Why on earth did the rating go UP???

What you are saying is true. However, if you look at the intial post, the final ratings are posted (ignored by many people in this forum).  The 2 unrated players ended up with ratings of 103 and 107, while the lone rated player ended up with a rating of 126. Therefore, the tournament is rerated with those ratings: so Peter's perfomance is based on those final ratings. 

Peter's performance rating was lower than his actual rating. Therefore his rating should go down. Unlike what some people said earlier, you can NEVER gain rating points from a loss. I had a friend rated 800, provisional 3 games, and he lost to a 2200. The result? His rating stayed the same.

@ ThrillerFan

But the two unrated players he faced, combined, scored 2 points in that tournament:

D vs 108
W vs 108
D vs 146

It's not like they went on to beat players rated 1000 or something like this.

@ Martin_Stahl

I didn't know about the 50xage.

Is the age thing really ever applied? Usually I've just seen little kids start as unrated. 

Yes, they start as unrated.

But that's not a number, and the formulas need something to use. So behind the scenes (so to speak) they're given numbers.

Without getting deep into the math, post 16 explains how the ratings would be initialized in this particular case. Based on that method,  he scored a half a point against an average rating of 300. 

Yes, this at least lets it make sense at a glance, thanks :)

By that logic, if two 200 rated players, both aged 8, drew each other, both their ratings would go up??

I read somewhere that although 100 is the theoretical lowest rating a player could acheive, most people have a set floor somewhat higher than that, despite not being revealed on the uscf website.  For example, if a 1100 player lost 500 games in a row, would his rating fall to 100?  No, probably not, it would likely bottom out at 140 or so. 

OK, so that could explain why his rating didn't go down...but why did it go UP?

I seem to remember that at the time (long ago) in FIDE the expected score in a single game was 1 when the rating diff. was something like 680/690 and above.

Don't know what they used at the time. I remember looking in some chart and above a certain diff. it was 100%, for sure.

Glicko is not the same as elo.

50 x age is only used if they're unrated and only for an initial rating.

Then a bunch of math and re-rating and stuff happens... I have no idea about any of that... but at least it makes a little sense now instead of seeming impossible (or like an error).

That is incorrect. They start off with a much higher rating, see post 16 and the rating document, and that is used to compute the rating of Peter based on his performace. The opponent's final rating is not used in his calculations.

Now, if he played another event against the same players, now that they have provisional ratings and he received the same score,  then his rating would most likely go down. I say most likely becsuse players with only losses or only wins are treated a bit differently in the formulas.

I am not aware of any floors under 1200, other than the absolute 100 floor. 

Where are the good ol' times when in my country there was only one (1 !) player who was rated below 1000. There were only 200 GM's around and a 2600+ player was absolute world class.

If they are rated 200 then the age formula isn't used.  If two unrated 8 year olds drew, then their rating would likely stay the same,  though the formulas are not done per game but per section of an event, so the other games would have a rating impact. 

So Peter Barendt played in another tournament: http://www.uschess.org/msa/XtblMain.php?201601160322.6-15838355

Here's the results:

Peter Berendt 111(p12) - 112(15)

r1: Loss  370(p8) - 397(p12)

r2: Loss 103(p4) - 108(p8)

r3: Loss unrated - 158(p4)

r4: BYE

That's right, Peter lost all 3 games, but gained a rating point. How can you explain that? A bye doesn't give you rating points, does it?

But there is - in fact, it completely explains the reason why this kid's rating keeps going up despite losing. I found the site that explains it here:

The formula for the absolute floor is 100 + 4(number wins) + 2 (number draws) + (number rated tournaments with at least 3 games played). It maxes out at 150.

So from this kid's stats online we see that in his 15 games, he has 1 win and 2 draws, in 4 tournaments played. So the formula fills out:

100 + 4(1) + 2(2) + 4 = 112. 

Thus, his floor increased simply by playing in another tournament. Someone could theoretically play 50 tournaments, lose every game, and see a rating increase each time.

You explain it by running the results through the rating formula. Or even read through the document.

To answer your question though, the overall score is used in the rating algorithm. So, he scored a point and apparently using that and the ratings of the opponents, one of which was unrated so gets initialized as previously stated, he apparently went up a point.

I've been told several times that Byes do not affect your rating whatsoever. Otherwise nobody would ever take a half point bye.

A bye on it's own doesn't change your rating, as it wasn't from a game played, however, your event score is used in the ratings calculations. Unless I'm missing something in the rating document, then byes are used in that score and calculation and play into the player's expected result for the event. If he did better than the expectancy formulas predicted, the rating increases.

You're worrying a lot over something very inconsequential really. In the end, it will all balance out.

Also, you said his floor increased which is incorrect. His floor is 100, which is the absolute minimum floor.  His rating, on the other hand, went up. To your last point, people take byes to get a break, still get a chance at prizes and as can be seen in the case you are worried about, can positively impact your rating (if your overall score was higher than expected based on the ratings of the players you played).