All about the USCF rating system (and how to manipulate it)

Hi all!

If you've been following me for a while, you'd realize something about me: I suck at chess. But do you know what I don't suck so much at? Math. I'd like to address things I've realized about the ELO rating system and how you can use it to your advantage.

*note: this is not a blog about improving your chess. it is about how you could possibly increase your rating without actually improving. if you can improve, that's an extra plus.

Without further ado

I. Rating inflation (or deflation?) and where do rating points come from?

If you've looked at ratings from a while ago (even since the 1970's) player's ratings haven't really moved up while their playing strength has undoubtedly increased. So why is that?

Well, almost everyone has always been improving at chess while their ratings don't necessarily move up with their strength. It just matters how much you improve RELATIVE to your opponents in your area. 

So why do younger players go up more than older players (on average)?

To understand this, we must look into the mind of a young 1 year-old prodigy. This prodigy became a WM (womb master) before they were even born. (jk lol) Basically younger peoples' brains are more receptive to learning and they improve faster. Here's a scientific article if you would like to learn more: https://www.sciencedaily.com/releases/2017/12/171221122925.htm

So wait a sec: If older players' ratings stay the same and younger players' ratings improve, where are these mysterious rating points come from? The Elo system is a zero-sum game.

According to my research, there are two possible sources:

1. Rating Floors

If a player has played for a while, they may have a rating floor. The rating floor is defined as 200 points below a player's peak rating (rounded to the nearest 100). Over time, if a player gets worse then 200 points below their peak, they may still have a floor e.g. a previous NM with a rating floor of 2000 who plays like a 1800. However, they can't go below 2000, so this means free rating point for everyone else! Hooray!

2. Rating bonuses:

"So for a 4 round tournament, you must gain more than 20 rating points in order to trigger bonus points. Suppose for a moment that you are rated 1900. Since the K factor for a 1900 in a 4 round tournament is also 20 (average between 1800 and 2000 in Table 2), you would need to score 1.0 higher than your expected score to barely trigger bonus points. If you don't meet this threshold, nothing happens (bonus points are only added, and never subtracted)."

"How do you know that you have triggered bonus points? Essentially, you need to perform considerably better than your rating would predict. For a 1900 player in a 4 round event, that means scoring more than 1.0 higher than your expected score for the tournament. Generally, it becomes easier to score bonus points for lower rated players, and harder as you approach master level, because of how the K factor varies with rating. Also, it becomes easier to score bonus points in longer tournaments (more games played)."

http://www.fpawn.com/uscfrating.html

Let's recap:

Tip #1:

Play in longer tournaments in order to induce a bonus. Bonuses are always added and never subtracted, creating free rating points. 

Now that we know that rating points are created and never destroyed, we can say that there is rating inflation although most people are improving. If you improve with the norm, your rating should go up slightly over time.

II: Living in different areas:

I know this is a hard one to measure, but basically try to play in an area where the players are playing below their rating. Here's my results based on my limited chess experience:

Northern Californian players play ~100 points above their rating. (meaning i think i should be 2000, this is reflected in my 2100 performance rating in the "averaged out" national open)

Texans play about their rating strength.

East Coast and New York players (I play them online and once when i played piano in Carnegie hall) play ~100 points above their strength.

What do the East and West coasts have in common that other states don't?

Population density.

Texas has about an average population density in line with the rest of the USA. California is about 2x as dense and the east coast as well (i think). You can read other people's opinions on this topic here: https://chess.stackexchange.com/questions/15889/difficulty-of-attaining-uscf-rating-in-different-states

So here's tip #2:

Tip #2:

If you can, try to play in an area (maybe even in your state!) where the population density is lower and where there are older (no offense) players.

III: The formulas (and how you can beat them)

The Elo rating system is defined as this: (all pics taken from https://www.youtube.com/watch?v=AsYfbmp0To0)

But how do you calculate the expected score? Well luckily, here’s the formula and visuals:

Haha! I don’t think you knew that it was a bell curve! The area to the left is the probability of winning, and to the right is the probability of the higher rated opponent winning. In case you haven’t realized, the other end of the bell curve should also have a 0. 

Here’s an example provided in the video:

sorry that was the formula. Here’s the example

Player A increases 21 points with this win, and player B loses 21 points.

Now idk about you, but I see 1656's beating 1763's almost as much as the other way around. This has happened in many tournaments as well.

If we calculate the win/loss percentage as if both ratings were the same, then the change is 16.

32(1 - 0.5) = 16

But the scenario above happens just as much and is just as likely. Soooo...

21-16 = 5

YOU CAN MAKE AN EXTRA 5 RATING POINTS

ok that might not seem like a lot, but yeah.

Even a draw results in

32(0.5 - 0.35) = 32*0.15 = 4.8

WAIT YOU CAN MAKE 5 RATING BY JUST DRAWING?

What if you lose?

32(0 - 0.35) = -11.2

YOU ONLY LOSE 11 IF YOU LOSE AND THE UPSIDE IS 2X THE DOWNSIDE?

Exactly. You get my point- this is rigged.

Which leads me to tip #3:

Tip #3:

Play up a section if possible. The system is rigged in your favor - and so is the risk-reward ratio. 

TL;DR

1. Play up

2. Play long tournaments with many rounds

3. Play in a rural area where there are preferably older players

Thanks for reading!