Analogy: Elo and bowling average

All Things Chess
1

I’ve been looking for a quick way to explain ratings to non chess players.

What chess rating would place you in the same relative peer group as a bowler with a 200 average? Is there a reasonable “conversion” formula? It seems Rating / 10 is close but maybe too optimistic. I haven’t bowled since the late '60s but I’d guess a 2200 player might equate to a bowler sporting a 200 average.

(Yes, I know this is kinda like asking how does having a PhD map to being really tall, but…)

(edited to correct “Rating * 10” to “Rating / 10”)

2

What percentage of league bowlers have a 200 (or higher) average? That might be comparable to what percentage of adult chess players have a XXXX (or higher) rating on the distribution of ratings from the 2012 annual rating list. See BINFO 201200327.

For example, suppose that 20% of adult league bowlers have a 200 or higher average. Then that might make them roughly comparable to 1900 players, since 20% of active adult players on the 2012 ratings list have a rating of 1892 or higher. (And if I limit it to those with established ratings, then 20% of active adult players have a rating of 1951 or higher.)

3

Not all bowling lanes are created equal. Some are more difficult than others. I never bowled above a 125 in my life until I became an alternate on my work bowling team and started regularly bowling above 150 (with a high of 212). Part of it was the increased practice. Most of it wasn’t.

Of course, some might say not all USCF ratings are created equal either.

4

Yeah, I did a little Googling on this and found that newer technologies of lane maintenance and ball construction have caused a massive inflation in bowling averages. So, if you bowl in an older alley with old bowling balls, you won’t do as well.

Anyway, it looks as if my guestimate of (rating / 10) being comparable to a bowling average wasn’t wildly off the mark.

5

This is a very good question. To non-players, a chess rating is just some number. Is it good or bad? They wouldn’t know, unless there was an easily understood comparison to match it against.

A bowling average has the advantage of having an absolute maximum of 300. If someone has a 300 average, they are obviously better than someone with only a 125 average. All that a non-bowler needs to know is that a perfect game is 300. The difference between bowlers becomes easy to see.

A baseball player with a .390 batting average after 500 at bats is clearly better than one who is only .190.

If there are 50,000 rated chess players, why not call the top rated player #1? Number 100 would be 100. Number 2876 would be #2876, etc., etc. Or, use a percentile rating. A news story could say that a local player was “in the top 5% of all tournament players in America.” Instead of having to say “a rating of 2104”, which is a meaningless number unless you include a lengthy explanation about ratings.

There must be some way to explain relative playing strength to non-players that would be easily understood.

6

George, we do rank active chess players at msa.uschess.org. (You aren’t ranked there because you are considered inactive, as your last tournament was in 2007.)

7

GM = great white shark
Master = tiger shark
Class A= barracuda
Class C = catfish
Class E= goldfish
U600 = guppy

8

From time to time I’ve seen some kind of percentile attached to ratings like a yearbook or annual ratings.

My attempt to explain ratings start with a simple difference between established players who have ratings of 1500 and 1700 and the higher player is expected to score 75% against the lower player. The higher player picks up 8 points for a win, loses 8 points for a draw, or 24 points for a loss to the lower player. If the players meet frequently with results like win/draw/win/draw or win/win/win/loss, neither player’s rating will change.

Yes, but what about an unrated player. Suppose someone plays five rated games against a field whose average rating is 1500 and scores 2 points. That would be a fantastic result for someone whose rating was 800 but would be a disaster for someone whose rating was 2200. Somewhere between those extremes there is a rating that wouldn’t change for that result–that’s a little better than a 1400 would be expected to do and somewhat worse than a 1500 player would expect. That number, about 1420, would be a provisional rating given to the new player, based on 5 games. If the player performed at a 1580 level in his next five games, he would then have a provisional rating of 1500 based on 10 games. After 25 games, a player’s rating becomes established.

9

(I’ve had 2 sanctioned 300 games /thread started about bowlers vs chess players)
My somewhat related question:
USChess.org shows me as 1735/5. I played more than 5 rated tournament games.
But I’m 68 and it’s been 40 years since my last tournament and that was in Canada.
If I entered a tournament now, would it be as a 1735 or unrated/provisional player?

