing machine.
You feed the sigmoid any number. It always hands back a percentage between 0% and 100%. It can never sneak below 0%, and it can never climb above 100%.
Here, $z$ stands for the team's power score. Feed in the number 0, and the machine always hands back exactly 50%. That's the tipping point, right in the middle, where the guess could flip either way.
- Some questions are yes or no, but nobody knows the answer for sure.
- A percentage says how sure you are, from 0% (never) to 100% (for sure).
- A confidence machine uses a curvy line, called a sigmoid, to turn team strength into a percentage.
- 50% is the tipping point: right in the middle, where the guess could flip either way.
🎮 3D Vox game: Win or Lose Parade
Green birds are WINS, red birds are LOSSES. Watch a team’s results fly past in a pattern and predict the next result!
Next: you be the AI referee and make an offside call.