Elo Rating worksheet

1. Player A's new rating: 1,592.3

1. Work out player A's expected score from the rating gap, because a bigger gap means the stronger player should score more

   $\mathrm{E\_A}$$=\frac{1}{1+{10}^{\frac{\mathrm{1,450}-\mathrm{1,600}}{400}}}$$=\frac{1}{1+{10}^{\mathrm{-0.375}}}$$=0.703385$

2. Player B's expected score is the remainder, since the two always sum to 1

   $\mathrm{E\_B}$$=1-0.703385$$=0.296615$

3. Player A scored 0.5 (1 for a win, 0.5 for a draw, 0 for a loss); the change is K times (actual minus expected), so a bigger surprise moves the rating more

   $38\times \left(0.5-0.703385\right)$$=\mathrm{-7.72863}$

4. Add the change to player A's old rating

   $\mathrm{R\prime \_A}$$=\mathrm{1,600}+\left(\mathrm{-7.72863}\right)$$=\mathrm{1,592.27137}$

5. Player B scored 0.5; with the same K the change mirrors player A's

   $\mathrm{R\prime \_B}$$=\mathrm{1,450}+38\times \left(0.5-0.296615\right)$$=\mathrm{1,457.72863}$

2. Player A's new rating: 1,278.9

1. Work out player A's expected score from the rating gap, because a bigger gap means the stronger player should score more

   $\mathrm{E\_A}$$=\frac{1}{1+{10}^{\frac{\mathrm{1,375}-\mathrm{1,275}}{400}}}$$=\frac{1}{1+{10}^{0.25}}$$=0.359935$

2. Player B's expected score is the remainder, since the two always sum to 1

   $\mathrm{E\_B}$$=1-0.359935$$=0.640065$

3. Player A scored 0.5 (1 for a win, 0.5 for a draw, 0 for a loss); the change is K times (actual minus expected), so a bigger surprise moves the rating more

   $28\times \left(0.5-0.359935\right)$$=3.92182$

4. Add the change to player A's old rating

   $\mathrm{R\prime \_A}$$=\mathrm{1,275}+3.92182$$=\mathrm{1,278.92182}$

5. Player B scored 0.5; with the same K the change mirrors player A's

   $\mathrm{R\prime \_B}$$=\mathrm{1,375}+28\times \left(0.5-0.640065\right)$$=\mathrm{1,371.07818}$

3. Player A's new rating: 1,605.7

1. Work out player A's expected score from the rating gap, because a bigger gap means the stronger player should score more

   $\mathrm{E\_A}$$=\frac{1}{1+{10}^{\frac{\mathrm{1,300}-\mathrm{1,600}}{400}}}$$=\frac{1}{1+{10}^{\mathrm{-0.75}}}$$=0.84902$

2. Player B's expected score is the remainder, since the two always sum to 1

   $\mathrm{E\_B}$$=1-0.84902$$=0.15098$

3. Player A scored 1 (1 for a win, 0.5 for a draw, 0 for a loss); the change is K times (actual minus expected), so a bigger surprise moves the rating more

   $38\times \left(1-0.84902\right)$$=5.737223$

4. Add the change to player A's old rating

   $\mathrm{R\prime \_A}$$=\mathrm{1,600}+5.737223$$=\mathrm{1,605.737223}$

5. Player B scored 0; with the same K the change mirrors player A's

   $\mathrm{R\prime \_B}$$=\mathrm{1,300}+38\times \left(0-0.15098\right)$$=\mathrm{1,294.262777}$

4. Player A's new rating: 1,215.1

1. Work out player A's expected score from the rating gap, because a bigger gap means the stronger player should score more

   $\mathrm{E\_A}$$=\frac{1}{1+{10}^{\frac{\mathrm{1,160}-\mathrm{1,200}}{400}}}$$=\frac{1}{1+{10}^{\mathrm{-0.1}}}$$=0.557312$

2. Player B's expected score is the remainder, since the two always sum to 1

   $\mathrm{E\_B}$$=1-0.557312$$=0.442688$

3. Player A scored 1 (1 for a win, 0.5 for a draw, 0 for a loss); the change is K times (actual minus expected), so a bigger surprise moves the rating more

   $34\times \left(1-0.557312\right)$$=15.051404$

4. Add the change to player A's old rating

   $\mathrm{R\prime \_A}$$=\mathrm{1,200}+15.051404$$=\mathrm{1,215.051404}$

5. Player B scored 0; with the same K the change mirrors player A's

   $\mathrm{R\prime \_B}$$=\mathrm{1,160}+34\times \left(0-0.442688\right)$$=\mathrm{1,144.948596}$

5. Player A's new rating: 1,498.5

1. Work out player A's expected score from the rating gap, because a bigger gap means the stronger player should score more

   $\mathrm{E\_A}$$=\frac{1}{1+{10}^{\frac{\mathrm{2,000}-\mathrm{1,500}}{400}}}$$=\frac{1}{1+{10}^{1.25}}$$=0.05324$

2. Player B's expected score is the remainder, since the two always sum to 1

   $\mathrm{E\_B}$$=1-0.05324$$=0.94676$

3. Player A scored 0 (1 for a win, 0.5 for a draw, 0 for a loss); the change is K times (actual minus expected), so a bigger surprise moves the rating more

   $28\times \left(0-0.05324\right)$$=\mathrm{-1.490726}$

4. Add the change to player A's old rating

   $\mathrm{R\prime \_A}$$=\mathrm{1,500}+\left(\mathrm{-1.490726}\right)$$=\mathrm{1,498.509274}$

5. Player B scored 1; with the same K the change mirrors player A's

   $\mathrm{R\prime \_B}$$=\mathrm{2,000}+28\times \left(1-0.94676\right)$$=\mathrm{2,001.490726}$

