Forums / Guides and Articles / Note on MT Range
| Note on MT Range | ||||
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| 06:40:18 Nov 29th 19 - Percy (Mr. Percy The Noble): TL;DR - Found exact equation that calculates MT range (for an Elf) and is within an accuracy of 50 MTs from 10 MTs up to 35000 MTs. Have graphs to show it. Enjoy! X distance away, need Y number of MTs: Y = 55.174X^2 - 116.75X + 76.052 There's not a sure-fire way to go the opposite direction, so either use Excel and that equation to guess and check your way to an answer, or use the graph below as a quick reference. Efforts to easily create a similar equation by inverting data requires a sixth order equation that is just really ugly and doesnt describe the equation. Just dont feel like breaking out the calculus for this :P I conducted a fair amount of research with the aide of the wonderful people of Mantrax, and from these experiments I have gathered the equation that determines the amount of range you get for a given number of MTs. While not the verbatim equation ZeTa uses, it is within an accuracy of 50 MTs at any given point from 10 MTs up to 35000 MTs (max tested). I wont bore with the details (feel free to PM if you have questions), but here are the results:  MT numbers are on the y axis, and the range (as counted in scout tick distances) is the x axis. Now what do I mean by scout tick distance: each large X away from the MC in question is one tick. Even though movement-wise this is actually two ticks, a Scout Tick here is simply adding the large X's you see. Below is an example I actually used early on during Mantrax this era:  The city in the green circle is an MC, and they want to cast on Lazypug Inn. By dragging a scout over, you can drag around (dont actually move it) in a straight line outwards to get the range in scout ticks needed to cast (in this case 3.25 ticks) and can use the equation on the graph to get the number of MTs required. Likewise, if you had a given MT count and wanted to know how far away you can reach, just use the inverse of the equation. Hope this helps others out there! Let me know if something needs clarified or anything else :P | ||||
| 07:17:21 Nov 29th 19 - Endless (Mahatma Gandhi): or you could look at magic power and figure it out :p you should really ask someone in FW for Binh’s guide, unless you just like to do this kind of stuff ... | ||||
| 07:21:30 Nov 29th 19 - Mr. Oenomaos: Thx for the tests, very useful to know. | ||||
| 07:26:17 Nov 29th 19 - Percy (Sir Inception): That’s what I did to get these numbers :P but for myself, knowing what drives the range equation is worthwhile. Cause I can’t use that same MP checking method on an enemy as I cant check his power ;) Just last era on Fant when I had a primitive version, I was able to predict the exact moment a new enemy MC would be casting on us because we knew his MT count and these estimations. Very valuable on the battlefield, more so to check enemy ranges than your own! | ||||
| 20:20:33 Nov 29th 19 - Dakarta (Prince Dakarta): Does this all mean when somebody will be able to cast on any given city/army with full power and max %? | ||||
| 20:27:08 Nov 29th 19 - Endless (Ms. Evil): found Binh's old post, probably common knowledge since it's been floating around for over 10 years Magic table: Mus' magic power per magical unit: Magic power = .2A*B*(1+C) where A = magic level and B = # of mus and C = tower mp bonus Tower mp bonus = A/B where A = # of magic towers and B = Total buildings in that magic city. Note: max tower mp bonus is 50% Level 1 2 3 4 5 6 7 8 9 MO:MD (Magic Offense:Magic Defense) 0.25 6% 1% 0.5 15% 5% 2% 1% 0.75 25% 9% 5% 2% 1% 1 34% 15% 8% 3% 1% 1% - 0% 1.25 42% 20% 11% 5% 3% 1% - 