10

Once rated, always rated. Since FIDE has no record of you having a rating (not surprising if you haven’t played in 40 years), there would be no adjustment to that rating. If your rating is based on five games, then you would be provisional, but many/most tournaments don’t discriminate based on that.

Alex Relyea

11

Bowling’s a bit of a different rating problem than chess. A bowling game results in a score 0-300. It would make sense for one’s bowling rating to be expressed as a number in the same range, something like your expected bowling score. So you can use half of our chess rating machinery, which we really didn’t invent, and you don’t need the other half which is more specific to chess and similarly scored games.

A chess game results in a score: 0, 0.5 or 1. But it makes all the difference who that result was achieved against. You’re not playing an unchanging (or nearly unchanging, standardized at least) setup of bowling ball, lane and pins. You’re playing an opponent. So we have to convert your game score to a performance rating. That’s easy if the game was a draw: the performance rating is the opponent’s rating. If you drew against a 1500, that’s a 1500 performance. Assigning performance ratings to wins and losses requires a few more assumptions.

Then once you have those performance ratings, you use them to update your old rating to a new rating. It’s an AutoRegressive (AR) stochastic process:

Rn = (1-a) Ro + a Rp

where Rp = performance rating
Ro = old rating
Rn = new rating.

where a is a “speed” factor, 0<a<1 . OK that’s the Elo chess rating system, which is simple and is still close to our current USCF rating system and all the other important ones I know of including FIDE.

(Rant: chess rating literature is not usually expressed this way, but in some other way that makes it appear separate from the rich literature on statistics, econometrics, stochastic processes and control and stability theory. That is our failing imho, definitely not theirs.)

You could use the same autoregressive idea for bowling ratings, but it’s simpler because you use bowling scores directly:

Rn = (1-a) Ro + a Rp

where Rp = latest bowling game score
Ro = old rating
Rn = new rating.

where again 0<a<1 .

This will behave well in that it will ensure that the ratings stay in the 0 - 300 range. It might have some undesired behavior at the extremes: is bowling a 270 and a 290 equivalent to bowling two 280’s ? In other words, is the quality increase (however you choose to define “quality” intuitively) from 270 to 280 the same as from 280 to 290 ? But these are essentially matters of interpretation. At the gross level, this AR system will work satisfactorily.

12

I used to use this same analogy to explain ratings to my students and others who were non-chessplayers. I would mention that bowling averages were eqivalant to chess ratings when you multipied the bowling average by 10. I would start by mentioning the 150 bowler and compare this person to a 1500 player (I did this back in the days when the 1500 player was average). I then went on to say that no bowler (other than a cartoon character) had a 300 bowling average and there were no 3000 rated players ( Nakamura & Carlsen are trying to make this obsolete as well). The bowlers fit for television compare well with GMs using this analogy. A 200 bowler is like an expert but the 230 bowler would mop the floor with this guy. Doesn’t this demonstrate that ratings are a measure of consistency?

13

You forgot:

Expert = minnow

(I may be guilty of projection here.)

14

You missed my favorite fish: flounder.

15

Without which, Rocky and Bullwinkle would receive less fan mail. (youtube.com/watch?v=dZvWrjmaXLA see 5:54 in for the specific reference)

16

I like the bowling average analogy, which also seems to hold for variants. E.g., a bowler will play at different bowling centers, play under different oiling patterns, etc., but probably over the long run (after learning to make their adjustments) most will play within around plus or minus 10 pins of their average.

Likewise, in addition to chess under classical time controls, one can play rapid, blitz, Fischer random, etc. Most players will say they’re stronger in one or two than the others, but I’d guess that most will play within 100 points of their classical rating as well.

17

I’d probably use a somewhat wider estimate, maybe 200-300 points. A 1600 slow chess player might be a 1400 or an 1800 player at faster time controls, but isn’t likely to be a 1000 or 2200 player.

And for some reason there are players who do much better or worse than normal against certain opponents. We had a low master here in Nebraska who for some reason had a terrible record (under .500) against one 1800 player.