Although it might prove impossible to find worldwide statistics that show the percentage success of “attempted conversions” or how much it costs per attempted conversion, there is one denomination that does keep records of their activities and costs with regard to bringing people into their organisation to be baptised. They are Jehovah’s Witnesses.
However, please bear in mind that virtually all of their “publishers” (members who go from door to door and conduct home studies with interested people) work voluntarily and they receive no payments. Those who devote their lives to missionary work and “pioneers” who work full-time receive financial assistance.
Here are the statistics from their annual Yearbook for 2020. Bear in mind Covid-19 restrictions had a negative impact on how much work they were able to do “out in the field”.
8,424,185 publishers (average over 12 months)
241,994 persons baptised (but not all would be new converts – some would have been brought up from birth into a Jehovah’s Witness family and were baptised later in life)
This represents a percentage decrease of 0.6% over 2019
Between publishers and 1.3 million pioneers, they spent a staggering 1,669,901,531 hours in active field service, going from door to door and conducting home studies with interested people.
Over the year, the society spent $231 million on costs/overheads including pioneers, missionaries and circuit overseers.
I don’t think there is any way to calculate how much it costs per “attempted conversion” because it could take months, if not years, of studying with an individual before they were baptised and joined the organisation. Likewise, it is not known if those individuals were nominal Christians, atheists or belonged to a completely different religion or faith (such as Buddhist or Hindu to name but two).
If you were to take the total number of hours spent doing this evangelising work and divide it into the number of persons baptised in that same year, you might get some sort of a guide. However, I’m a mathematical dunce and I don’t think my little calculator is capable of crunching those numbers. It would be interesting to find out, though...
P.S. Hundreds of Protestant biographies of missionaries over the past 200 years or more show that conversions often don't happen until after the missionary has either died or gone elsewhere. Sometimes it's only after a tribe has murdered a missionary that (in following decades) the tribe starts to become Christian.
Even one genuine convert after many years of missionary work is a miracle of grace akin to the creation (for a new creature is 'born' after the Holy Spirit has brought them to spiritual newness of life). On the other hand, where large numbers seem to convert at about the same time, there may be more than a few who are only going along with the others, and have not actually put faith in Jesus Christ.
Also, many missionaries have 'paid' in ways impossible to relate to mere money. Sometimes they have paid with their lives.
“Success” can never be measured by numbers or by financial input. True conversion is spiritual and is therefore unquantifiable. God knows who belong to Him. We don’t need charts or graphs or statistics. It is the work of the Holy Spirit to bring sinners to a point of repentance and to acknowledge they are sinners in need of a saviour. God’s grace abounds to all who turn to Him.