Parent DirectoryA team's rating is the average of its opponents' ratings plus 100 for a win or minus 100 for a loss. Wins that lower the rating and losses that raise the rating count one twentieth as much as the other games. Post-season games count double.
The ratings are calculated by setting everyone's rating to a default value based on division and then calculating the ratings using the above definition over and over again until they settle down. The default values used actually has no effect on the final ratings except for teams in those conferences that play no non-conference games.
For this example, we'll use the record of one such isolated conference--the New England Small College Athletic Conference (NESCAC) as of 10/23/99. Here are the game results. "Win" or "Loss" refers to how the team at the left did. Each game appears in the table twice.
At the time I worked out this example, the weight for wins that lower a rating and losses that raise a rating was one hundreth (0.01) rather than the current one twentieth (0.05).
| Amherst | Bates | Bowdoin | Colby | Hamilton | Middlebury | Trinity | Tufts | Wesleyan | Williams | |
| Amherst | Loss | Win | Win | Loss | Win | |||||
| Bates | Win | Loss | Loss | Loss | Loss | |||||
| Bowdoin | Loss | Win | Loss | Loss | Loss | |||||
| Colby | Loss | Win | Loss | Loss | Win | |||||
| Hamilton | Loss | Loss | Loss | Loss | Loss | |||||
| Middlebury | Win | Win | Win | Loss | Loss | |||||
| Trinity | Win | Win | Win | Win | Loss | |||||
| Tufts | Win | Win | Win | Loss | Loss | |||||
| Wesleyan | Loss | Win | Loss | Win | Win | |||||
| Williams | Win | Win | Win | Win | Win |
This is all the information needed to calculate the ratings. Other information, such as margin of victory, home field advantage or order of the games is not used in this system.
All the teams start with an initial rating of 360, the average rating for other Division III teams. Here's the first step rating calculation for Trinity:
Trinity, Conn. Oppon. Game
Opponent Result Rating Rating Weight Product
-------------- ------ ------ ------ ------ -------
Colby WIN 360.0 460.0 1.00 460.0
Williams LOSS 360.0 260.0 1.00 260.0
Hamilton WIN 360.0 460.0 1.00 460.0
Tufts WIN 360.0 460.0 1.00 460.0
Bowdoin WIN 360.0 460.0 1.00 460.0
===== =======
5.00 2100.0
2100.0
Trinity, Conn.'s rating = ------ = 420.0
5.00
The new estimate for Trinity's rating is not 420, however. The new estimate
is set at 390, half way between the old estimate (360) and this newly
calculated rating (420). This is done because the new rating calculation
tends to overestimate the change that should be made.
| step | Amherst | Bates | Bowdoin | Colby | Hamilton | Middlebury | Trinity | Tufts | Wesleyan | Williams |
| 0 | 360.0 | 360.0 | 360.0 | 360.0 | 360.0 | 360.0 | 360.0 | 360.0 | 360.0 | 360.0 |
| 1 | 370.0 | 330.0 | 330.0 | 350.0 | 310.0 | 370.0 | 390.0 | 370.0 | 370.0 | 410.0 |
| 2 | 370.0 | 324.0 | 320.0 | 346.0 | 286.0 | 378.0 | 402.0 | 372.0 | 368.0 | 434.0 |
Now, let's look at the calculation of Trinity's rating for the third step.
Trinity, Conn. Oppon. Game
Opponent Result Rating Rating Weight Product
-------------- ------ ------ ------ ------ -------
Colby WIN 346.0 446.0 1.00 446.0
Williams LOSS 434.0 334.0 1.00 334.0
Hamilton WIN 286.0 386.0 0.01 3.9
Tufts WIN 372.0 472.0 1.00 472.0
Bowdoin WIN 320.0 420.0 1.00 420.0
===== =======
4.01 1675.9
1675.9
Trinity, Conn.'s rating = ------ = 417.9
4.01
Even after adding the 100 points to Hamilton's rating for the win, the
game rating of 386 is below Trinity's rating of 402 at the end of step 2.
