SELECT DISTINCT Subquery

I the following table:

table1
member_name legacy_id team_name
-----------------------------------------
Bill 1234 nationals
Bill 1234 nationals
Tom 3456 nationals
Tom 3456 orioles

I wish I could restructure the data or normalize it but this is unfortunately what I have to deal with.

I need a query that returns the team name and the number of times it appears in the table excluding duplicates for each person. I have duplicates all over the place in this tables. Bill could have nationals listed a couple hundred times.

My query should return

team_name count
-----------------
nationals 2 - because it occurs for bill, and tom
orioles 1 - because it occurs for tom


If I do something like:

select
distinct(team_name),
count(team_name)
from table1
group by team_name

I get back:

team_name count
-------------------
nationals 3 - because it occurs for bill twice, and tom once
orioles 1 - because it occurs for tom once


I've tried something like:

select
team_name,
count(team_name)
from
table1
where legacy_id in (
select distinct legacy_id from table1
)

I get a syntax error. Regardless, I'm not sure this will give me what I need.

I've tried over a dozen variations of select distinct, joins, etc but with no luck.

Any of you sql gurus know how to solve this problem? I've been banging my head against it for a couple days and boy does my head hurt.