How to make a fair comparison between average of two groups? Here's the scenario.
When users add an item in an auction listing, they can opt for an "upgrade" where more people are likely to bid.
How can I get how times more, that items in the auction listing with the "upgrade" get bids than those without?
Here is the current data. This is an example only.


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*There are more items with no upgrade.


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*Count of items w/o upgrade: 1500

*Count of items w/ upgrade: 300


*Total no. of all bids


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*Bids on items w/o upgrade: 30000

*Bids on items w/ upgrade: 10500



I could simply get the number of bids per item and compare between those with and w/o upgrades


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*Bids per item w/o uprade: 30000 / 1500 = 20

*Bids per item w/ upgrade: 10500 / 300 = 35


So it's 75% (35/20 - 1) more bids if an item has upgrade.
So my question is, how to make a more fair comparison how much bids an item gets with upgrade vs without? Since according to data, there are much more items with no upgrades and these are usually low-valued ones (say avg of 100 USD versus avg 500 USD for those w/ upgrades). Should I also put dollar value in the formula here?
 A: Ideally, if you want to know how much upgrading helps, you would compare those items that were upgraded and those that were not amongst similar items. Otherwise, you may compare non-comparable things (perhaps users have a very good feeling for when it is worthwhile to upgrade and only do it when it is a good idea).
One type of approach that you could use is stratification by a propensity score - one builds a model based on product characteristics (e.g. product category, value - as long as it is not established by the bidding process, which would be influenced by the upgrading - and whatever else you might have). Hopefully you have the majority of characteristics that might influence the decision to upgrade (if you are missing really important things, it is very difficult to do a really good analysis). Then you get a predicted probability to upgrade for each item and stratify by this (e.g. by deciles of predicted probabilities) and compare bids within these strata. If you want an estimate across strata, then something like a stratified negative binomial model (or negative binomial model with stratum as a factor, or zero-inflated negative binomial model etc. - it depends a bit on what the data truly looks like and whether more items received no bids than predicted by a standard negative binomial model) for the number of bids could be a logical option.