6. Player A's new rating: 2,250.6

1. Work out player A's expected score from the rating gap, because a bigger gap means the stronger player should score more

   $\mathrm{E\_A}$$=\frac{1}{1+{10}^{\frac{\mathrm{1,575}-\mathrm{2,250}}{400}}}$$=\frac{1}{1+{10}^{\mathrm{-1.6875}}}$$=0.979878$

2. Player B's expected score is the remainder, since the two always sum to 1

   $\mathrm{E\_B}$$=1-0.979878$$=0.020122$

3. Player A scored 1 (1 for a win, 0.5 for a draw, 0 for a loss); the change is K times (actual minus expected), so a bigger surprise moves the rating more

   $32\times \left(1-0.979878\right)$$=0.643905$

4. Add the change to player A's old rating

   $\mathrm{R\prime \_A}$$=\mathrm{2,250}+0.643905$$=\mathrm{2,250.643905}$

5. Player B scored 0; with the same K the change mirrors player A's

   $\mathrm{R\prime \_B}$$=\mathrm{1,575}+32\times \left(0-0.020122\right)$$=\mathrm{1,574.356095}$

7. Player A's new rating: 1,597.9

1. Work out player A's expected score from the rating gap, because a bigger gap means the stronger player should score more

   $\mathrm{E\_A}$$=\frac{1}{1+{10}^{\frac{\mathrm{1,550}-\mathrm{1,600}}{400}}}$$=\frac{1}{1+{10}^{\mathrm{-0.125}}}$$=0.571463$

2. Player B's expected score is the remainder, since the two always sum to 1

   $\mathrm{E\_B}$$=1-0.571463$$=0.428537$

3. Player A scored 0.5 (1 for a win, 0.5 for a draw, 0 for a loss); the change is K times (actual minus expected), so a bigger surprise moves the rating more

   $30\times \left(0.5-0.571463\right)$$=\mathrm{-2.143894}$

4. Add the change to player A's old rating

   $\mathrm{R\prime \_A}$$=\mathrm{1,600}+\left(\mathrm{-2.143894}\right)$$=\mathrm{1,597.856106}$

5. Player B scored 0.5; with the same K the change mirrors player A's

   $\mathrm{R\prime \_B}$$=\mathrm{1,550}+30\times \left(0.5-0.428537\right)$$=\mathrm{1,552.143894}$

8. Player A's new rating: 1,600.5

1. Work out player A's expected score from the rating gap, because a bigger gap means the stronger player should score more

   $\mathrm{E\_A}$$=\frac{1}{1+{10}^{\frac{900-\mathrm{1,600}}{400}}}$$=\frac{1}{1+{10}^{\mathrm{-1.75}}}$$=0.982528$

2. Player B's expected score is the remainder, since the two always sum to 1

   $\mathrm{E\_B}$$=1-0.982528$$=0.017472$

3. Player A scored 1 (1 for a win, 0.5 for a draw, 0 for a loss); the change is K times (actual minus expected), so a bigger surprise moves the rating more

   $30\times \left(1-0.982528\right)$$=0.524163$

4. Add the change to player A's old rating

   $\mathrm{R\prime \_A}$$=\mathrm{1,600}+0.524163$$=\mathrm{1,600.524163}$

5. Player B scored 0; with the same K the change mirrors player A's

   $\mathrm{R\prime \_B}$$=900+30\times \left(0-0.017472\right)$$=899.475837$

9. Player A's new rating: 2,000.4

1. Work out player A's expected score from the rating gap, because a bigger gap means the stronger player should score more

   $\mathrm{E\_A}$$=\frac{1}{1+{10}^{\frac{\mathrm{1,200}-\mathrm{2,000}}{400}}}$$=\frac{1}{1+{10}^{\mathrm{-2}}}$$=0.990099$

2. Player B's expected score is the remainder, since the two always sum to 1

   $\mathrm{E\_B}$$=1-0.990099$$=0.009901$

3. Player A scored 1 (1 for a win, 0.5 for a draw, 0 for a loss); the change is K times (actual minus expected), so a bigger surprise moves the rating more

   $38\times \left(1-0.990099\right)$$=0.376238$

4. Add the change to player A's old rating

   $\mathrm{R\prime \_A}$$=\mathrm{2,000}+0.376238$$=\mathrm{2,000.376238}$

5. Player B scored 0; with the same K the change mirrors player A's

   $\mathrm{R\prime \_B}$$=\mathrm{1,200}+38\times \left(0-0.009901\right)$$=\mathrm{1,199.623762}$

10. Player A's new rating: 1,800.2

1. Work out player A's expected score from the rating gap, because a bigger gap means the stronger player should score more

   $\mathrm{E\_A}$$=\frac{1}{1+{10}^{\frac{900-\mathrm{1,800}}{400}}}$$=\frac{1}{1+{10}^{\mathrm{-2.25}}}$$=0.994408$

2. Player B's expected score is the remainder, since the two always sum to 1

   $\mathrm{E\_B}$$=1-0.994408$$=0.005592$

3. Player A scored 1 (1 for a win, 0.5 for a draw, 0 for a loss); the change is K times (actual minus expected), so a bigger surprise moves the rating more

   $34\times \left(1-0.994408\right)$$=0.190127$

4. Add the change to player A's old rating

   $\mathrm{R\prime \_A}$$=\mathrm{1,800}+0.190127$$=\mathrm{1,800.190127}$

5. Player B scored 0; with the same K the change mirrors player A's

   $\mathrm{R\prime \_B}$$=900+34\times \left(0-0.005592\right)$$=899.809873$