This means that averaging this game rating in with the others would lower
Trinity's rating. Games such as this where a win would lower the rating
(and the loss would raise the rating when Hamilton's rating is calculated)
are given a wieght of 0.01 in the average. Thus, there is a small lowering
of Trinity's rating for playing such a weak opponent.
The new estimate for Trinity's rating is set at 410, half way between the old estimate (402) and this newly calculated rating (417.9). After this step, the average rating for all ten teams was 360.7, so all ratings were reduced by 0.7 to keep the average rating at 360.
| step | Amherst | Bates | Bowdoin | Colby | Hamilton | Middlebury | Trinity | Tufts | Wesleyan | Williams |
| 3 | 367.9 | 322.4 | 313.1 | 342.7 | 268.2 | 382.5 | 409.3 | 371.9 | 363.7 | 458.1 |
| 4 | 366.3 | 321.9 | 308.7 | 340.4 | 254.1 | 386.7 | 415.2 | 373.7 | 360.2 | 472.7 |
| 5 | 365.4 | 322.3 | 304.0 | 338.9 | 240.2 | 389.9 | 422.4 | 377.1 | 357.4 | 482.5 |
| 6 | 363.7 | 322.2 | 299.0 | 336.7 | 231.0 | 391.4 | 427.2 | 379.7 | 355.5 | 493.5 |
| 7 | 362.2 | 322.3 | 295.3 | 335.4 | 216.4 | 392.8 | 431.5 | 381.0 | 354.3 | 508.7 |
| 8 | 361.0 | 322.4 | 291.1 | 335.2 | 207.3 | 393.1 | 436.2 | 381.8 | 353.6 | 518.4 |
| 9 | 359.7 | 322.2 | 287.2 | 335.1 | 200.5 | 392.8 | 442.3 | 382.1 | 352.9 | 525.2 |
| 10 | 358.5 | 321.8 | 284.0 | 334.7 | 195.2 | 392.3 | 447.0 | 382.6 | 352.2 | 531.6 |
| 12 | 356.5 | 321.1 | 278.2 | 333.6 | 187.9 | 391.2 | 454.6 | 384.2 | 351.1 | 541.7 |
| 14 | 354.6 | 320.6 | 273.3 | 332.3 | 182.0 | 390.1 | 460.8 | 387.1 | 349.9 | 549.4 |
| 16 | 352.8 | 320.3 | 269.4 | 331.0 | 177.3 | 389.0 | 466.0 | 389.8 | 348.8 | 555.5 |
| 18 | 351.3 | 320.0 | 266.4 | 329.8 | 173.6 | 388.0 | 470.4 | 392.2 | 347.7 | 560.6 |
| 20 | 350.0 | 319.8 | 263.9 | 328.6 | 170.7 | 387.0 | 474.1 | 394.3 | 346.7 | 564.8 |
| 25 | 347.5 | 319.2 | 259.5 | 326.2 | 165.6 | 385.0 | 481.1 | 398.2 | 344.7 | 572.9 |
| 30 | 345.7 | 318.7 | 256.8 | 324.5 | 162.6 | 383.6 | 485.8 | 400.7 | 343.2 | 578.3 |
| 35 | 344.5 | 318.3 | 255.0 | 323.4 | 160.7 | 382.6 | 488.9 | 402.4 | 342.2 | 581.9 |
| 40 | 343.7 | 318.1 | 253.9 | 322.6 | 159.4 | 381.9 | 491.0 | 403.5 | 341.5 | 584.3 |
| 45 | 343.2 | 317.9 | 253.2 | 322.0 | 158.7 | 381.4 | 492.4 | 404.3 | 341.0 | 585.9 |
| 50 | 342.9 | 317.8 | 252.7 | 321.6 | 158.1 | 381.1 | 493.3 | 404.8 | 340.7 | 587.0 |
| 60 | 342.5 | 317.6 | 252.2 | 321.2 | 157.6 | 380.7 | 494.4 | 405.3 | 340.3 | 588.2 |
| 70 | 342.3 | 317.6 | 252.0 | 321.0 | 157.3 | 380.5 | 494.8 | 405.6 | 340.2 | 588.7 |
