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Subject: Thumbs UP for 3 digits of precision! rss

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John Earles
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I noticed this morning that the Games Listing is now showing 3 digits after the decimal for Geek Rating!



thumbsupthumbsup

Good call, as the games are getting more and more clumped together in places.
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Maarten D. de Jong
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3 decimals of precision is silly nonsense if you ask me given that people rate games without any decimals whatsoever. I wouldn't even go beyond 1 decimal had I any say in this matter.
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John Earles
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cymric wrote:
3 decimals of precision is silly nonsense if you ask me given that people rate games without any decimals whatsoever. I wouldn't even go beyond 1 decimal had I any say in this matter.


Maybe you rate games with no decimals, but I often will use .25, .5 and .75 to differentiate between games I would have otherwise rated the same integer value.

Edit: The system allows you input the decimals, so I would presume they are used in calculations at that precision. The rating graph flattens the ratings as it just shows 1 - 10 on the axis.
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Eric O. LEBIGOT
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cymric wrote:
3 decimals of precision is silly nonsense if you ask me given that people rate games without any decimals whatsoever. I wouldn't even go beyond 1 decimal had I any say in this matter.
Even if people were rating only with integers, the precision on the average would be of the order of 0.5/square_root(number of voters) (which is about 0.004 for Puerto Rico, if I'm not mistaken). 3 decimals is therefore quite reasonable.
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Tomello Visello
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cymric wrote:
3 decimals of precision is silly nonsense if you ask me
I am reminded of reading the engineering data for a consumer digital thermometer some time back. The display provides a reading down to the tenth of a degree but the spec sheet says it is only accurate within plus or minus 2 full degrees. Wonderfully misdirecting confidence.

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Robert Buciak
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This 3rd digit makes ranking more sense. Unfortunately, xml api data still doesn't work properly, so we haven't 5 digits historical data and ranking.
 
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Maarten D. de Jong
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jearles wrote:
Maybe you rate games with no decimals, but I often will use .25, .5 and .75 to differentiate between games I would have otherwise rated the same integer value.

I see you do not use the full scale, but stick to numbers between 9 and 5 (with one exception). So in effect those fractions are not 'real': they are in fact the result of you not using the full scale from 1 to 10. On that scale you would've used halves at most, I think. Perhaps you will now counter with the argument that you wish to adhere to BGG's interpretation of the integers, which is fine; but by introducing fractions you are making up some definitions of your own anyway. I don't know what a 7.25 means compared to a 7.5 or 7.75, for example. I would then say: a) keep it simple, b) use integers only, and c) scrap the definitions of BGG and supply your own. As long as a 10 is in some way better than a 9, and a 9 in some way better than an 8, and so forth, you'd be okay. And since you'd be using integers then, the 3 decimals in the computed average lose their meaning.

Also you use not a 'normal' decimal fraction which can take on any value (7.18, 6.42, 4.0932, and so forth), but restrict yourself to 'nice numbers': quarters and halves. That means the double decimals in your rates are in some way less precise than they otherwise could be, most certainly not comparable to the 3 decimals used now in the ratings overview.

Basically it amounts to saying that the computed average is a continuous number and the rate an ordinal number. You cannot really mix the two without taking precautions, and in my opinion the precautions in place do not warrant the precision currently offered. As I stated previously I would in fact applaud chopping off two decimals as it makes people aware of the fact that they're dealing with things which are practically equal in terms of our appreciation of them. The difference between 8.210 (= 8.2) and 8.207 (= 8.2) is simply not important; the difference between 8.2 and 7.2 however is, and between 8.2 and 6.2 even more so.
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Maarten D. de Jong
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lebigot wrote:
cymric wrote:
3 decimals of precision is silly nonsense if you ask me given that people rate games without any decimals whatsoever. I wouldn't even go beyond 1 decimal had I any say in this matter.
Even if people were rating only with integers, the precision on the average would be of the order of 0.5/square_root(number of voters) (which is about 0.004 for Puerto Rico, if I'm not mistaken).

