Pixies are unbalanced
Pixies have Superior Invisibility that makes them and any equipment they carry invisible. They also have a whopping Stealth +7 on top. They can all cast Druidcraft (at will), and all of the following once per day.
- Cantrips: dancing lights
- Level 1: entangle, sleep, detect evil and good
- Level 2: phantasmal force, detect thoughts
- Level 3: dispel magic, fly
- Level 4: polymorph, confusion
The spell contingent is nearly as good as a level 7 spellcaster (They have one less first, second and third level spell and one more 4th level spell, so they are two levels short).
To balance it they only have one hit point and no damaging attacks.
I think this is a good example on how extreme strengths and weaknesses do not sum up to a balanced creature.
As Thomas is pointing out, the first issue is that pixies rarely appear all by themselves. Typically, there are other woodland creatures, wolves, bears, boars etc., that they are friends with. In the case of them being conjured, these are the PCs.
That means, in many cases they will not even have to do the fighting or damage dealing by themselves, they can entirely focus on their overpowered control aspects, casting confusion on the opponents, or polymorphing other higher CR monsters to double their combat life. So their underpowered weak side does not matter, while their overpowered upside does.
But let's ignore these situations, and look just at what they could do all by themselves.
According to the encounter budgeting math on DMG p. 82, a party of 4 PCs of second level has an XP threshold for a medium encounter of 400XP. A pixie at CR 1/4 is worth 50 XP, and with a multiplier of 2 for 3-6 appearing, an encounter for such a party with 4 pixies should be a medium difficulty encounter that they suffer "no casualties. One or more of them might need to use healing resources."
Realistically, with their stealth and invisibility, pixies will be able to get surprise and ambush a party of PCs pretty much every time. Their spell DC does not even matter in such an encounter: they can all cast sleep, which will generate enough hp (on average 22) to put every party member of a level 2 party to sleep.
They can then polymorph into wolves and kill the sleeping PCs with pack attacks, one after the other. With advantage to the attack and average 7 damage per bite, and auto crits on a hit due to unconsciousness, the prone and sleeping PCs are unlikely to survive.
Alternatively, they could use the polymorph spells on the sleeping PCs turning them into snails. They then can carry all PCs who failed their save and now are snails up 60 feet per round, and drop them to the ground for 20d6 of fall damage, the first point of damage of will turn the PCs back to their normal form, and the remaining damage will kill them.
There is a high likelyhood that such an encounter will result in the death of at least one PC, and quite possibly in a total party kill. This is clearly not within the range of a medium encounter suggested by their CR.
Just based on the spellcasting arsenal they have and the implied level, they should likely be somewhere around CR 3. Their weaknesses pull this down as they are ridiculously easy to kill, once you get a drop on them, even with a decent Armor Class of 15 and Magic Resistance, that side is more like what you see in CR 0 or CR 1/8 creatures.
I think this imbalance in abilities makes them hard to correctly put at any CR, but a CR like at least 1/2 or 1 would be more appropriate for how they play. At CR 1/2 they would constitute a "deadly" encounter for a party of level 2, meaning it "could be lethal for one or more player characters", at CR 1 it would be so for a level 3 party.
PS. The calculated CR for pixies is 1
While I do not put much stock into the calculation of CRs using the DMG rules for Creating a Monster on p. 274, they can give us a benchmark value for the Pixie CR.
Defensive Challenge Rating: 1 hp, CR 0. Modified by Armor Class 15, Magic Resistance for effective AC 17, Superior Invisibility for effective AC 19 and flight for effective AC 21. Increase by one step for each 2 points of AC over 13 means increase by 4 steps: New CR 1.
Offensive Challenge Rating: Damage per round: 0, CR 0. Use the save DC instead of damage per round, as the monster relies more on spells, instead of attacks, to modify. DC <= 13 does not change this. Spellcasting increasing damage per round to 9 increases this (still unmodified by the save DC) to: New CR 1.
Average Challenge Rating: (1 + 1)/2 rounded down = 1
CR-modifying special abilities
This section covers the detailed features that modify the base CR rating numbers from hp, AC, to hit, damage and DC.
Some special traits (such as Magic Resistance), special actions (such as Superior Invisibility), and special reactions (such as Parry) can improve a monster's combat effectiveness and potentially increase its challenge rating.
Magic Resistance: increase the effective AC by 2.
Flying Monster: Increase the effective AC by 2. This one is debatable, as it requires the monster can deal damage at range. I'll take the use of phantasmal force as meaning it can. The argument that characters under level 10 have a harder time to deal with flyers remains valid, especially in combination with stealth and invisibility.
Innate spellcasting: The rule for this says
The impact that the Innate Spellcasting and Spellcasting special
traits have on a monster's challenge rating depends on the spells that the monster can cast. Spells that deal more damage than the monster's normal attack routine and spells that increase the monster's AC or hit points need to be accounted for when determining the monster's final challenge rating
The monsters normal attack routine deals no damage, so that is an easy bar to clear. This section does not apply only to direct damage spells, as it does not say so. It only requires that the spell "can deal more damage than the monster's normal attack routine", here more than none. Phantasmal Force can deal 1d6 psychic damage per round, and would qualify.
For sleep it depends if you count the effect as "damage". One can argue that sleep damage is no "real" damage and should not count, but it takes opponents out of combat based on hit points dealt, just like real damage, and in practical terms against lower hp opponents, is one of the most effective attacks the Pixie has. If you count it as damage, you would apply the following rule
If a monster's damage output varies from round to round, calculate its damage output each round for the first three rounds of combat, and take the average.
This would mean 22.5 points of sleep damage the first round (on average), and then 3.5 points of psychic damage in the second and third round (7 for both), for a total of 29.5 damage, or divided by 3 rounded down, 9 damage per round.
Polymorph on itself can transform it to, for example a wolf, which would deal 7 damage and have 11 hit points, but would have lower AC and no flight, turning it into another CR 1/4 creature, so do I think polymorph, while at the root of this question, does not actually change the CR as per the calculation rules.
It is well known that these rules do not capture all the possible interactions that a creature's features can generate -- for example here the pixie polymorphing its victim to something tiny and harmless and then dropping it with flight from a large height to kill it. Therefore the MM monsters often differ, both in individual cases, and even systematically. Moreover, even the monsters in the MM vary widely when it comes to combat strength. I do agree with Matthieu, that CR may not be a good gauge of power to begin with, and it at best a clunky and unreliable tool.
Creating a monster isn't just a number-crunching exercise. The guidelines in this chapter can help you create monsters, but the only way to know whether a monster is fun is to playtest it. After seeing your monster in action, you might want to adjust the challenge rating up or down based on your experiences.
So it is clear that the CR should NOT just be based on the hp, AC, damage and to hit stats, but on how the monster plays in actual encounters. I think that the calculated CR of 1 (or even of 1/2, if you are more conservative in how to treat sleep or flight) is both a better match for this than the MM's CR 1/4.