Lowest rated player to defeat a world champion?

Who has been the lowest rated player to defeat a reigning world champion in a single game at equal odds (other than move)?

Who has been the lowest rated player to draw a reigning world champion in a single game at equal odds (other than move)?

Elo ratings have existed for almost 50 years. How many chess games have been played by the world champions while reigning during that period?

I heard of this thing called Google. It has all the answers.

At least, tell us that you've tried it yourself.

From

http://www.chessgames.com/player/magnus_carlsen.html

Magnus has played a total of 2500 games - since 1999.

After excluding of games at odds, rabid chess and exhibition games (927 of them), Magnus has played 1573 games that count, of which lost 263.

Taking just the games Magnus has lost - 446 total, including the disqualified games.

http://www.chessgames.com/perl/chess.pl?page=18&pid=52948&result=2nd

In this year, discounting 1 simultaneous game, sounds like 3 losses - to Jobava, Andreikin and Rapport.

How many people have defeated Magnus while World Champion?

Let's at least start with something. Wolfram Hartmann, 2290 ELO, defeats Karpov, the then reigning WCC:

http://www.chessgames.com/perl/chessgame?gid=1068351

World Champions are protected from losing to low-rated players in regulation games, because they don't play many low-rated players.  I've seen GMs upset by 1700 players in early rounds of open weekend tournaments, but World Champions don't play in many Open events where 1700 players can enter.

My sister won a game against GM Short of the UK.He was rated at 2644 and my sister 1569

Simul games are obviously not equal odds.  If there were ratings to refer to, the lowest rated player to beat a WC would probably be one of Steinitz's opponents...

I think the Karpov-Hartmann game is a good place to start.  I'll also note that Karpov is known for more than the average WC's share of horrendously famous blunders.

Official FIDE ratings started in 1970, I believe?  So, Spassky is a good bet to have lost to someone rated lower, since chess ratings were lower then.

'World Champion' is an awfully high bar. In simuls, maybe it's happened but in tournament play? I haven't found any on the Google machine. 

But up until the last 20 years or so, if you weren't rated at least 2200 FIDE then you had no FIDE rating.  (I think it was 2100 for women.)  I played in a couple of FIDE rated "Futurity Events," over 30 years ago, where you hoped to play at least 5(?) FIDE rated opponents and emerge with a rating performance of at least 2205 (back then FIDE ratings were in increments of 5 for some reason) and THEN you would be a "bigshot," which meant that you would get free entry into many events where they wanted as many FIDE rated players as possible.  (oh, yeah, I didn't come with 200 points of 2205.)

I would accept a non-FIDE rating (like USCF).