No, because rates are ordinal numbers, not continuous numbers. Therefore the statistic you apply is not valid. BGG does something similar by calculating the average because it's a simple procedure, but one really should use a different analysis. That the procedure of averaging the numbers more or less works is the result of the monotonicity of the rating scale, but the absurdity of the calculations quickly becomes clear if you ask yourself what it means that you add up a 1 ('defies a descripion of a game') to a 3 ('bad') and a 6 ('okay game, some challenge at least') to end up with a 10 ('outstanding') which is then 'divided' by 3.

TVis wrote:
I am reminded of reading the engineering data for a consumer digital thermometer some time back. The display provides a reading down to the tenth of a degree but the spec sheet says it is only accurate within plus or minus 2 full degrees. Wonderfully misdirecting confidence.

Actually, that's a different matter. Temperature is a continuous property, at least in the classical macroscopic world. Although the thermometer is only accurate to +/- 2 degrees, it means that a single measurement will give me a result that is +/- 2 degrees off. But I can get around that by taking many measurements (presumably in very rapid succession!), apply the central limit theorem of the mean, and come up with a pretty accurate notion of the actual temperature of the object, including the uncertainty in the reading, which can in fact be lower than the actual accuracy of the device.

Yes, statistics is truly the invention of the devil... sauron.
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John Earles
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cymric wrote:
I see you do not use the full scale, but stick to numbers between 9 and 5 (with one exception).

I research my games before I buy. Why would I rate a game I enjoy a 4 just to have a bell curve? My bell curve is just shifted because I do pre-screening.

cymric wrote:
I don't know what a 7.25 means compared to a 7.5 or 7.75

Seriously? It means I enjoy the 7.25 game less than a 7.5 game. Is that hard to comprehend?

cymric wrote:
As long as a 10 is in some way better than a 9, and a 9 in some way better than an 8, and so forth, you'd be okay. And since you'd be using integers then, the 3 decimals in the computed average lose their meaning.

What is the average of 4, 5, 5, 6, 7, 8, and 10? My calculator says: 6.4285714285714285714285714285714. I'm happier seeing 6.429 than I am seeing 6. I'm also happier seeing 6.501 than I am seeing 7.

cymric wrote:
Also you use not a 'normal' decimal fraction which can take on any value (7.18, 6.42, 4.0932, and so forth), but restrict yourself to 'nice numbers': quarters and halves. That means the double decimals in your rates are in some way less precise than they otherwise could be, most certainly not comparable to the 3 decimals used now in the ratings overview.

Basically it amounts to saying that the computed average is a continuous number and the rate an ordinal number. You cannot really mix the two without taking precautions, and in my opinion the precautions in place do not warrant the precision currently offered. As I stated previously I would in fact applaud chopping off two decimals as it makes people aware of the fact that they're dealing with things which are practically equal in terms of our appreciation of them. The difference between 8.210 (= 8.2) and 8.207 (= 8.2) is simply not important; the difference between 8.2 and 7.2 however is, and between 8.2 and 6.2 even more so.

Let's just agree to disagree, shall we. I understand your point... I just don't agree with it. The BGG system is based on rating games, for better or worse. The game ranking system puts one game in front of another for a reason. More precision simply elucidates that reason.
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Russ Williams
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cymric wrote:
No, because rates are ordinal numbers, not continuous numbers.

Many people seemingly do use them as continuous numbers, not discrete values.

But I agree with you that it seems kind of silly to care about the 3rd decimal digit of the game ratings, as if it would have any serious significance that game A has an average rating of 8.342 and game B has an average rating of 8.343.
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Tomello Visello
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russ wrote:
But I agree with you that it seems kind of silly to care about the 3rd decimal digit of the game ratings, as if it would have any serious significance that game A has an average rating of 8.342 and game B has an average rating of 8.343. :)
I just checked. Apparently is does make difference thought between 8.210 and 8.207, to judge by the threads proclaiming/complainging the status at the top of some list people often seem to examine.

actually, I gues it should be game "A" and game "P".



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This is a definite thumbs down as all it does is make people think it matters.
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Maarten D. de Jong
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jearles wrote:
cymric wrote:
I see you do not use the full scale, but stick to numbers between 9 and 5 (with one exception).

I research my games before I buy. Why would I rate a game I enjoy a 4 just to have a bell curve? My bell curve is just shifted because I do pre-screening.

