# Usage In Rating Systems

Piotr
Piotr
It's possible to use number bases in rating systems. (Not general use, but for sake of interest.)
Base 12

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``````1&#58; Â  Â 12/12
1/2&#58; Â 6/12
1/3&#58; Â 4/12
1/4&#58; Â 3/12
2/5&#58; Â 5/12
3/5&#58; Â 7/12
1/6&#58; Â 2/12
1/12&#58; 1/12

0/12 Â  1/12 Â  2/12 Â  3/12 Â  4/12 Â  5/12 Â  6/12 Â  7/12 Â  8/12 Â  9/12 Â 10/12 Â 11/12 Â 12/12
0 Â  Â  Â 1/12 Â  1/6 Â  Â 1/4 Â  Â 1/3 Â  Â 2/5 Â  Â 1/2 Â  Â 3/5 Â  Â 2/3 Â  Â 3/4 Â  5/6 Â  Â 11/12 Â 1
Â  Â  Â  Â 1/8 Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  3/8 Â  Â  Â  Â  Â  5/8 Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â 7/8
``````
In base 12, many fractions can be exactly represented, 2/5 and 3/5 can be easily approximated, and preset roundings are set for eights to avoid collision with other fractions.

Base 24

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``````1&#58; Â  Â 24/24
1/2&#58; Â 12/24
1/3&#58; Â 8/24
1/4&#58; Â 6/24
1/5&#58; Â 5/24
1/6&#58; Â 4/24
1/8&#58; Â 3/24
1/12&#58; 2/24
1/24&#58; 1/24
``````
Base 24 adds additional binary power to 12, giving clean eights. Alpha relationship to 5Â² allows for good approximations to fifths. Next wishes are sixteenths, ninths and sevenths.

Base 36

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``````1&#58; Â  Â 36/36
1/2&#58; Â 18/36
1/3&#58; Â 12/36
1/4&#58; Â 9/36
1/5&#58; Â 7/36
1/6&#58; Â 6/36
1/7&#58; Â 5/36
1/9&#58; Â 4/36
1/12&#58; 3/36
1/18&#58; 2/36
1/36&#58; 1/36
``````
Sevenths and fifths are introduced by omega 5Ã—7. Ninth would probably get more usage as eighth. So only sixteenths and ninths remain.

Base 48

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``````1&#58; Â  Â 48/48
1/2&#58; Â 24/48
1/3&#58; Â 16/48
1/4&#58; Â 12/48
1/5&#58; Â 10/48
1/6&#58; Â 8/48
1/7&#58; Â 7/48
1/8&#58; Â 6/48
1/9&#58; Â 5/48
1/10&#58; 5/48
1/12&#58; 4/48
1/16&#58; 3/48
1/24&#58; 2/48
1/48&#58; 1/48
``````
By adding additional binary power to 24, sixteenths are exact. There is enough precision to distinguish eights and ninths. This base borrows alpha from 24 to get fifths and its additional binary power extends it to tenths. Its alpha 7Â² allows for good representation of sevenths.

Base 60

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``````1&#58; Â  Â 60/60
1/2&#58; Â 30/60
1/3&#58; Â 20/60
1/4&#58; Â 15/60
1/5&#58; Â 12/60
1/6&#58; Â 10/60
1/10&#58; 6/60
1/12&#58; 5/60
1/15&#58; 4/60
1/20&#58; 3/60
1/30&#58; 2/60
1/60&#58; 1/60
``````
This base has boring life, being primeflank. Would be better if it borrowed sevenths and ninths from 63 and used preset roundings for eights, filling major gap between 6 and 10. It can also modify its 15 for sixteenths. This "rating" system is used in time (minutes and seconds).

Base 64

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``````1&#58; Â  Â 64/64
1/2&#58; Â 32/64
1/3&#58; Â 21/64
1/4&#58; Â 16/64
1/5&#58; Â 13/64
1/6&#58; Â 11/64
1/7&#58; Â 9/64
1/8&#58; Â 8/64
1/9&#58; Â 7/64
1/10&#58; 6/64
1/11&#58; 6/64
1/12&#58; 5/64
1/13&#58; 5/64
1/16&#58; 4/64
1/20&#58; 3/64
1/32&#58; 2/64
1/64&#58; 1/64
``````
This base relies on omega (3Â²Ã—7) and alpha (5Ã—13), these factors making 64 similar to 65520. When it must touch semitotative, it goes to 66 or 60. Base 64 is what made 60 unfair compared to others. Rich for binary powers.

