Is this that-clause for set comparison or a relative?

[i] It was lucky that Harry had tea with Hagrid to look forward to,
because the Potions lesson turned out to be the worst thing that had

happened to him so far.

–– Harry Potter and the Sorcerer's Stone

[ii] a. Ed made the most mistakes of them all.
b. It sold for the highest price ever paid for a Cezanne.

–– CGEL, p.1101

[ii] is called set comparison, for “one member is picked out as being

at the top of the scale. In [ii] the set is identified by the NP them
all: the comparison is between the members of this set with respect to
how many mistakes they each made, with Ed ranked at the top of the
scale. It is possible to omit the PP of them all, in which case the
set being compared is identified contextually. In [iib] the comparison
is between the prices paid for painting by Cezanne, and again one is
picked out as being at the top of the scale - CGEL,1102”.

It seems like [i] is a kind of the set comparison, but I’m not sure for [i] has that-clause that could be understood as a relative one. Is the that-clause a set one or a relative?

Answer

At first blush, it seems that your example sentence involves both an integrated relative clause and a set comparison.

(For relative clause: another member has already addressed that.)

For "set comparison": The set is "the things that had happened to him so far", and a member of that set is "the Potions lesson" which also happens to be the worst member of that set with respect to the attribute of badness.

In other words, the "Portions lesson" is being, or has been, compared to all the other "things" that had happened to him. Thus, a set comparison is being made in that example sentence.