I cannot deduce from your reply how you interpret the words 'bell curve': it can either be your description for how the ratings graph happens to look, or it can mean that you insist that all ratings should have a bell curve-shape and must be juggled to make it so. I'll use the 'proper' word distribution instead: all bell curves are distributions, but not all distributions are bell curves.

Pre-screening should not shift your distribution. Taking your lowest rating to be 5 for the moment tells me one and one thing only: that '5' to you means 'this is the level of least appreciation I can harbour for a game'. I cannot assume that there are levels of even less appreciation below that number, for if there were, there would be games with a rating of 4, 3, or -1000000—whatever suits your fancy. As it happens, you do have a game with a lower rate, at 2. So apparently your level of appreciation can become lower. However, I cannot make assumptions about what is in between 5 and 2; all that I know is that your appreciation for a 5-game is higher than that for a 2-game. Instead you could have used 5 and 4.9, or 5 and 4.99, or even -1000 and -1001: the effect would have been identical. That is the weirdness of ordinal numbers meeple: 'in between' ordinals has no meaning.

Quote:
cymric wrote:
I don't know what a 7.25 means compared to a 7.5 or 7.75

Seriously? It means I enjoy the 7.25 game less than a 7.5 game. Is that hard to comprehend?
[/q]
No; in fact that's what I'm trying to argue. If you feel comfortable enough to distinguish between a 7.25 and 7.5 game then that's fine. The numbers suggest something fairly close, but that needn't be at all the case: the meanings can be lightyears apart. The point is that these fractions are not really fractions in the normal sense of the word; they are instead levels of appreciation between levels 7 and 8. The same effect would be obtained if you relabeled 8 as '11', and the fractions as 8, 9 and 10 respectively. (Admittedly the system will not accept such an entry, but if the new ranking system is introduced then such a restriction could be removed. We can finally rate games 11 or 12 or even 1 million! Weee!) Hence my scepticism for the need for 3 decimals in the ranking overview.

Quote:
What is the average of 4, 5, 5, 6, 7, 8, and 10? My calculator says: 6.4285714285714285714285714285714. I'm happier seeing 6.429 than I am seeing 6. I'm also happier seeing 6.501 than I am seeing 7.

Must be my professional training then. I grow suspicious of lots of digits behind the separator; it means something completely different to me, with good reason.

Quote:
The game ranking system puts one game in front of another for a reason. More precision simply elucidates that reason.

I look forward to the day when we see the first thread appear that game A is pegged at 8.196 and game P too, and why then P is ranked below/above game A. And so on until machine floating point accuracy, which is probably 15 digits or so. Weeee...

As you said, it'll probably remain an agree to disagree.
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Eric O. LEBIGOT
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cymric wrote:
lebigot wrote:
cymric wrote:
3 decimals of precision is silly nonsense if you ask me given that people rate games without any decimals whatsoever. I wouldn't even go beyond 1 decimal had I any say in this matter.
Even if people were rating only with integers, the precision on the average would be of the order of 0.5/square_root(number of voters) (which is about 0.004 for Puerto Rico, if I'm not mistaken).

No, because rates are ordinal numbers, not continuous numbers. Therefore the statistic you apply is not valid. BGG does something similar by calculating the average because it's a simple procedure, but one really should use a different analysis. That the procedure of averaging the numbers more or less works is the result of the monotonicity of the rating scale, but the absurdity of the calculations quickly becomes clear if you ask yourself what it means that you add up a 1 ('defies a descripion of a game') to a 3 ('bad') and a 6 ('okay game, some challenge at least') to end up with a 10 ('outstanding') which is then 'divided' by 3.
I fully agree with you when you say that averaging BGG ratings gives a result which does not have a simple interpretation. However, the fact remains that there is a statistical error on this average, which you can roughly estimate (or more precisely estimate, if need be, with bootstrap methods). Thus, giving 3 decimal digits on a BGG average is not out of place, for games with 10k+ voters.
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cymric wrote:
Also you use not a 'normal' decimal fraction which can take on any value (7.18, 6.42, 4.0932, and so forth), but restrict yourself to 'nice numbers': quarters and halves....The difference between 8.210 (= 8.2) and 8.207 (= 8.2) is simply not important

Well, I am one of the many who do use decimals and not just the pretty ones. And for me, the difference between 8.207 and 8.210 is very important. The lower rated game is one I don't like as much as the higher rated one.
 
