Simple formula for scoring rank

[Ed]

Hi,

I'm after a simple formula expression to give rank to items based on their number of votes and their score from one to five.

------------
Item #1
Votes = 1,000
Score = 3.9 out of 5
------------
Item #2
Votes = 1
Score = 4 out of 5
------------

Should item #2 rank above item #1? I'm looking for a simple way to flatten item scores out to a number which is meaningful as the owners of the items could find this highly contentious.

Thanks.

 

[Ed]

Need more sample data.

The sample data above is only in principle; it's the point of determining position given those two scenarios, and what's deemed fair.

There's lot of different calculations you could use to order them but nobody can answer your question for you: does item #2 rank above item #1?
You need to decide on the answer to that first.

The most common ways I can think of would be:
Rank by average of votes
Rank by average of votes once items have more than a certain number of votes
Artificially add some 1* votes to each item (not visible to users) which will favour items with more votes.

They are good points and highlight the meaningless of rank in this context which is what I'm battling with.

Honestly, I wouldn't even rank an item until it had over 100 votes, and even then I'd still consider leaving it out. If you go by average votes a single voted 5-star item could rank top even if it's poor.

Questions that you need to consider is what quantity of votes is each item willing to get?

Are you having a single score board? You could have items with 100-1000 votes in one scoreboard and anything over 1000 in a separate one.

As a quick idea I would just having something like:

IF NO_OF_VOTES < 100 THEN IGNORE
ELSE ORDER BY AVERAGE_SCORE

I'm thinking of going down this route. Numbers of votes having a certain weight would certainly be "fairer" than overall score but it just needs to be balanced.

I'll play with the data and see what looks "right" and get some layman feedback too as it's all subjective anyway.

 

[Ed]

Thank you for everyone's contribution; I knew it would be a tricky subject.

Or you can use the votes to sort of stretch out the scale, so more of a high score makes it higher, more of a low score makes it lower, like so:

As long as it's a reasonable expectation of position given the numbers, this would do it.

https://math.stackexchange.com/ques...d-on-multiple-reviews-using-both-review-score

I did see this but didn't fancy the task of PHP'ing it. It's something I can turn to later on to refine the service.