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Currently we have a line of text showing total results, similar to :

67 results for 'Smith'

and we are told to make an expanded search option by incremental distances available if the total results is less than X number.

My thinking is if it's less than say 15 or so, offer it, but they could get back over 100. We have a 200 search results limit as it doesn't seem feasible a user would ever want that many choices to select from. However, I don't know how many results the user is expecting, other than they are going to only select one.

The results would always be the total number within a 200 mile radius, but we only show the first 10 results, then another 10 each time the user scrolls down the list. The search subject is for a medical professional, if that helps.

My question is, what is the best number for X from a UX standpoint?

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As far as I understand, you need to provide a filter that would allow Users to select if they want to see results in their vicinity, then the ones who are farther and farther away.

If you are not sure about the distance returned, maybe you could build the selector based on the relation between the distance and the number of results, e.g. showing the top 10 closest ones in the first place, and then allow Users to extend this range. This way, no matter if the closest one is within 5 miles or 100 miles, you would always get results matching the filter (of course, provided that there would be any results in the particular case).

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It sounda like you want to show them a certain amount of results rather than giving them the results within a certain range. So why not do that, but properly? Perhaps look up the nearest 100 people and order them by distance, with a separator every 10 or 25 or however many miles.

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