# Examples of Point Changes

This page gives examples of point changes for various scenarios. See How the Rating System Works for an explanation of how the rating system works and the terminology used below. The example categories are

- Point Changes for One Match
- Small Point Changes May Just Reflect Opportunity
- Effect of League Grouping
- Same Players Playing Two Matches
- Not Playing as a Way to Gain Points

## Point Changes for One Match

The number of points gained or lost in a single match depends on both the ratings (means) of the two players and on their standard deviations. Ignoring the standard deviations when looking at point changes is a frequent cause of confusion. The larger the standard deviation of a player’s rating, the less sure we are of the player’s playing strength, and so a single match result should have more effect, i.e., the match should be given more weight. Conversely, the smaller a player’s standard deviation, the surer we are of the player’s playing strength, and so a single match should have less effect.

The standard deviation takes into account how many results we have for a player, how informative each was (win or loss, opponent’s rating and standard deviation), how long ago each was, and any prior information (about the player or the subpopulation that the player is from).

While the website displays ratings with a plus/minus (±) sign before the standard deviation, this does not mean that the player’s playing strength must be within one standard deviation of the mean. While it is likely that the player’s playing strength is within one standard deviation, it might be as much as two (or rarely three) standard deviations from the mean.

This section contains examples of point changes for a single match. Keeping the preceding comments in mind should make the values in the tables agree with your intuition.

The tables give the points gained or lost by player P when player P plays player Q. The values in blue with the plus signs (+) are the number of points P gains if P wins the match, and the values in red with the minus signs (−) are the number of points P loses if P loses the match.

P’s Rating | Q’s Rating | |||
---|---|---|---|---|

500±30 | 500±50 | 500±100 | 500±200 | |

1500±30 | +0 −13 | +0 −13 | +0 −13 | +0 −13 |

1500±50 | +0 −37 | +0 −37 | +0 −37 | +0 −36 |

1500±100 | +0 −149 | +0 −149 | +0 −149 | +0 −138 |

1500±200 | +0 −577 | +0 −573 | +0 −550 | +0 −435 |

P’s Rating | Q’s Rating | |||
---|---|---|---|---|

1000±30 | 1000±50 | 1000±100 | 1000±200 | |

1500±30 | +0 −13 | +0 −13 | +0 −13 | +0 −9 |

1500±50 | +0 −37 | +0 −37 | +0 −36 | +0 −25 |

1500±100 | +0 −146 | +0 −145 | +1 −135 | +2 −90 |

1500±200 | +7 −405 | +8 −396 | +9 −360 | +15 −264 |

P’s Rating | Q’s Rating | |||
---|---|---|---|---|

1300±30 | 1300±50 | 1300±100 | 1300±200 | |

1500±30 | +1 −12 | +1 −12 | +1 −10 | +1 −5 |

1500±50 | +2 −33 | +3 −32 | +3 −26 | +4 −15 |

1500±100 | +12 −107 | +13 −102 | +14 −85 | +15 −54 |

1500±200 | +59 −239 | +59 −234 | +59 −214 | +57 −163 |

P’s Rating | Q’s Rating | |||
---|---|---|---|---|

1500±30 | 1500±50 | 1500±100 | 1500±200 | |

1500±30 | +6 −6 | +6 −6 | +5 −5 | +3 −3 |

1500±50 | +16 −16 | +15 −15 | +13 −13 | +8 −8 |

1500±100 | +52 −52 | +50 −50 | +44 −44 | +32 −32 |

1500±200 | +136 −136 | +134 −134 | +126 −126 | +104 −104 |

P’s Rating | Q’s Rating | |||
---|---|---|---|---|

1700±30 | 1700±50 | 1700±100 | 1700±200 | |

1500±30 | +12 −1 | +12 −1 | +10 −1 | +5 −1 |

1500±50 | +33 −2 | +32 −3 | +26 −3 | +15 −4 |

1500±100 | +107 −12 | +102 −13 | +85 −14 | +54 −15 |

1500±200 | +239 −59 | +234 −59 | +214 −59 | +163 −57 |

P’s Rating | Q’s Rating | |||
---|---|---|---|---|

2000±30 | 2000±50 | 2000±100 | 2000±200 | |

1500±30 | +13 −0 | +13 −0 | +13 −0 | +9 −0 |

1500±50 | +37 −0 | +37 −0 | +36 −0 | +25 −0 |

1500±100 | +146 −0 | +145 −0 | +135 −1 | +90 −2 |

1500±200 | +405 −7 | +396 −8 | +360 −9 | +264 −15 |

P’s Rating | Q’s Rating | |||
---|---|---|---|---|

2500±30 | 2500±50 | 2500±100 | 2500±200 | |

1500±30 | +13 −0 | +13 −0 | +13 −0 | +13 −0 |

1500±50 | +37 −0 | +37 −0 | +37 −0 | +36 −0 |

1500±100 | +149 −0 | +149 −0 | +149 −0 | +138 −0 |

1500±200 | +577 −0 | +573 −0 | +550 −0 | +435 −0 |

You may be wondering why the points gained decreases as the opponent’s standard deviation increases. Suppose P is 1500±50. Let Q1 be 1500±30. Let Q2 be 1500±200. P will gain more points for beating Q1 than for beating Q2. Now, Q2 might be 1700, but might only be 1300. P should gain more points if Q2 is really 1700, and less points if Q2 is really 1300. So, you might think this would average out to the same point change as when P beats Q1. The key to understanding what is happening is to realize that Q2 lost to P. So, it is more likely that Q2 is 1300 than that they are 1700. So, Q1 is probably a stronger player than is Q2. So, P gains more points for beating Q1 than for beating Q2.