Base 96

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``````1&#58; Â  Â 96/96
1/2&#58; Â 48/96
1/3&#58; Â 32/96
1/4&#58; Â 24/96
1/5&#58; Â 19/96
1/6&#58; Â 16/96
1/7&#58; Â 14/96
1/8&#58; Â 12/96
1/9&#58; Â 11/96
1/10&#58; 10/96
1/11&#58; 9/96
1/12&#58; 8/96
1/13&#58; 7/96
1/14&#58; 7/96
1/15&#58; 6/96
1/16&#58; 6/96
1/18&#58; 5/96
1/19&#58; 5/96
1/20&#58; 5/96
1/24&#58; 4/96
1/32&#58; 3/96
1/48&#58; 2/96
1/96&#58; 1/96
``````
New improvement on 48. Borrows are from 95, 98, 99, 100, 91 and 90.

Base 120

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``````1&#58; Â  Â  120/120
1/2&#58; Â  60/120
1/3&#58; Â  40/120
1/4&#58; Â  30/120
1/5&#58; Â  24/120
1/6&#58; Â  20/120
1/7&#58; Â  17/120
1/8&#58; Â  15/120
1/9&#58; Â  13/120
1/10&#58; Â 12/120
1/11&#58; Â 11/120
1/12&#58; Â 10/120
1/13&#58; Â 9/120
1/14&#58; Â 9/120
1/15&#58; Â 8/120
1/16&#58; Â 7/120
1/17&#58; Â 7/120
1/18&#58; Â 7/120
1/20&#58; Â 6/120
1/24&#58; Â 5/120
1/30&#58; Â 4/120
1/40&#58; Â 3/120
1/60&#58; Â 2/120
1/120&#58; 1/120
``````
My favorite rating system. 1/16 uses preset rounding. Omega (7Ã—17) and alpha (11Â²) give huge advantage. It also borrows from 117.

Other bases:
2: Simple rating, with none, half or full.
4: Used in 5-star ratings (1â€”5 changed to 0â€”4), allowing none, half, full or quarters.
16: Small, with nice omega and binary.
20: Decimal improved with check of sevenths.
21: Prime detector.
34: Prime detector with exact halves.
72: If 8 and 9 are more important than 5.
84: Largely divisible prime detector.
100: Used in percents.
144: Gross. Combines powers of 36 and 48 and adds extra precision.
1000: Precision percents (percents with one decimal place).

EDIT: It seems like no one posts to it. I'm sad for it and want people to come here.

Dozens Demigod
icarus
Dozens Demigod
Joined: Apr 11 2006, 12:29 PM
Piotr, give it time. I think the tables are well thought out, exploring the nearest integer divided by base that would represent a common fraction. They demonstrate your intelligence.

Many posters are folks that are working and doing other things and might not have a great deal of instant time to spend replying to the material on the forum.

I have this system for dividing a unit length. It's one of my secret weapons in my business. I use them for milestones in a construction schedule.

I have two digits, _ _, that I can use for the milestones, and I am limited to decimal numerals. Thus there are 100 positions maximum that I can use for milestones.

The "decades" are used for major milestones. 00 represents existing conditions, 90 the final condition. 10 represents enabling work or demolition, 30 foundations complete, 50 top out structural frame.

Usually my clients are interested in intermediate milestones. So I use this system:

Divide the segment by 2 (i.e., one intermediate): _0, _6
divide by 3: _0, _4, _8.
divide by 4: _0, _3, _6, _9
divide by 5: _0, _2, _4, _6, _8
divide by 6: _0, _3, _4, _6, _8, _9 (this is the default)
divide by 10: use all unit digits.

Sometimes I have an idea of the chronology of intermediate milestones and will attempt to gauge their placement and have irregular intervals such as _0, _1, _4, _5, _8. The default is to try to use dozenal divisions with only decimal numerals because the alphanumeric sort jogs everything in an unexpected way (places mixed character combos in a completely different place than solely numeric character combos.) I use dozenal because it is the most flexible. I can get divisions of 2, 3, 4, and 6 and these usually adequately cover a major milestone interval. I will sooner use the division-by-6 than division-by-5 even if I only have 5 points and just not use _6.

This "secret weapon" helps me assemble "4d" construction visualizations faster than my competition (married to Gantt charts), including in-house teams and is a major underpinning of my company.

Piotr
Piotr
icarus @ Aug 17 2015, 07:43 PM wrote: Piotr, give it time. I think the tables are well thought out, exploring the nearest integer divided by base that would represent a common fraction. They demonstrate your intelligence.

Many posters are folks that are working and doing other things and might not have a great deal of instant time to spend replying to the material on the forum.

I have this system for dividing a unit length. It's one of my secret weapons in my business. I use them for milestones in a construction schedule.

I have two digits, _ _, that I can use for the milestones, and I am limited to decimal numerals. Thus there are 100 positions maximum that I can use for milestones.

The "decades" are used for major milestones. 00 represents existing conditions, 90 the final condition. 10 represents enabling work or demolition, 30 foundations complete, 50 top out structural frame.

Usually my clients are interested in intermediate milestones. So I use this system:

Divide the segment by 2 (i.e., one intermediate): _0, _6
divide by 3: _0, _4, _8.
divide by 4: _0, _3, _6, _9
divide by 5: _0, _2, _4, _6, _8
divide by 6: _0, _3, _4, _6, _8, _9 (this is the default)
divide by 10: use all unit digits.

