You need to add a new
rank_point attribute field to your data; either the buffers prior to doing a spatial join or intersect, or to the results of the spatial join/intersect. With the field added you'll then need to populate the values.
If you have a single set of buffers, you can populate the values for each buffer manually. If you have multiple sets of buffers you'll want to use a Field Calculator. You could either select all buffers of the same distance, field calculate those selected records only, then select the next distance, or you could use either a nested if or a case statement (we have questions on those, depending on your software) in a single field calculation to do them all at once. It mostly depends on how many distances/rings you have and how comfortable you are with more complex statements in the field calculator.
With the base point value added, you can either do the spatial join/intersect or if you have already done so add another field to your result attribute table called
score. To populate its values, use another simple field calculation of
count * rank_point.
Note there are two ways to create multi-ring buffers - either as separate concentric features, or a stack of overlapping polygons (where all outer buffers would also include anything inner from them). Be sure to use the appropriate geometry depending on whether you want counts of all farms within 50 miles or just farms between 25 and 50 miles.