New table row autopopulated with data from other rows?
If you want the average for all horses:

insert into horse (id, name, stat1)
select nextid, 'name', avg(stat1)
from horse;


If you want the average for a subset of horses you can add a where clause:

insert into horse (id, name, stat1)
select nextid, 'name', avg(stat1)
from horse
where ... ;


If id is autogenerated:

insert into horse (name, stat1)
select 'name', avg(stat1)
from horse
where ... ;