Hong Life CalculatorsUnderstanding the rank ladder games-to-promote calculator — concept and principle
Ranked ladders in games such as League of Legends, Valorant or Overwatch award points for a win and take points for a loss. This calculator estimates how many games you need on average to gain a target number of points, given what you gain per win, what you lose per loss and your win rate. It also shows the break-even win rate, below which you drift down the ladder no matter how many games you play.
How it is calculated
- Net points per game (expected value) = p × gain − (1 − p) × loss, where p is your win rate as a decimal.
- Expected games = points needed ÷ net points per game, rounded up to a whole game. If the net value is zero or negative, the target is never reached on average.
- Break-even win rate = loss ÷ (gain + loss) × 100.
The principle
Each game is treated as an independent trial: with probability p you add the win amount, otherwise you subtract the loss amount. Averaging over many games gives the expected change per game, and the total grows roughly in a straight line with the number of games. Setting the expected value to zero and solving for p gives the break-even point: p × gain = (1 − p) × loss, so p = loss ÷ (gain + loss). When gains are larger than losses, the break-even rate falls below 50%; when losses are larger, you must win more than half your games just to stay level.
Worked example
- Inputs: 100 points needed, +22 per win, −18 per loss, 55% win rate.
- Net per game = 0.55 × 22 − 0.45 × 18 = 12.1 − 8.1 = 4 points.
- Expected games = 100 ÷ 4 = 25 games.
- Break-even win rate = 18 ÷ (22 + 18) × 100 = 45%.
| Your win rate (%) | Net points per game |
|---|---|
| 13.8 | -12.5 |
| 27.5 | -7 |
| 41.2 | -1.5 |
| 55 | 4 |
| 68.8 | 9.5 |
| 82.5 | 15 |
| 110 | 26 |
How to read the result
Expected games is an average, not a promise. Because results are random, the real path wanders: with a small edge such as +4 per game, streaks of losses can set you back for dozens of games, and the spread grows with the size of each gain and loss. The further your win rate is above break-even, the faster and more reliably you climb.
Common mistakes
- Entering the win rate from a handful of games; a 10-game sample is very noisy.
- Assuming points per win stay fixed; most systems adjust them as your rank and hidden rating converge.
- Forgetting promotion series, demotion shields or rank decay, which this model does not include.
Frequently asked questions
Why do I lose more points than I gain?
In most ranked systems this signals that your visible rank is above your hidden matchmaking rating; winning consistently usually brings the two back in line.
What win rate do I need to climb if gains and losses are equal?
Anything above 50%. With equal gains and losses the break-even rate is exactly half.
How many games until my win rate estimate is reliable?
Uncertainty shrinks with the square root of games played; after 100 games the standard error of a win rate near 50% is still about 5 percentage points.
Sources: Sheldon M. Ross, A First Course in Probability (expected value and random walks) · Arpad E. Elo, The Rating of Chessplayers, Past and Present