MongoDB sort using a custom function - mongodb

Question

Let's say I have a collection that looks like:
{
_id: 'aaaaaaaaaaaaaaaaaaaaaaaaa',
score: 10
hours: 50
},
{
_id: 'aaaaaaaaaaaaaaaaaaaaaaaab',
score: 5
hours: 55
},
{
_id: 'aaaaaaaaaaaaaaaaaaaaaaaac',
score: 15
hours: 60
}
I want to sort this list by a custom order, namely
value = (score - 1) / (T + 2) ^ G
score: score
T: current_hours - hours
G: some constant
How do I do this? I assume this is going to require writing a custom sorting function that compares the score and hours fields in addition to taking a current_hours as an input, performs that comparison and returns the sorted list. Note that hours and current_hours is simply the number of hours that have elapsed since some arbitrary starting point. So if I'm running this query 80 hours after the application started, current_hours takes the value of 80.
Creating an additional field value and keeping it constantly updated is probably too expensive for millions of documents.
I know that if this is possible, this is going to look something like
db.items.aggregate([
{ "$project" : {
"_id" : 1,
"score" : 1,
"hours" : 1,
"value" : { SOMETHING HERE, ALSO REQUIRES PASSING current_hours }
}
},
{ "$sort" : { "value" : 1 } }
])
but I don't know what goes into value

Answer 1

I think value will look something like this:
"value": {
$let: {
vars: {
score: "$score",
t: {
"$subtract": [
80,
"$hours"
]
},
g: 3
},
in: {
"$divide": [
{
"$subtract": [
"$$score",
1
]
},
{
"$pow": [
{
"$add": [
"$$t",
2
]
},
"$$g"
]
}
]
}
}
}
Playground example here
Although it's verbose, it should be reasonably straightforward to follow. It uses the arithmetic expression operators to build the calculation that you are requesting. A few specific notes:
We use $let here to set some vars for usage. This includes the "runtime" value for current_hours (80 in the example per the description) and 3 as an example for G. We also "reuse" score here which is not strictly necessary, but done for consistency of the next point.
$ refers to fields in the document where $$ refer to variables. That's why everything in the vars definition uses $ and everything for the actual calculation in in uses $$. The reference to score inside of in could have been done via just the field name ($), but I personally prefer the consistency of this approach.