You may find it curious that a 1500±50 player gains the same number of points beating a 2000±30 player as they do beating a 2500±30 player. But, with a standard deviation of 50, P’s previous results have convinced us that P can’t be more than about 1600, so we are just as surprised when P beats a 2500 player as when P beats a 2000 player. While we adjust our estimate, we are not going to throw out all of P’s previous results because of one win.

The examples on this page assume that the player laws are normal. While a player’s very first law is normal, after that it will be only approximately normal (i.e., approximately bell shaped). In particular, the jump process in the temporal update is not normal and can have a significant effect on point changes (which is why it is part of the model). Also, ratings and standard deviations are rounded to the nearest integer when displayed on the website. For these reasons, actual point changes will probably be different from the examples on this page, even if the players’ ratings and standard deviations appear to be identical to those in the tables.

You can calculate examples like the ones above using the Punkteänderung im NewTTRS nach einem Spiel webpage.

## Small Point Changes May Just Reflect Opportunity

Suppose you are 1500±50, and suppose you are playing at the 1500 level. If you go to a tournament and play two 1600±50 players, you will probably lose both matches and lose 13 points. On the other hand, if you go to a tournament and play two 1400±50 players, you will probably win both matches and gain 13 points. However, playing the 1600 players, you might have won both matches, and so had the opportunity to gain 45 points. But, playing the 1400 players and winning, although you gained 13 points, you had no opportunity to gain more (and could have lost 45 points if you had lost both matches).

Don’t obsess over small point changes. Just play your best, and let the ratings take care of themselves.

## Effect of League Grouping

For leagues, event directors have some flexibility in how they group matches into events. In particular, an event director may submit each week of a weekly league as an individual event or may combine several weeks into one event. This section gives an example to show how different choices can produce different ratings. (See the Cantor User’s Manual, Chapter 5, Section 1, “Multiple-Day Events”, for a discussion of the options.)

The example is for a player who has significantly improved since the previous season and is now beating higher-rated players. Suppose the following: The player plays in a weekly league. The season is four consecutive weeks. The player plays one match each week and wins the match. The four opponents are different players. At the beginning of the league season, the player is 1500±75 and the four opponents are all 1700±75.

In one scenario, each week is submitted as an individual event. In the other scenario, the four weeks are submitted as a single combined event (arbitrarily using the middle of the four weeks as the event date). The table gives the ratings of the player and opponents at the end of the four-week season.

Scenario | Player | Opponent 1 | Opponent 2 | Opponent 3 | Opponent 4 |
---|---|---|---|---|---|

Individual events | 1669±62 | 1641±72 | 1648±71 | 1654±71 | 1659±70 |

Combined event | 1673±65 | 1660±71 |

The two scenarios produce similar results for the player who improved. But in the combined scenario, all of the opponents have the same rating and this rating is higher than their ratings in the individual scenario, especially for the opponents who play the player in the earlier weeks. This is because information in the rating system only flows forward in time. In particular, the player’s subsequent wins do not affect the rating of the earlier opponents.

## Same Players Playing Two Matches

After an event is processed, the rating system no longer remembers which opponents a player played. So, if two players play each other more than once, the system will calculate slightly different ratings if the matches are in the same event than if they are in different events. This might happen if your club plays matches on several days a week or over several weeks where there is a choice as to how to group the matches into events.

Suppose the following: The player plays the opponent twice and wins both matches. Both players are 1500±75. The table gives the ratings of the player and opponent after the two matches.

Scenario | Player | Opponent |
---|---|---|

Individual events | 1547±65 | 1453±65 |

Combined event | 1544±67 | 1456±67 |

The combined event produces less change in the player’s and opponent’s ratings because there is less information playing one opponent twice than playing two different opponents. But, the effect is not large.

## Not Playing as a Way to Gain Points

If your standard deviation is larger, you gain more points when you win a match. However, it does not follow that waiting for your standard deviation to increase (i.e., not playing) is an effective strategy to increase your rating.

To see why not playing does not help, consider an example: Suppose that you currently are rated 1500, and you think that soon you will be playing at the 1700 level. Suppose that there are two tournaments that you are considering entering: one in six months and another in twelve months. What should you do to increase your rating the most? Should you enter both tournaments? Or, should you skip the first tournament to give your standard deviation more time to increase? (Of course, if you enter neither, then your rating will still be 1500, so that won’t accomplish your goal.)

Suppose that you think that in six months you will still be only playing at the 1500 level. Then you should probably skip the first tournament. But, this is true for any rating system that uses historical information: you shouldn’t play when you are not at your best. And, every rating system must use historical information in some way.

So, suppose that you think that in six months you will be playing at the 1700 level. Should you skip the first tournament? This is a fair question. (It is also very relevant since most players believe that they are currently under-rated!)

Assuming that you do play at the 1700 level in both tournaments, your rating will be higher after the second tournament if you play both than if you only play one.

Here is a numerical example: Suppose you are 1500±75 now. Suppose in the tournament in one year, you beat a 1500±75 player. Suppose that if you play the tournament in six months, you beat another 1500±75 player in that tournament. (Since we are assuming that you will be playing at the 1700 level in both tournaments, it is very likely that you will beat opponents who are 1500.) The table gives your ratings under the two scenarios:

Scenario | First Tournament | Second Tournament | ||
---|---|---|---|---|

Before | After | Before | After | |

Skip first tournament | 1507±109 | 1559±99 | ||

Play first tournament | 1503±94 | 1545±86 | 1548±103 | 1586±96 |

Therefore, there is no advantage to not playing. In other words, you cannot game the system by not playing. Just get out there and play, and the ratings will take care of themselves.