| 80 | 342.2 | 317.5 | 251.9 | 321.0 | 157.2 | 380.5 | 495.0 | 405.7 | 340.1 | 589.0 |
| 90 | 342.2 | 317.5 | 251.8 | 320.9 | 157.2 | 380.4 | 495.1 | 405.7 | 340.1 | 589.1 |
| 100 | 342.1 | 317.5 | 251.8 | 320.9 | 157.2 | 380.4 | 495.1 | 405.7 | 340.0 | 589.1 |
| 120 | 342.1 | 317.5 | 251.8 | 320.9 | 157.1 | 380.4 | 495.2 | 405.7 | 340.0 | 589.2 |
At this point the ratings have stabilized and we have the final answer. The final rating calculations are:
Amherst Oppon. Game
Opponent Result Rating Rating Weight Product Effect
-------------- ------ ------ ------ ------ ------- ------
Bates LOSS 317.5 217.5 1.00 217.5 -124.6
Bowdoin WIN 251.8 351.8 1.00 351.8 +9.7
Middlebury LOSS 380.4 280.4 1.00 280.4 -61.7
Colby WIN 320.9 420.9 1.00 420.9 +78.8
Wesleyan WIN 340.0 440.0 1.00 440.0 +97.9
===== =======
5.00 1710.6
1710.6
Amherst's rating = ------ = 342.1
5.00
Bates Oppon. Game
Opponent Result Rating Rating Weight Product Effect
-------------- ------ ------ ------ ------ ------- ------
Amherst WIN 342.1 442.1 1.00 442.1 +124.6
Tufts LOSS 405.7 305.7 1.00 305.7 -11.8
Williams LOSS 589.2 489.2 0.01 4.9 +1.7
Wesleyan LOSS 340.0 240.0 1.00 240.0 -77.5
Middlebury LOSS 380.4 280.4 1.00 280.4 -37.1
===== =======
4.01 1273.2
1273.2
Bates's rating = ------ = 317.5
4.01
Bowdoin Oppon. Game
Opponent Result Rating Rating Weight Product Effect
-------------- ------ ------ ------ ------ ------- ------
Williams LOSS 589.2 489.2 0.01 4.9 +2.4
Amherst LOSS 342.1 242.1 1.00 242.1 -9.7
Tufts LOSS 405.7 305.7 0.01 3.1 +0.5
Hamilton WIN 157.1 257.1 1.00 257.1 +5.3
Trinity, Conn. LOSS 495.2 395.2 0.01 4.0 +1.4
===== =======
2.03 511.2
511.2
Bowdoin's rating = ------ = 251.8
2.03
Colby Oppon. Game
Opponent Result Rating Rating Weight Product Effect
-------------- ------ ------ ------ ------ ------- ------
Trinity, Conn. LOSS 495.2 395.2 0.01 4.0 +0.7
Middlebury LOSS 380.4 280.4 1.00 280.4 -40.5
Wesleyan WIN 340.0 440.0 1.00 440.0 +119.1
Amherst LOSS 342.1 242.1 1.00 242.1 -78.8
Hamilton WIN 157.1 257.1 0.01 2.6 -0.6
===== =======
3.02 969.1
969.1
Colby's rating = ------ = 320.9
3.02
Hamilton Oppon. Game
Opponent Result Rating Rating Weight Product Effect
-------------- ------ ------ ------ ------ ------- ------
Tufts LOSS 405.7 305.7 0.01 3.1 +1.5
Wesleyan LOSS 340.0 240.0 0.01 2.4 +0.8
Trinity, Conn. LOSS 495.2 395.2 0.01 4.0 +2.4
Bowdoin LOSS 251.8 151.8 1.00 151.8 -5.3
Colby LOSS 320.9 220.9 0.01 2.2 +0.6
===== =======
1.04 163.4
163.4
Hamilton's rating = ------ = 157.1
1.04
Middlebury Oppon. Game
