Elo rating difference to win probability table
Expected score for the higher-rated player at every 10-point rating gap from 0 to 800. The logistic column uses the standard Elo formula with a 400-point scale.[1] The FIDE column is FIDE's official lookup table 8.1.2.[2]
Want a value that isn't listed? Use the win probability calculator.
| Rating gap | Higher-rated expected | Lower-rated expected | Odds | FIDE table (H) |
|---|---|---|---|---|
| 0 | 50.0% | 50.0% | 1.00 : 1 | 50% |
| 10 | 51.4% | 48.6% | 1.06 : 1 | 51% |
| 20 | 52.9% | 47.1% | 1.12 : 1 | 53% |
| 30 | 54.3% | 45.7% | 1.19 : 1 | 54% |
| 40 | 55.7% | 44.3% | 1.26 : 1 | 56% |
| 50 | 57.1% | 42.9% | 1.33 : 1 | 57% |
| 60 | 58.5% | 41.5% | 1.41 : 1 | 58% |
| 70 | 59.9% | 40.1% | 1.50 : 1 | 60% |
| 80 | 61.3% | 38.7% | 1.58 : 1 | 61% |
| 90 | 62.7% | 37.3% | 1.68 : 1 | 62% |
| 100 | 64.0% | 36.0% | 1.78 : 1 | 64% |
| 110 | 65.3% | 34.7% | 1.88 : 1 | 65% |
| 120 | 66.6% | 33.4% | 2.00 : 1 | 66% |
| 130 | 67.9% | 32.1% | 2.11 : 1 | 68% |
| 140 | 69.1% | 30.9% | 2.24 : 1 | 69% |
| 150 | 70.3% | 29.7% | 2.37 : 1 | 70% |
| 160 | 71.5% | 28.5% | 2.51 : 1 | 71% |
| 170 | 72.7% | 27.3% | 2.66 : 1 | 72% |
| 180 | 73.8% | 26.2% | 2.82 : 1 | 74% |
| 190 | 74.9% | 25.1% | 2.99 : 1 | 75% |
| 200 | 76.0% | 24.0% | 3.16 : 1 | 76% |
| 210 | 77.0% | 23.0% | 3.35 : 1 | 77% |
| 220 | 78.0% | 22.0% | 3.55 : 1 | 78% |
| 230 | 79.0% | 21.0% | 3.76 : 1 | 79% |
| 240 | 79.9% | 20.1% | 3.98 : 1 | 80% |
| 250 | 80.8% | 19.2% | 4.22 : 1 | 81% |
| 260 | 81.7% | 18.3% | 4.47 : 1 | 82% |
| 270 | 82.6% | 17.4% | 4.73 : 1 | 83% |
| 280 | 83.4% | 16.6% | 5.01 : 1 | 84% |
| 290 | 84.1% | 15.9% | 5.31 : 1 | 84% |
| 300 | 84.9% | 15.1% | 5.62 : 1 | 85% |
| 310 | 85.6% | 14.4% | 5.96 : 1 | 86% |
| 320 | 86.3% | 13.7% | 6.31 : 1 | 87% |
| 330 | 87.0% | 13.0% | 6.68 : 1 | 88% |
| 340 | 87.6% | 12.4% | 7.08 : 1 | 88% |
| 350 | 88.2% | 11.8% | 7.50 : 1 | 89% |
| 360 | 88.8% | 11.2% | 7.94 : 1 | 90% |
| 370 | 89.4% | 10.6% | 8.41 : 1 | 90% |
| 380 | 89.9% | 10.1% | 8.91 : 1 | 91% |
| 390 | 90.4% | 9.6% | 9.44 : 1 | 91% |
| 400 | 90.9% | 9.1% | 10.00 : 1 | 92% |
| 410 | 91.4% | 8.6% | 10.59 : 1 | 92%* |
