Scoring system for collection of numbers (serial#) - php

Question

I'm looking for a formula (PHP) that I can use to assign a score base on rarity of a number inside a collection. Serial#1 being the rarest.
For example, I have few sets of collections.
Collection 1 - Total number of items = 10 (Serial #1 to Serial #10)
Collection 2 - Total number of items = 100 (Serial #1 to Serial #100)
Collection 3 - Total number of items = 3500 (Serial #1 to Serial #3500)
Based on the 3 example sets. Collection 1 is considered the rarest collection because of only 10 items available in the set.
In addition to this. Each item is assigned with its serials, #1 being the best (rarest)
Here is the table of how I visualize the scoring system.
Collection 1
| Serial#| Score |
|:------:| :-----:|
| 1 | 1000 |
| 2 | 900 |
| 3 | 800 |
| 4 | 700 |
| 5 | 600 |
| 6 | 500 |
| 7 | 400 |
| 8 | 300 |
| 9 | 200 |
| 10 | 100 |
Collection 2
| Serial#| Score |
|:------:| :----:|
| 1 | 800 |
| 2 | 700 |
| 3 | 600 |
| 4 | 500 |
| ... | ... |
| 99 | 12 |
| 100 | 10 |
I just made up those scores just for representation.
With the tables above, Serial #1 in Collection 1 has a higher score compared to Serial #1 in Collection 2 because of the rarity of Collection 1.
I have few collections ranging from 1 of a kind (rarest of them all),10, 20, 150, 350, 1000, 5000, 10000, 50000” What “score” is this item supposed to get then?
for the rarest 1 of 1 the score will be based on the score of the
other Serial #1. If for example Collection with 10 items the serial#
get 1000 points then the 1 of 1 i can give 5000 points (this one no
need to calculate)
2. Are all the scores inside a collection supposed to add up to the same value?
No. It doesn't need to add up to the same value as the other collections
Your “made up” scores aren’t really helpful in explaining what kind of scoring logic you want to apply here in the first place
In the example table (made up scores). I just want to show that the different serial number scores. The higher serial number will have a lower score compare to the lower serial#. But the scores will differ from the other collections with the same serial number. Thus I categorized them by collections. Lower item count collections are considered rarer than those with higher item count.
4. But Serial #1 is supposed to have a higher score, than Serial #2, inside the collection? If so, then what would that be based on? Just the ascending order of those #1, #2, etc.?
Maybe it will be based on the ascending order.
5. All 10 items in collection 1 could get the same score?
No.
I don't have any preference on the score the serial number will get. I mean Serial #1 can get X score as long as it will be relative to the rarity of the collection. Serial #1 score will not be the same across collection unless they belong to the same collection rarity.

Answer 1

If I understand you correctly you want to count occurrences of score (value) and sort that occurrence count in a way that the lowest number (serial) will represent the values (score) that are the rarest and the higher the serial number is the value is more common.
For the:
Input Colleciton:
Array
(
[0] => 5
[1] => 4
[2] => 3
[3] => 2
[4] => 1
[5] => 10
[6] => 10
[7] => 11
[8] => 11
[9] => 12
[10] => 12
[11] => 13
[12] => 13
[13] => 14
[14] => 14
[15] => 100
[16] => 100
[17] => 100
[18] => 101
[19] => 101
[20] => 101
[21] => 102
[22] => 102
[23] => 102
[24] => 103
[25] => 103
[26] => 103
[27] => 104
[28] => 104
[29] => 104
)
this code:
<?php
header('Content-Type: text/plain');
// generate colleciton
$collection = [];
# most unique values
$start = 5;
$end = 0;
for ($i = $start; $i > $end; $i--) {
$collection[] = $i;
}
# less unique values (2x the same values)
$start = 10;
$end = 15;
for ($i = $start; $i < $end; $i++) {
$collection[] = $i;
$collection[] = $i;
}
# least unique values
$start = 100;
$end = 105;
for ($i = $start; $i < $end; $i++) {
$collection[] = $i;
$collection[] = $i;
$collection[] = $i;
}
echo "Input Colleciton:\n";
print_r($collection);
# array of [value => how_many_occurences, ... => ...]
$valueCount = array_count_values($collection);
echo "Value count:\n";
print_r($valueCount);
$uniqueBins = [];
# convert to unique bins
foreach ($valueCount as $value => $key) {
$uniqueBins[$key][] = $value;
}
echo "Unique bins:\n";
print_r($uniqueBins);
// optionally sort by value
foreach ($uniqueBins as $key => $bin) {
asort($bin);
$uniqueBins[$key] = $bin;
}
echo "Unique bins after sort:\n";
print_r($uniqueBins);
generates the output:
Unique bins after sort:
Array
(
[1] => Array
(
[4] => 1
[3] => 2
[2] => 3
[1] => 4
[0] => 5
)
[2] => Array
(
[0] => 10
[1] => 11
[2] => 12
[3] => 13
[4] => 14
)
[3] => Array
(
[0] => 100
[1] => 101
[2] => 102
[3] => 103
[4] => 104
)
)
Where values from the array under the key 1 are rarest and values from the array under the key 3 are most common.
The key number is not starting from zero but from 1 because values that are rarest have only single (1) occurrence in the whole collection.
If you want the output bin array to have keys starting from zero and continues in numbering (0,1,2,...) then use array_values(), this way:
$uniqueBins = array_values($uniqueBins);
at the end. By doing that you loose the information about the count (rarity) of values however you still have arrays of values in the order of their rarity (starting from most to the least)
To make this code work you need to have all values into single array $collection but if you have your values in multiple arrays then you can merge all of them into single $collection by using array_merge

Answer 2

Here are headlines to get you started....
Create a DB
Like this
Category :Rarest
uniqueid item name score
hashed#125 Dragon 1000000
hashed#122 Hydra 800000
hashed#100 Medusa 750000
Category :Rarer
uniqueid item name score
hashed other1 50000
hashed other2 30000
hashed other3 10000
Category :Rare
uniqueid item name score
hashed other1 5000
hashed other2 2000
hashed other3 800
This is how you can approach this...
0.hidden readonly checkbox[contains uniquehash] associate with clickable images[showing name of item]
1.[Connect to DB] mysql here
2.[query from tables (all uniqueids 1,2,3 and...)]
3.[from Post get user inputs as array][say user click image showing medusa and hydra - the hidden checkboxes send hashed#100 and hashed#122]
4.[foreach DB values as #strings]( unique ids are broken to individual strings)
5.[foreach user array as #strings]( uniqueids from userinputs are broken to individual strings)
6.[if user string match DB #strings](match each hash]
7.[return query [score] and [name of item] from where #string is found ](only matching ids return their score in this case score 800000 and 750000 as well as Hydra + Medusa)
8.[then [score for match1]] + [score for match2] + match 3 and so on]
(800000+750000)
echo [total score for user selections] + [names of items]
(1.55mil,hydra + medusa ) you can even show they are from the rarest collection
Since the beginning of the process the user in the frontend does not know what the item score is and there is no way to know they just get the total