How ratings work

A KRKplaysTennis rating is a number, usually between 1000 and 1800 for amateur players, that predicts how a player does against other rated players. The rating starts from the player’s own assessment, then each rated match moves it toward what the results show. A confidence value says how far you can trust the current number.

The model is a variant of Elo, the system chess uses, with two changes: a confidence value that controls how fast the rating moves, and partial credit for matches that end in a retirement.

The starting rating

A new player picks a level on the NTRP self-rating scale, from 1.5 to 5.5. The API converts it to a starting rating:

starting rating = 1000 + (NTRP - 1.5) × 200

NTRP level	Starting rating
1.5	1000
2.0	1100
2.5	1200
3.0	1300
3.5	1400
4.0	1500
4.5	1600
5.0	1700
5.5	1800

Every new player starts with a confidence of 20, the lowest value. Self-assessments are often too optimistic or too modest, so the API treats the starting rating as a rough guess and lets the first results correct it quickly.

The rating isn’t an NTRP rating. NTRP only sets the starting point, and it never changes after that.

What happens after a match

After each rated match, the API compares what happened with what the two ratings predicted.

1. Expected score. The rating difference gives each player’s chance of winning, from 0 to 1:

   expected score = 1 / (1 + 10 ^ ((opponent rating - player rating) / 400))

   Equal ratings give 0.5. A player rated 120 points lower has an expected score of 0.334.

2. Actual score. A win is 1 and a loss is 0.

3. Change. The rating moves by the gap between the two, scaled by the K-factor:

   change = K × (actual score - expected score)

   The API rounds the expected and actual scores to 3 decimal places, and the change to the nearest whole number. A player who wins against the odds gains a lot. A favorite who wins as expected gains little.

The K-factor and confidence

The K-factor is the most a rating can move in one match. It depends on the player’s confidence:

Confidence	K-factor	Meaning
0 to 39	48	The rating is still a guess. It moves fast.
40 to 69	32	The rating is taking shape.
70 to 95	16	The rating is settled. It moves slowly.

Confidence changes like this:

• Each rated match adds 10, up to a maximum of 95. Confidence never reaches 100, because a rating is always an estimate.
• After 60 days without a rated match, confidence drops by 5 every 30 days, down to 20. The rating itself doesn’t change. A player who comes back after a break gets a higher K-factor, so the rating adapts quickly to their current form.

Each player uses their own K-factor. A match between a new player and a settled one changes the two ratings by different amounts, so the system isn’t zero-sum.

Worked example: a completed match

Ola K. and Kasia W. play in the Kraków Autumn League. Ola has a self-assessed NTRP level of 3.5 and no rated matches yet. Kasia has played 4 rated matches. Ola wins 6-4 3-6 [10-7].

	Ola K.	Kasia W.
Rating before	1400	1520
Confidence before	20	60
K-factor	48	32
Expected score	0.334	0.666
Actual score	1 (win)	0 (loss)
Change	48 × (1 - 0.334) = +32	32 × (0 - 0.666) = -21
Rating after	1432	1499
Confidence after	30	70

Ola was the underdog and won, so Ola gains more than Kasia loses. Ola’s K-factor is also higher, because one match says more about a new rating than about a settled one. These are the numbers you get from the API in the quickstart.

Worked example: a retired match

Tomek B. and Marta Z. are both new, with confidence 20. Marta retires injured at 6-2 2-1 for Tomek. Tomek won 8 of the 11 games played.

For a retired match, the actual score isn’t 1 or 0: it’s each player’s share of the games played. This way, a result that stops early still counts, but only for what the players showed on court.

	Tomek B.	Marta Z.
Rating before	1300	1400
K-factor	48	48
Expected score	0.360	0.640
Actual score	8 / 11 = 0.727	3 / 11 = 0.273
Change	48 × (0.727 - 0.360) = +18	48 × (0.273 - 0.640) = -18
Rating after	1318	1382

In a match tiebreak format, a completed match tiebreak counts as one game for its winner.

Matches that don’t change ratings

• Walkovers. When a player doesn’t show up or withdraws before the match, nothing was played, so there’s nothing to rate. The match gets rating_status: not_rated, and neither rating nor confidence changes.
• Matches waiting to be rated. The API rates matches a few minutes after they’re submitted. Until then, the match has rating_status: pending.

See every change for yourself

Every change to a rating is recorded in the player’s rating history, with the reason and, for matches, every number used in the calculation. To reproduce a change from the API data, follow Explain a rating change.