| 420 | 91.8% | 8.2% | 11.22 : 1 | 92%* |
| 430 | 92.2% | 7.8% | 11.89 : 1 | 92%* |
| 440 | 92.6% | 7.4% | 12.59 : 1 | 92%* |
| 450 | 93.0% | 7.0% | 13.34 : 1 | 92%* |
| 460 | 93.4% | 6.6% | 14.13 : 1 | 92%* |
| 470 | 93.7% | 6.3% | 14.96 : 1 | 92%* |
| 480 | 94.1% | 5.9% | 15.85 : 1 | 92%* |
| 490 | 94.4% | 5.6% | 16.79 : 1 | 92%* |
| 500 | 94.7% | 5.3% | 17.78 : 1 | 92%* |
| 510 | 95.0% | 5.0% | 18.84 : 1 | 92%* |
| 520 | 95.2% | 4.8% | 19.95 : 1 | 92%* |
| 530 | 95.5% | 4.5% | 21.13 : 1 | 92%* |
| 540 | 95.7% | 4.3% | 22.39 : 1 | 92%* |
| 550 | 96.0% | 4.0% | 23.71 : 1 | 92%* |
| 560 | 96.2% | 3.8% | 25.12 : 1 | 92%* |
| 570 | 96.4% | 3.6% | 26.61 : 1 | 92%* |
| 580 | 96.6% | 3.4% | 28.18 : 1 | 92%* |
| 590 | 96.8% | 3.2% | 29.85 : 1 | 92%* |
| 600 | 96.9% | 3.1% | 31.62 : 1 | 92%* |
| 610 | 97.1% | 2.9% | 33.50 : 1 | 92%* |
| 620 | 97.3% | 2.7% | 35.48 : 1 | 92%* |
| 630 | 97.4% | 2.6% | 37.58 : 1 | 92%* |
| 640 | 97.5% | 2.5% | 39.81 : 1 | 92%* |
| 650 | 97.7% | 2.3% | 42.17 : 1 | 99%* |
| 660 | 97.8% | 2.2% | 44.67 : 1 | 99%* |
| 670 | 97.9% | 2.1% | 47.32 : 1 | 99%* |
| 680 | 98.0% | 2.0% | 50.12 : 1 | 99%* |
| 690 | 98.2% | 1.8% | 53.09 : 1 | 99%* |
| 700 | 98.3% | 1.7% | 56.23 : 1 | 99%* |
| 710 | 98.3% | 1.7% | 59.57 : 1 | 99%* |
| 720 | 98.4% | 1.6% | 63.10 : 1 | 99%* |
| 730 | 98.5% | 1.5% | 66.83 : 1 | 99%* |
| 740 | 98.6% | 1.4% | 70.79 : 1 | 100%* |
| 750 | 98.7% | 1.3% | 74.99 : 1 | 100%* |
| 760 | 98.8% | 1.2% | 79.43 : 1 | 100%* |
| 770 | 98.8% | 1.2% | 84.14 : 1 | 100%* |
| 780 | 98.9% | 1.1% | 89.13 : 1 | 100%* |
| 790 | 99.0% | 1.0% | 94.41 : 1 | 100%* |
| 800 | 99.0% | 1.0% | 100.00 : 1 | 100%* |
* For players rated below 2650, FIDE counts any gap above 400 as 400, so the expected score stays at 92%. For players rated 2650 and above, FIDE uses the real gap. The table then reaches 99% at 620–735 points and 100% above 735.[2]
How close is FIDE's table to the formula?
For gaps up to 400, FIDE's table and the logistic formula above never differ by more than 1.2 percentage points. That's our own comparison of the two columns. FIDE's table is rounded to whole percentages, so small gaps of 0–3 points all show 50%.
