HTP vs MoN avoidability analysis

HTP and MoN are the two endgame pendants in the game. There is some debate about which one is better for which class. A 10atk mon seems to give a slightly bigger range boost (~roughyl 3 atk compared to a non-chaosed HTP, this varies depending on class/level/gear), but the extra luk and avoid stats from the HTP seems to give a differential of ~ 50 avoid. Recently someone seems to have cracked the formula for the dodge rate(https://forum.maplelegends.com/index.php?threads/maplelegends-avoidability-formula.26694/). Assuming this is accurate, we can now calculate the dodge rate difference that 50 avoid results in. Of course this is going to depend on the class and avoid rate, so I will be doing this calculation specifically for lategame archers, NLs, warriors, and Corsairs, and the context will be inside HT.

The General Formula
If your level is higher than the monsters level, the Dodge Rate against magical attacks (which is was is relevant in HT) is given by
Dodge Rate= 10/9 - Monster Accuracy/(0.9*Avoid)

HT has an accuracy of 250, so we can simplify this to

Dodge Rate = 10/9 - (250/0.9)/(Avoid)

This formula is of course non-linear, but we assume that the addition of 50 avoid is "small"( that is 50 / original avoid << 1) we can taylor expand up to the linear term about the original avoid and get an estimate for the "dodge rate % per unit avoid".

Differentiation the Dodge Rate with respect to "Avoid"

Avoid Rate per unit Avoid = (250/0.9) / (Avoid)^(2)

Now we can apply this formula for Various classes.

Archer
Endgame archers will have around ~350 avoid fully buffed with a MoN.
Avoid Rate per unit Avoid ~ (250/0.9) / (350)^(2) = ~0.23%

This means that every point of avoid will add roughly ~0.23% chance of dodging an attack from Horntail. From this we can estimate that 50 avoid translates to roughly ~11% dodge rate.

If you dont want to bother with the taylor expansions, we can just look at the difference between the avoid rates at 400 avoid(HTP) and 350 avoid(MoN)

Dodge Rate(Avoid = 400) ~ 41.6%
Dodge Rate(Avoid = 350) ~ 31.7%

Roughly a 10% difference in dodge rate, which is close to the answer from our linearized analysis. This means that during HT an archer will dodge roughly 2-3 more attacks per min with an HTP. To any archer that has HTed before, it should be clear that this is much more significant than a mere 3atk.

For a slightly more quantitative approach, we can estimate that HT will hit you roughly 25 times in 1 min. An extra 10% dodge rate amounts to about 2.5 extra dodges. Each dodge saves roughly 1second (taking into account time to get back into position and initial hurricane start up animation). This means you saves 2.5 seconds out of 60 seconds, increassing your dpm by ~4%. To evaluate the DPM increase of ~3atk, we have to make some assumptions the total attack of the character. For a reasonably well geared archer on HT buff or conc, this should be around ~200. This means that you get an extra 3/200 ~1.5% dpm increase from the 3atk. SHould be pretty clear that the avoid rate is superior in this situation.

NLs
Endgame NLs have around somewhere in the neighborhood ~700 avoid, but we also have to take into account shifter. Assuming that shifter modifies the Hit Rate by a factor of 0.7, the new hit rate formula is,

Hit Rate(with Shifter) = 0.7(1- Dodge Rate(no shifter)) = 0.7(Monster Accuracy/(0.9*Avoid) - 1/9)
Dodge Rate(with shifter) = 1-Hit Rate (with Shifter)
=1 - 0.7(Monster Accuracy/(0.9*Avoid) - 1/9)

Taking the derivative again,

Dodge Rate per unit avoid = 0.7(Monster Accuracy/0.9)(1/Avoid)^2
= 0.7(250/0.9) / (Avoid)^(2)

Avoid Rate per unit Avoid ~ 0.7(250/0.9) / (700)^(2) = ~0.04%

Clearly NLs benefit a lot less from the addition of avoid, this has to do with the non-linear nature of the formula that causes diminishing returns at high values of avoid.

An HTP will give roughly 2% more avoid rate for an NL. I can't quite tell if this is worth the ~3atk loss from the MoN.

Corsair/warriors
To the best of my understanding corsairs have roughly 200 avoid at 18x using MoN. This is a weird one since if you plug these values into the formula you get a negative dodge rate. The same problem seems to arise with warriors as they have even less avoid. This seems to suggest you can never dodge an attack from HT. I don't know if this is right, perhaps there is some kind of lower cap on the magical avoid. However if this is true, then sairs and warriors should get no benefit from the extra avoid.