Calculate your win/loss ratio and win rate from wins and losses, or how many wins you need to reach a target win rate from matches played and current WR.
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Calculator Functions
| Function | What it does | What it requires |
|---|---|---|
| Ratio and win rate | Finds the win/loss ratio and the win rate of a record | Requires the number of wins and the number of losses |
| Wins for target rate | Finds how many wins in a row lift a record to a target win rate | Requires the wins, the losses and the target win rate |
| Wins needed from matches and win rate | Finds how many wins in a row reach a target win rate when only the match count and current win rate are known | Requires the total matches played, the current win rate and the target win rate |
| Record from win rate | Finds the missing wins, losses or total games behind a win rate | Requires the win rate and one known count: total games, wins or losses |
The first two functions accept ties as an optional entry, with a choice of counting each tie as half a win, leaving ties out or giving them no win credit. The last two functions assume no ties. Results list the wins, losses, games counted, win rate and win/loss ratio, plus the ratio in lowest terms when the counts are whole numbers.
Win to Loss Ratio Formulas
| R | Win/loss ratio: wins for every loss |
| W | Number of wins |
| L | Number of losses |
Ratio and win rate
The wins are divided by the losses. A record of 15 wins and 5 losses has a ratio of 15 ÷ 5 = 3, or 3 : 1. With no losses the ratio is undefined, because nothing can be divided by zero. The win rate uses a different divisor, the number of games:
The same 15 and 5 record has a win rate of 15 ÷ 20 × 100 = 75%. A record of 239 wins and 240 losses has a ratio of 0.9958 and a win rate of 49.896%. Ties never change the win/loss ratio, but they change the win rate according to the setting chosen:
| Ties in win rate | Win rate formula | 9 wins, 6 losses, 1 tie |
|---|---|---|
| Half a win | (W + T ÷ 2) ÷ (W + L + T) × 100 | 59.375% |
| Exclude ties | W ÷ (W + L) × 100 | 60% |
| No win credit | W ÷ (W + L + T) × 100 | 56.25% |
The NFL counts a tie as half a win and half a loss [1]. Other leagues and games use other conventions, so the setting should match the record being compared.
Wins for target rate
n is the number of wins in a row needed, p is the target win rate as a decimal, G is the games counted and W is the wins, including any tie credit. The brackets round up to a whole win. From 10 wins and 10 losses, a 60% target takes (0.6 × 20 − 10) ÷ 0.4 = 5 more wins, which makes the record 15 of 25. A 100% target is rejected once any game has not been won.
Wins needed from matches and win rate
The current wins are worked out first as W = matches × current win rate ÷ 100, and the formula above is then applied. With 100 matches at a 65% win rate, a 70% target takes (0.7 × 100 − 65) ÷ 0.3 = 16.67, rounded up to 17 wins in a row, for 82 wins in 117 matches (70.085%).
Record from win rate
L = G − W
With the total games known, the wins are the win rate times the games and the losses are the rest: 100 games at 65% is 65 wins and 35 losses. With the wins known, G = W ÷ p, so 552 wins at 73.6% is 750 games and 198 losses. With the losses known, G = L ÷ (1 − p). A rounded win rate can give counts that are not whole numbers.
How to Calculate Win Loss Ratio and Win Rate
Count the wins and the losses over the same set of games. Divide wins by losses for the win/loss ratio. Divide wins by wins plus losses and multiply by 100 for the win rate, also called the win percentage. For 20 wins and 5 losses, the ratio is 20 ÷ 5 = 4 and the win rate is 20 ÷ 25 × 100 = 80%.
Limits of This Estimate
- The win/loss ratio is undefined with zero losses, and the win rate is undefined with no games counted.
- The wins-needed functions assume every added game is a win. Any loss along the way raises the number required.
- Record from win rate assumes no ties. A percentage that was rounded before it was entered gives an estimate of the record, not an exact count.
Sources
- National Football League, NFL Tiebreaking Procedures: a tie counted as half a win and half a loss