FIDE table 8.1.2 as published
| Rating gap | Higher (H) | Lower (L) |
|---|---|---|
| 0–3 | 0.50 | 0.50 |
| 4–10 | 0.51 | 0.49 |
| 11–17 | 0.52 | 0.48 |
| 18–25 | 0.53 | 0.47 |
| 26–32 | 0.54 | 0.46 |
| 33–39 | 0.55 | 0.45 |
| 40–46 | 0.56 | 0.44 |
| 47–53 | 0.57 | 0.43 |
| 54–61 | 0.58 | 0.42 |
| 62–68 | 0.59 | 0.41 |
| 69–76 | 0.60 | 0.40 |
| 77–83 | 0.61 | 0.39 |
| 84–91 | 0.62 | 0.38 |
| 92–98 | 0.63 | 0.37 |
| 99–106 | 0.64 | 0.36 |
| 107–113 | 0.65 | 0.35 |
| 114–121 | 0.66 | 0.34 |
| 122–129 | 0.67 | 0.33 |
| 130–137 | 0.68 | 0.32 |
| 138–145 | 0.69 | 0.31 |
| 146–153 | 0.70 | 0.30 |
| 154–162 | 0.71 | 0.29 |
| 163–170 | 0.72 | 0.28 |
| 171–179 | 0.73 | 0.27 |
| 180–188 | 0.74 | 0.26 |
| 189–197 | 0.75 | 0.25 |
| 198–206 | 0.76 | 0.24 |
| 207–215 | 0.77 | 0.23 |
| 216–225 | 0.78 | 0.22 |
| 226–235 | 0.79 | 0.21 |
| 236–245 | 0.80 | 0.20 |
| 246–256 | 0.81 | 0.19 |
| 257–267 | 0.82 | 0.18 |
| 268–278 | 0.83 | 0.17 |
| 279–290 | 0.84 | 0.16 |
| 291–302 | 0.85 | 0.15 |
| 303–315 | 0.86 | 0.14 |
| 316–328 | 0.87 | 0.13 |
| 329–344 | 0.88 | 0.12 |
| 345–357 | 0.89 | 0.11 |
| 358–374 | 0.90 | 0.10 |
| 375–391 | 0.91 | 0.09 |
| 392–411 | 0.92 | 0.08 |
| 412–432 | 0.93 | 0.07 |
| 433–456 | 0.94 | 0.06 |
| 457–484 | 0.95 | 0.05 |
| 485–517 | 0.96 | 0.04 |
| 518–559 | 0.97 | 0.03 |
| 560–619 | 0.98 | 0.02 |
| 620–735 | 0.99 | 0.01 |
| > 735 | 1.00 | 0.00 |
Score to rating difference (dp), for performance ratings
FIDE uses table 8.1.1 (repeated as 1.4.9 in the title regulations) to turn a fractional score p into a rating difference dp, so that Rp = Ra + dp.[3] Scores below 0.50 use the same values with a minus sign. For example, p = 0.30 gives −149.
| p | dp | p | dp | p | dp |
|---|---|---|---|---|---|
| 1.00 | 800 | 0.83 | 273 | 0.66 | 117 |
| 0.99 | 677 | 0.82 | 262 | 0.65 | 110 |
| 0.98 | 589 | 0.81 | 251 | 0.64 | 102 |
| 0.97 | 538 | 0.80 | 240 | 0.63 | 95 |
| 0.96 | 501 | 0.79 | 230 | 0.62 | 87 |
| 0.95 | 470 | 0.78 | 220 | 0.61 | 80 |
| 0.94 | 444 | 0.77 | 211 | 0.60 | 72 |
| 0.93 | 422 | 0.76 | 202 | 0.59 | 65 |
| 0.92 | 401 | 0.75 | 193 | 0.58 | 57 |
| 0.91 | 383 | 0.74 | 184 | 0.57 | 50 |
| 0.90 | 366 | 0.73 | 175 | 0.56 | 43 |
| 0.89 | 351 | 0.72 | 166 | 0.55 | 36 |
| 0.88 | 336 | 0.71 | 158 | 0.54 | 29 |
| 0.87 | 322 | 0.70 | 149 | 0.53 | 21 |
| 0.86 | 309 | 0.69 | 141 | 0.52 | 14 |
| 0.85 | 296 | 0.68 | 133 | 0.51 | 7 |
| 0.84 | 284 | 0.67 | 125 | 0.50 | 0 |
Use the performance rating calculator to apply it.
Sources
- Glickman, M. E. & Doan, T. The US Chess Rating System (specification dated 2026-04-06), sections 3 and 4.2 — US Chess Federation
- FIDE Rating Regulations, effective 1 March 2024 (with the 400-point rule as amended from 1 October 2025), sections 7–8 — FIDE Handbook
- FIDE Title Regulations, effective 1 January 2024, sections 1.4.6–1.4.9 — FIDE Handbook