Sometimes I have an idea of the chronology of intermediate milestones and will attempt to gauge their placement and have irregular intervals such as _0, _1, _4, _5, _8. The default is to try to use dozenal divisions with only decimal numerals because the alphanumeric sort jogs everything in an unexpected way (places mixed character combos in a completely different place than solely numeric character combos.) I use dozenal because it is the most flexible. I can get divisions of 2, 3, 4, and 6 and these usually adequately cover a major milestone interval. I will sooner use the division-by-6 than division-by-5 even if I only have 5 points and just not use _6.

This "secret weapon" helps me assemble "4d" construction visualizations faster than my competition (married to Gantt charts), including in-house teams and is a major underpinning of my company.
Which rating system do you prefer of these all? (rating, milestones, hour/minutes, etc...) I prefer base 120 rating system, due to many exact fractions and good approximations.
I will also give usefulness of each prime:
2: Very commonly we divide in half, and also word "most" means 50% or more.
3: Annoying runner in decimal, may be more useful in dozenal.
5: Its usefulness in decimal may be hugely reduced after move to dozenal.
7: Not so useful. We only may use it for week (for example 1 day is 7/48 weeks)
11: ISBN checksums using base 11 were already deprecated, not to mention fractions using 11 are very rare for any usage.

Dozens Demigod
icarus
Dozens Demigod
Joined: Apr 11 2006, 12:29 PM
I think 120 is a great substitute for what we now call "percent". If we assessed things in parts of 120 we could represent thirds as 40 "perhund" and quarters as 30 "perhund".

If you're talking rating movies or restaurants, we tend to see very low "bases", usually 5. I don't mind five stars, etc. It's fairly simple. There, we can say something is "extremely bad" 1 star, "just bad", 2 stars, "fair or neutral" 3 stars, "good but not great" 4 stars, and "extremely good" 5 stars. There you want an odd number.

Another way to look at five stars is maybe to see this as +/- 2 with 0 being neutral. The fivefoldness isn't quite as prominent seen that way. Seven is good if we see this as +/- 3.

it would seem that dozen or especially 120 would be much too fine a gradation for anyone to seriously consider using on a daily basis for rating, unless we are aggregating a pool of individual ratings. If a restaurant got 1000 reviews, you could use a finer distinction and say it got 96/120 or essentially 4.00 stars. But then using the "fractions of a star" come into play. In our current world it's a decimal rendition.

I am not sure if this is the sort of rating system you mean, Piotr. It's an interesting consideration.

Piotr
Piotr
icarus @ Sep 10 2015, 12:12 AM wrote: I think 120 is a great substitute for what we now call "percent". If we assessed things in parts of 120 we could represent thirds as 40 "perhund" and quarters as 30 "perhund".

If you're talking rating movies or restaurants, we tend to see very low "bases", usually 5. I don't mind five stars, etc. It's fairly simple. There, we can say something is "extremely bad" 1 star, "just bad", 2 stars, "fair or neutral" 3 stars, "good but not great" 4 stars, and "extremely good" 5 stars. There you want an odd number.

Another way to look at five stars is maybe to see this as +/- 2 with 0 being neutral. The fivefoldness isn't quite as prominent seen that way. Seven is good if we see this as +/- 3.

it would seem that dozen or especially 120 would be much too fine a gradation for anyone to seriously consider using on a daily basis for rating, unless we are aggregating a pool of individual ratings. If a restaurant got 1000 reviews, you could use a finer distinction and say it got 96/120 or essentially 4.00 stars. But then using the "fractions of a star" come into play. In our current world it's a decimal rendition.

I am not sure if this is the sort of rating system you mean, Piotr. It's an interesting consideration.
5-star system uses base 4. Note that you said there are these values:
0 = 1 star
1 = 2 stars
2 = 3 stars
3 = 4 stars
4 = 5 stars
0 is zero, 4 is full. Inbetween there are quarters. Similarly 0--255 color system isn't base 256. There is no half. A value of 85 means 85/255=1/3.

Dozens Demigod
icarus
Dozens Demigod
Joined: Apr 11 2006, 12:29 PM
Hi Piotr!

Sure the lowest value is zero and the highest is 4 or 255 in the cases you mention. But in these cases we have 5 and 2^8 positions respectively. 1/2 of 255 in the latter system ought to be Floor(1/2 * 255) = 127 but instead we see 128,128,128 (0x808080) used to signify medium gray in RGB color specs. So indeed the systems are 5 and 256 value systems.

Nice to hear from you again!

Piotr
Piotr
icarus @ Oct 21 2015, 03:23 PM wrote: Hi Piotr!

Sure the lowest value is zero and the highest is 4 or 255 in the cases you mention. But in these cases we have 5 and 2^8 positions respectively. 1/2 of 255 in the latter system ought to be Floor(1/2 * 255) = 127 but instead we see 128,128,128 (0x808080) used to signify medium gray in RGB color specs. So indeed the systems are 5 and 256 value systems.

Nice to hear from you again!
Yes, these are 5 and 256 value systems, but base 4 and 255. And why the floor in this calculation? 255/2 is 127.5, and halves are usually rounded up. I wouldn't call percentages base 101, though they have 101 values.