0% 1.5 48% 25% 15% 7% 4% 2% - 0% 1.75 54% 30% 18% 9% 5% 3% - 0% 2 58% 34% 22% 11% 6% 4% - 0% 2.25 62% 38% 25% 13% 7% 4% - 0% 2.5 65% 42% 28% 15% 9% 5% - 0% 2.75 67% 45% 31% 17% 10% 6% - 0% 3 70% 48% 34% 19% 11% 7% - 1% 3.25 72% 51% 37% 20% 12% 8% - 1% 3.5 74% 54% 40% 22% 14% 9% - 1% 3.75 75% 56% 42% 24% 15% 10% - 1% 4 77% 58% 44% 26% 16% 11% - 1% 4.5 79% 62% 48% 29% 18% 12% - 2% 5 81% 65% 52% 31% 20% 14% - 2% 5.5 82% 67% 55% 34% 18% 15% - 3% 6.5 85% 72% 60% 38% 26% 18% - 4% 7.5 87% 75% 65% 42% 29% 21% - 5% 8.5:1 88% 78% 68% 45% 31% 23% - 6% 9.5:1 89% 80% 71% 47% 34% 25% - 7% 10:1 90% 81% 72% 48% 35% 26% - 7% 15:1 93% 87% 81% 56% 42% 32% - 12% 20:1 95% 90% 85% 61% 46% 36% - 15% 30:1 96% 93% 90% 65% 50% 40% - 21% 40:1 97% 95% 92% 67% 52% 42% - 24% 50:1 98% 96% 94% 69% 54% 44% - 26% 100:1 99% 98% 97% 72% 57% 47% - 31% Cap % 100% 100% 100% 75% 60% 50% 42% 37% 33% MP Cap% 74% 74% 74% 55% 44% 37% 31% 27% 24% Magic protection lower your success rate by (.25*A+1)% when A = your base success rate. Magic protection is a double edge sword as it also protect you against your own utility spell. New max chance table for spells Level 1: Max chance = 100% Level 2: Max chance = 95% Level 3: Max chance = 89% Level 4: Max chance = 82% Level 5: Max chance = 75% Level 6: Max chance = 67% Level 7: Max chance = 59% Level 8: Max chance = 50% Level 9: Max chance = 40% Level 10: Max chance = 31% | ||||
| 22:57:19 Nov 29th 19 - Percy (Sir Inception): @Dakarta yes, that’s the equation to find distance for max power casts, which in turn yields the max chance you will get for the number of MTs and MUs you have. I did the math and found the inverse of that equation too, I’ll post it soon. The (now two) equations I found are a perfect supplement to Binh’s guide, as his write up gives the magic power scaling as you increase MUs and Magic Level, while mine gives you how far a given set of MTs will reach on the map at a high level of accuracy and precision. | ||||
| 14:21:24 Dec 1st 19 - Binh (Mr. Lone Swordsman): Would be nice if you can do the same for non-elves also. I like how you use scout ticks as a measurement unit as it is easier to figure out than the x,y distance coded in the Vu map. | ||||
| 14:47:05 Dec 1st 19 - Percy (Mr. Percy The Noble): My goal is to replicate a few data points as non-Elf, which I might be able accomplish on GvE as Halfer, otherwise it will have to wait till I start a new world again, likely as Orc lol That was my goal: make an easy-to-use metric that can be used quickly. Glad you think it as easy as I do :) | ||||
| 01:48:31 Dec 2nd 19 - Matthew (Chief Mathew): Thank you for this information, it is quite useful. | ||||
| 20:49:17 Dec 3rd 19 - Percy (Mr. Percy The Noble): As a follow up, I have both forms of the MT-range equation. Required MTs to achieve a target range (in scout tick distance): MTs = 55.174*Range^2 - 116.78*Range + 76.052 Total range (scout tick distance) achieved by a target number of MTs: Range = [116.78 + sqrt(-3146.8 + 220.696*MTs)] / 110.348 | ||||
| 21:41:45 Dec 3rd 19 - Stormy (Lord Herman Webster Mudgett): tooooo muuuccchhhhh maaaattthhhhhh | ||||
| 22:20:26 Dec 3rd 19 - Percy (Sir Inception): Lol it’s not for everyone, but for those who want to do a quick calc on enemy range or how many MTs you need to reach an enemy, it can come in quite handy ;) Same as the equation to calculate prep time is a lot of math, but that’s also an incredibly useful tool as well! | ||||
| 22:44:45 Dec 3rd 19 - Stormy (Lord Herman Webster Mudgett): Lol you know us historians over here at Murray building Percy we need to take our shoes off to count to 20 (Percy and I went to the same university😜) | ||||
