Query Results with the same parameters are cached for a week. In those cases you don't need to click run query. There is no option to have a query be run with only a link. Anonymous users need to solve the reCaptcha as well to prevent abuse.
You need to query the votes tables (votetypes 1 (accept), 2 (up-mod), 3 (down-mod) and 9 (bounty) are of interest.
This query will probably do it:
select sum(case v.votetypeid
when 1 then 15 -- accepted
when 2 then 10 -- up vote
when 3 then -2 -- down vote
when 9 then v.bountyamount -- bounty earned
else 0
end
) [answer rep]
from posts p
inner join votes v on v.postid = p.id
where posttypeid = 2 -- Answers
and p.owneruserid = ##user?int:2377343##
and p.communityowneddate is null -- only non community wiki answers
and v.votetypeid in (1,2,3,9)