There’s a new bonus-point system for CFC ratings. It’s supposed to counterbalance overall rating deflation (as strong players retire from the system and beginners join), it’s supposed to correct the artificial rating inflation of our strongest players (which was a problem under the old bonus-point system), and it’s supposed to push underrated juniors up to more accurate ratings faster. And this time, it’s been statistically tested.

**Paul Leblanc**, CFC ratings auditor, in an article in the July issue of *Canadian Chess News* (hopefully, you got the password in your email), provides three formulas to define the bonus system. I’ve given a brief smary of each one, below.

## A. Lifetime-High Bonus

**Formula**: BONUS 1 = Rmax BONUS × a × Ke

**Brief Summary**: The first bonus is simple. If you hit a lifetime rating high, before bonuses, you get an automatic bonus of 20 points. (But if your rating is over 2200, the bonus is only 10 points.)

**Explanation of the Formula**: “Rmax BONUS” is currently set at 20 (this and a few other constants have been tweaked using regression analysis); “a” is an on-off switch – it’s zero if you don’t qualify, 1 if you do; “Ke” is ½ for players over 2200, which is why they get only 10 points – it’s based on the ratio of “K factors”: 16/32 = ½.

## B. Rating-Jump Bonus

**Formula**: BONUS 2 = b × RATING CHANGE BONUS × (Rnew – Rold – THRESHOLD) × Ke

**Brief Summary**: The second bonus is a bit like overtime pay. There’s a “threshold” for rating jumps. The threshold is currently set at 13 times the square root of the number of rounds in the tournament – see table below.* Once your rating increase is over the threshold, the over-threshold part gets almost tripled.** (The actual factor is 2.75, or a bonus of 1.75 for every 1 point of over-threshold increase.) It’s like getting paid time and a half – or actually double time and three-quarters – for “overtime” rating increases.

**Explanation of the Formula**: “b” is zero if you didn’t hit the threshold; “RATING CHANGE BONUS” is 1.75; “Rnew – Rold” is the rating increase; “THRESHOLD” is Ke × 13 root n, where n is the number of rounds in the tournament; Ke, once again, is ½ for players over 2200.

Number of rounds | Threshold rating increase |
---|---|

4 | 26.0 |

5 | 29.1 |

6 | 31.8 |

7 | 34.4 |

8 | 36.8 |

9 | 39.0 |

**Notes – for players over 2200
*** Threshold levels are halved for players over 2200, which is only fair since their rating changes are halved; it just makes the targets comparable. (Those familiar with the rating system know that your K factor is reduced from 32 to 16 once you hit 2200).

** The bonus factor for players over 2200 is also halved, which seems a little unfair, but past bonus-point systems have disproportionately benefited top players. In this system, masters get less than double, not almost triple, their over-threshold increase (and the increases are already halved). Specifically, their factor is only 1.875 (1+0.875) instead of 2.75 (1+1.75).

## C. Total Bonus

**Formula**: TOTAL BONUS = BONUS 1 + BONUS 2

**Summary / Explanation**: You can get both bonuses.

## Examples:

Paul lays out three instructive examples:

### Example One:

Joe Bloggins, an experienced player (rated 1925) had a good result in a 6-round weekend Swiss, resulting in a natural (un-bonused) rating gain of 50 rating points. However, this didn’t take him over his all-time high, since his previous rating high (once upon a time) was 2075.

a. Lifetime-high Bonus

Sorry. If Joe didn’t hit an all-time high, he doesn’t get these 20 points.

b. Rating-jump bonus

The threshold for a 6-round event, for players under 2200, is about 32. Since Joe gained 50 rating points, his rating gain of 50 is broken down into 32 points of “normal increase,” plus an extra 18 points of “super increase.” These 18 super-points are almost tripled to 50 (18 * 2.75 = 50).

c. Total

His total increase gets bumped from 50 to 82 (32 + 50 = 82), so his new rating is 2007 (1925 + 82 = 2007).

*Note: The fact that he ended up with a 32-point bonus (82 – 50 = 32), while the threshold was also 32, is just a coincidence.
*

### Example Two:

Marie Morphy, an underrated junior (rated 1150), was in the same event as Joe. She had an annoyingly good result (&@%# underrated juniors!) defeating several established A-Class players and drawing two experts. She gained 80 rating points, taking her to a new personal high of 1230. But now the bonuses kick in:

a. Lifetime-high Bonus

20-point bonus for achieving a new lifetime high.

b. Rating-jump bonus

The rating-gain threshold for this event, just as for Joe Bloggins, was about 32. Since Marie’s rating gain exceeded the threshold, her 80-point increase is broken in two: 32 points of normal increase plus an extra 48 points of super increase. These 48 points are almost tripled to 132 (48 * 2.75 = 132).

c. Total

Her 80-point rating increase is bumped to 164 (32 + 132 = 164) under Bonus 2, plus she gets the 20-point bonus under Bonus 1, so her new rating is 1334 (1150 + 164 + 20 = 1334).

### Example Three:

Magnus Smith, a very strong player (rated 2600), won the 9-round Canadian Closed. He gained 25 rating points. (Keep in mind that rating increases for players over 2200 are halved.) However, he didn’t achieve a new lifetime high.

a. Lifetime-high Bonus

Nope. It would have been only 10 points, since he’s rated over 2200, but he didn’t hit a lifetime high, so he doesn’t get it.

b. Rating-jump bonus

Since the event had 9 rounds, the threshold is 39, but it’s reduced to 19.5 for players over 2200. His rating increase of 25 is broken down into 19.5 points of normal increase plus 5.5 points of super increase. These 5.5 points are almost doubled to 10.5 points (5.5*1.875=10.5)

c. Total

His 25-point rating increase is bumped to 30 points (19.5+10.5=30). Magnus’s new rating will be 2630 (2600 + 30 = 2630).

## Rationale and Testing

Roger Patterson’s rationale for and sample testing of the proposed (and now adopted) bonus-point system can be found at: Victoria Chess

Excellent article. Thanks for spreading the word. Paul

My rating shot up by 95pts after the Toronto International. I was expecting only ~50 points but I received some of those Bonus 1 and 2 bumps. I had a good tournament, but not sure if my new 2200+ rating is really deserved.

The CFC rating system is so messed up