Real cases
The idea you practise, in a real situation. Choose, see what actually happens, then reflect.
A case · you decide
Devi and the hot start
Devi — the tournament statistician of a teen chess club
The idea in play: one game is an anecdote; a season is data.
A new player wins their first three club games. People are already calling them the strongest in the club.
Devi knows early ratings are uncertain. Three games can come from luck, easy pairings or opponents having an off day.
Elo-style ratings settle as games pile up. Early swings are large because the system knows little.
What should the rating sheet do after the three wins?
Early results are real, and they don't prove much yet.
By game twenty, the new player settles into third place: strong, not the strongest. The season sorted it out.
A case · you decide
Rourke tunes the K-factor
Rourke & Devi — the rating-system designer, working with the statistician
The idea in play: every choice in a rating system is a trade-off — ask what it optimises and who it costs.
The club's ratings move slowly. Improving players complain they're stuck. Rourke considers raising K, the size of each rating update.
High K reacts fast to real improvement and also bounces around on luck. Low K is steady and slow.
Devi's data shows both problems happen at once: improving players stuck, and lucky streaks inflating.
What should Rourke change?
A rating system encodes what the designers value.
The club adopts a games-played K. Rourke posts the rule where everyone can read it, trade-offs included.
A case · you decide
Priyanka and the upset
Priyanka — a 16-year-old chess-club player who just beat the club champion
The idea in play: the expected score sets the reward: beating a much stronger player earns far more than beating an equal.
Maya is rated 1400. She beats the club champion, rated 1800. The club's K-factor is 20.
Priyanka's formula: Maya's expected score is 1 ÷ (1 + 10^(400/400)), which is about 0.09. The rating change is K × (actual − expected).
For comparison, beating another 1400 would have been 20 × (1 − 0.5) = +10.
About how many points does Maya gain?
Why does the champion lose exactly the points Maya gains?
A rating system rewards surprise. The bigger the upset, the bigger the move.
A case · you decide
Imre and the new member
Imre — a 17-year-old running the club's rating spreadsheet
The idea in play: a rating based on a few games is uncertain, so it should move faster until the games add up.
Two players are both rated 1500. Jonah has played 300 club games. Ines joined last week and has played 3. Both win tonight against the same 1500 opponent.
Imre's point: Jonah's 1500 is backed by 300 games, so one result says little. Ines's 1500 is mostly a guess.
The spreadsheet has a K value for each player: how far one result can move that rating.
How should the two ratings change?
What would go wrong if new players used the same small K as veterans?
How much a rating should move depends on how much you already know.
A case · you decide
Priyanka and Imre and the playoff seeds
Imre & Priyanka — a 17-year-old deciding the club's playoff seeding
The idea in play: a big upset by a player with an uncertain rating is a strong signal but a noisy one.
Ines, with 5 games played, has just beaten the champion. Her provisional rating jumped from 1500 to about 1650. Seeding for the playoffs closes tomorrow.
Priyanka's point: the upset was a big surprise, so it moved her rating a lot.
Imre's point: with five games, that rating is still very uncertain. It might be right, or it might be one great night.
How should the club seed Ines?
How is a surprising result different from a reliable one?
A rating is a measurement. Some measurements need a second reading.