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ronster0 wrote:
They are fighting on the internet.


Nah, that's just foreplay.devil
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lebigot wrote:
cymric wrote:
3 decimals of precision is silly nonsense if you ask me given that people rate games without any decimals whatsoever. I wouldn't even go beyond 1 decimal had I any say in this matter.
Even if people were rating only with integers, the precision on the average would be of the order of 0.5/square_root(number of voters) (which is about 0.004 for Puerto Rico, if I'm not mistaken). 3 decimals is therefore quite reasonable.


So you pick one of the most extreme examples you possibly could, and it still indicates that three places is *barely* worthwhile (Personally, I'd call it not worthwhile once that hit 0.005 myself, but could be swayed to bump my "threshold" up a bit given a solid argument), and you think that *supports* the argument that three digits is reasonable?

PR has ~20k ratings, only beaten out by Settlers and Carcassonne (both at 22k and a bit) Only 13 game entries (out of 46,000+) even have more than 10k ratings. You don't have to go too far past that before that number goes below 5k (middle of page 2 of 461 pages) and you hit less than 1k ratings somewhere in page 6 (again out of 461 pages) bring it to 0.016. And at that point we're still only talking about well under 2% of the games, and at 0.016, I'd argue even hundreths are silly, and tenths are more than sufficient for >98% of the games.

So if we are actually talking integer ratings, I think the third place isn't terribly relevant in practice. Of course, as has been pointed out, they're not integer ratings (unless someone from BGG itself chimes in and says they're truncated/rounded/whatever). But since different people use or don't use the decimals at all it becomes pretty tricky to do much more detailed estimations (at least without me getting in over my head statistically)

Practically speaking, I don't give a rat's ass how many places are displayed. They get rounded to the 10th as soon as I look at them in my head anyhow. If people want them, great, they're welcome to them. I'm certainly not saying they shouldn't be there.

On the other hand, those thousandths places are the ones the self-proclaimed "police" of the ratings system think it's their job to influence though. I sometimes wonder if not displaying them might make those idiots give up. Probably not, they'd just find another way to whine about people manipulating the system, so they have to counter-manipulate it. What a waste of time.

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lebigot wrote:
. Thus, giving 3 decimal digits on a BGG average is not out of place, for games with 10k+ voters.


I'll go with you 100% there. But (and we were typing at the same time, so I'm not knocking you), as I mentioned before (though I didn't actually do the math till now) 0.028% of the games have more than 10k voters. 99.97% are below that threshold.

EDIT: But as has been pointed out, the integer assumption is flawed, so all math based on it is equally flawed. And just an interesting exercise.

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jearles wrote:
Good call, as the games are getting more and more clumped together in places.

No, it's misleading, meaningless, and innumerate.
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Aldaron wrote:
jearles wrote:
Good call, as the games are getting more and more clumped together in places.

No, it's misleading, meaningless, and innumerate.



BGG Ranking Game Rating
99 7.264
100 7.255


vs.


BGG Ranking Game Rating
99 7.26
100 7.26



How is 7.264 vs. 7.255 more misleading, meaningless, and innumerate than 7.26 vs. 7.26?
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jearles wrote:
How is 7.264 vs. 7.255 more misleading, meaningless, and innumerate than 7.26 vs. 7.26?

Did I say "more"? Both are misleading. I'm not sure how to compare misleadingness.
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Aldaron wrote:
jearles wrote:
How is 7.264 vs. 7.255 more misleading, meaningless, and innumerate than 7.26 vs. 7.26?

Did I say "more"? Both are misleading. I'm not sure how to compare misleadingness.


Yep.

One is potentially misleading because you can't necessarily tell why one is higher than the other.

The other is potentially misleading because in the vast majority of cases, it's going to imply an imaginary level of precision that just doesn't exist (see also: innumerate).

lebigot did an excellent job of demonstrating this assuming integer inputs.

The complications inherent in some people pretending that they are integers and some not, etc puts it beyond my ability to usefully estimate the actual precision. It becomes apples and oranges all in one bushel. But I'm fairly certain it's still well below three decimal places in almost every case.

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