HP percent indicator research

HP bar horizontal length in USUM is 86 pixels; in SM, it is 99 pixels. Pokemon uses school rounding (round up on >= 0.5, round down on < 0.5) for determining how many pixels should be drawn relative to that Pokemon's HP. For example, 684/688 HP is 86/86 pixels, but 683/688 HP is 85/86 pixels. You can use ratios to generalize this:

current HP   current pixels
__________ = ______________
total HP           86

For the following tests, I used a level 92 Blissey that had 600 total HP, Wi-Fi Singles No Restrictions.

The HP bar turns different colors based on % HP. This is independent of current pixel length (for example, 43/86 pixels could represent a yellow or green HP bar)
301/600 - Green
300/600 - Yellow
121/600 - Yellow
120/600 - Red

Conclusion:
Green: 50% < x <= 100%
Yellow: 20% < x <= 50%
Red: 0% < x <= 20%

Messages that appear upon switching in are based on % HP. These only occur in Single Battles.

486/600 - Go! Pokemon!
483/600 - Go! Pokemon!
482/600 - Go! Pokemon!
481/600 - Go! Pokemon!
480/600 - Go! Pokemon!
479/600 - Go! Pokemon!
476/600 - Go! Pokemon!
475/600 - Go! Pokemon!
474/600 - Go! Pokemon!
473/600 - Go! Pokemon!
472/600 - Go! Pokemon!
471/600 - Go! Pokemon!
470/600 - Go! Pokemon!
467/600 - Go! Pokemon!
466/600 - Go! Pokemon!
465/600 - Go! Pokemon!
464/600 - You're in charge, Pokemon!
463/600 - You're in charge, Pokemon!
456/600 - You're in charge, Pokemon!
450/600 - You're in charge, Pokemon!
400/600 - You're in charge, Pokemon!
350/600 - You're in charge, Pokemon!
330/600 - You're in charge, Pokemon!
329/600 - Go for it, Pokemon!
320/600 - Go for it, Pokemon!
309/600 - Go for it, Pokemon!
301/600 - Go for it, Pokemon!
292/600 - Go for it, Pokemon!
290/600 - Go for it, Pokemon!
240/600 - Go for it, Pokemon!
226/600 - Go for it, Pokemon!
220/600 - Go for it, Pokemon!
219/600 - Go for it, Pokemon!
218/600 - Go for it, Pokemon!
210/600 - Go for it, Pokemon!
208/600 - Go for it, Pokemon!
207/600 - Go for it, Pokemon!
201/600 - Go for it, Pokemon!
200/600 - Go for it, Pokemon!
199/600 - Go for it, Pokemon!
198/600 - Go for it, Pokemon!
197/600 - Go for it, Pokemon!
196/600 - Go for it, Pokemon!
195/600 - Go for it, Pokemon!
194/600 - Just a little more! Hang in there, Pokemon!
186/600 - Just a little more! Hang in there, Pokemon!
182/600 - Just a little more! Hang in there, Pokemon!
108/600 - Just a little more! Hang in there, Pokemon!
107/600 - Just a little more! Hang in there, Pokemon!
139/600 - Just a little more! Hang in there, Pokemon!
119/600 - Just a little more! Hang in there, Pokemon!
84/600 - Just a little more! Hang in there, Pokemon!
76/600 - Just a little more! Hang in there, Pokemon!
75/600 - Just a little more! Hang in there, Pokemon!
72/600 - Just a little more! Hang in there, Pokemon!
71/600 - Just a little more! Hang in there, Pokemon!
67/600 - Just a little more! Hang in there, Pokemon!
66/600 - Just a little more! Hang in there, Pokemon!
63/600 - Just a little more! Hang in there, Pokemon!
62/600 - Just a little more! Hang in there, Pokemon!
61/600 - Just a little more! Hang in there, Pokemon!
60/600 - Just a little more! Hang in there, Pokemon!
59/600 - Your opponent's weak! Get 'em, Pokemon!
49/600 - Your opponent's weak! Get 'em, Pokemon!
47/600 - Your opponent's weak! Get 'em, Pokemon!

Conclusion:
"Go! <Pokemon>!": 77.5-100%
"You're in charge, <Pokemon>!": 55% <= x < 77.5%
"Go for it, <Pokemon>! ": 32.5% <= x < 55%
"Just a little more! Hang in there, <Pokemon>!": 10% <= x < 32.5%
"Your opponent's weak! Get 'em, <Pokemon>!": 0 < x < 10%

Messages upon switching out (e.g. "Good job <Pokemon>"! Come back!") do not appear in Wi-Fi battles. Curiously, they will appear in Battle Videos.