Opponent Result Rating Rating Weight Product Effect
-------------- ------ ------ ------ ------ ------- ------
Wesleyan LOSS 340.0 240.0 1.00 240.0 -140.4
Colby WIN 320.9 420.9 1.00 420.9 +40.5
Amherst WIN 342.1 442.1 1.00 442.1 +61.7
Williams LOSS 589.2 489.2 0.01 4.9 +1.1
Bates WIN 317.5 417.5 1.00 417.5 +37.1
===== =======
4.01 1525.4
1525.4
Middlebury's rating = ------ = 380.4
4.01
Trinity, Conn. Oppon. Game
Opponent Result Rating Rating Weight Product Effect
-------------- ------ ------ ------ ------ ------- ------
Colby WIN 320.9 420.9 0.01 4.2 -0.7
Williams LOSS 589.2 489.2 1.00 489.2 -6.0
Hamilton WIN 157.1 257.1 0.01 2.6 -2.4
Tufts WIN 405.7 505.7 1.00 505.7 +10.6
Bowdoin WIN 251.8 351.8 0.01 3.5 -1.4
===== =======
2.03 1005.2
1005.2
Trinity, Conn.'s rating = ------ = 495.2
2.03
Tufts Oppon. Game
Opponent Result Rating Rating Weight Product Effect
-------------- ------ ------ ------ ------ ------- ------
Hamilton WIN 157.1 257.1 0.01 2.6 -1.5
Bates WIN 317.5 417.5 1.00 417.5 +11.8
Bowdoin WIN 251.8 351.8 0.01 3.5 -0.5
Trinity, Conn. LOSS 495.2 395.2 1.00 395.2 -10.6
Williams LOSS 589.2 489.2 0.01 4.9 +0.8
===== =======
2.03 823.7
823.7
Tufts's rating = ------ = 405.7
2.03
Wesleyan Oppon. Game
Opponent Result Rating Rating Weight Product Effect
-------------- ------ ------ ------ ------ ------- ------
Middlebury WIN 380.4 480.4 1.00 480.4 +140.4
Hamilton WIN 157.1 257.1 0.01 2.6 -0.8
Colby LOSS 320.9 220.9 1.00 220.9 -119.1
Bates WIN 317.5 417.5 1.00 417.5 +77.5
Amherst LOSS 342.1 242.1 1.00 242.1 -97.9
===== =======
4.01 1363.5
1363.5
Wesleyan's rating = ------ = 340.0
4.01
Williams Oppon. Game
Opponent Result Rating Rating Weight Product Effect
-------------- ------ ------ ------ ------ ------- ------
Bowdoin WIN 251.8 351.8 0.01 3.5 -2.4
Trinity, Conn. WIN 495.2 595.2 1.00 595.2 +6.0
Bates WIN 317.5 417.5 0.01 4.2 -1.7
Middlebury WIN 380.4 480.4 0.01 4.8 -1.1
Tufts WIN 405.7 505.7 0.01 5.1 -0.8
===== =======
1.04 612.7
612.7
Williams's rating = ------ = 589.2
1.04
New England Smalls
360 Ave. Rating /--Conference---\ /---Over-all----\ Perf
W L Pts Opp W L Pts Opp Rate
- - --- --- - - --- --- ----
Williams 5 0 146 31 5 0 146 31 589
Trinity, Conn. 4 1 105 44 4 1 105 44 495
Tufts 3 2 107 89 3 2 107 89 406
Middlebury 3 2 88 94 3 2 88 94 380
Amherst 3 2 82 71 3 2 82 71 342
Wesleyan 3 2 119 97 3 2 119 97 340
Colby 2 3 100 121 2 3 100 121 321
Bates 1 4 77 102 1 4 77 102 318
Bowdoin 1 4 42 128 1 4 42 128 252
Hamilton 0 5 74 163 0 5 74 163 157
David Wilson / dwilson@cae.wisc.edu