| 23:29:36 Dec 3rd 19 - Percy (Sir Varro The Adept): Lol and you know us engineers don’t mind crunching numbers if it makes things more efficient ;) that’s why I gave both the graph and the raw equations. Can estimate from the graph or do number crunching, your choice! What most don’t realize is that also means we share the same constant heartache of having our favorite sports team disappoint year after year... | ||||
| 09:44:32 Dec 4th 19 - Endless (Ms. Zetian): pray to Odin and be done with it :p | ||||
| 14:25:46 Dec 4th 19 - Dakarta (Duke Dekarta): Percy and Stormy.. Don't talk about heartache of sports teams... I'm a Cleveland fan.. so that means Browns, Cavs and Indians... | ||||
| 18:05:37 Dec 4th 19 - Dakarta (Lord Dacarta): Based on the calculations here, I created this little chart in excel... The Magic Power takes into account the max MP Bonus of 50%, i.e. if it goes above 50%, it just stays at 50% but it'll go down based off of MT:Total Buildings if it drops below 50%  | ||||
| 20:00:17 Dec 4th 19 - Percy (Sir Varro The Adept): Nice incorporation! At low MT counts (less than 200) there is as much as a 40 MT discrepancy at the very low end, but after 200 it’s within +-10 MTs of accuracy. I only mention that cause you used a very low MT number, which has a known large error :P casting with that low of MTs is like casting from an army, which the equation doesn’t do well. I do have that number though, you get full power casting range of 0.9 scout ticks from an army | ||||
| 20:36:10 Dec 4th 19 - Dakarta (Prince Dakarta): I only used that low of MTs to show that the MP Bonus would change from 50% to whatever it is and wouldn't go more than 50%.    | ||||
| 16:54:08 Apr 14th 20 - Percy (Sir Percy The Something): Not to revive an old thread, but a table posted by Endless has recently caught my attention. Can anyone interpret the Magic Table posted a few posts above? It doesnt make too much sense to me right now.. In particular, the MO/MD ratio seems to yeidl very strange results. When casting EITS (level 1 spell) I can have less overall magic power and still have a >50% chance to cast, but according to the table the max should be around 34% at max. Am I interpreting something wrong? I ask cause I was trying to back out an enemy's magic level using EITS on the city, but that table (as I understand it) doesnt seem to hold the data it claims to hold, which prevents that :/ | ||||
| 05:30:40 Apr 16th 20 - Binh (Mr. Forgotten Dead): Very old table that i made to find out how much more magic power i need to get a certain % if i already have x% on it. As magic defense formula isnt 100% known, the above table is only 100% good for comparison purposes. It used to be that magic defense provided by mus varies upon the defender's magic level. Now each mu defense only calculate as if it had level 5 magic. Say you used 1 mu with level 8 magic in a city that provide 50% mp bonus from mts. Thats 1*(.2*8)*1.5 = 2.4 magic power. If you cast eits with that on an army with 1 mu with level 9 magic, the magic defense is around 1*(.2*5)=1 So magic offense to defense ratio is 2.4/1 This would give around 64% for eits. | ||||
| 05:38:24 Apr 16th 20 - Binh (Mr. Forgotten Dead): Note that the precise magic defense provided by units that are not mus (very low), buildings(medium), and magic towers(high) are unknown. | ||||
| 06:14:02 Apr 16th 20 - Percy (Sir Percy The Hillbilly): Ah, I gotcha. So because there's so many unknowns it’s all approximations for quick math. Man, would be cool to figure that stuff out, but the sheer amount of testing would be overwhelming for a non-essential data point lol I can see why it hasn’t been done. Thanks for the reply though, puts to rest my thoughts on that | ||||
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