Statistically optimal 0-Vigor skill distribution at level 60

#1Peng_WayPosted 8/7/2013 8:47:50 AM
The short answer: 87 Power, 153 Endurance

The quantity to be maximized here is the "total boost factor": damage multiplier times the vitality multiplier. Pre-update, before power/endurance got hit by the nerf hammer, each increased their respective multiplier by 0.5% per point; post-update, each point in endurance increases vitality by 0.3%, while each point in power increases damage by 0.25%.

(Freshman-level calculus ahead; math-phobes be warned)

Pre-Update, at level 50:

I'll do the calculation for pre-update first just as an illustration, since the numbers are slightly easier to work with. Let F = boost factor, D = damage multiplier, V = vitality multiplier; let x = # points to put in power, y = # of points to put in endurance.

We are trying to maximize F = DV = (1 + 0.005x)(1 + 005y), where x + y = 200.

Substituting y = 200 - x, we have
F = (1 + 0.005x)(1 + 0.005(200-x)) = 2 + 0.005x - 0.000025x^2

F' = dF/dx = 0.005 - 0.00005x, F' = 0 when x = 100 (the only critical point)

The domain for x is [0, 200]; plugging in the two endpoints x = 0, x = 200 both give F = 2, as expected (meaning, you either get double damage or double vitality). At the critical point x = 100, we get F = 1.5 * 1.5 = 2.25, which is our maximum.


Post-Update, at level 60:

Now the numbers get a little more messy, but the setup is the same as before.

We want to maximize F = DV = (1 + 0.0025x)(1 + 0.003y), where x + y = 240. Again we substitute y = 240 - x, so that the problem becomes maximization over a single variable, x.

Solving this by setting F' = 0, we get x = 260/3 as the only critical point; at this point, F = 5329/3000, which is 1.77633333... Now, skill points only come as integers, so we'll have to settle for x = 87 (as 260/3 ~= 86.7). For x = 87, we have y = 153 and F = 1.7763325. Note that a 200-power, 40-endurance build yields F = 1.5 * 1.12 = 1.68, while a 40-power, 200-endurance build yields F = 1.1 * 1.6 = 1.76. Interestingly, the statistically optimal build is only very marginally (less than 1%) better than a 40-power, 200-endurance build.


NOTE: this is for putting 0 points in Vigor, which is not clearly understood at this point and someone over at TekkenZaibatsu did some extensive testing of the stats and found vigor to be pretty useless, his results are posted in one of the stickied threads in the TR forum on TZ.
#2IKillFanboysPosted 8/7/2013 8:52:16 AM
Nice job it's good to see the scientists come out with their discoveries. I myself am wondering about the mysteries of Vigor.
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#3Darkflare_EXPosted 8/7/2013 9:05:45 AM
Looks like I'll definitely be putting more points toward endurance.

May even have to use the free reset to move the points I have in vigor to either of the other two.
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#4Han_the_DragonPosted 8/7/2013 9:56:33 AM(edited)
Nice job!

I was thinking in not using the free reset, but am starting to get second thoughts..

Anyway I have a question, do I need to recalculate everything if I want to put points into Vigor? Not sure how linear that equation is to make an approximation.. and I don't feel like giving away my 50 Vigor, specially after fighting people with 150+ Vigor and see that I got 0 criticals in the match, while they probably got 100% critical rate..

Edit: The approximation I am talking is a linear one, like finding out what much percent each of those 2 status are (87/240*100 for power), and then use that to calculate the amount of the status with a new limit (190 instead of 240), like just throwing away the amount of points that I want to put into Vigor.

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#5_HaradaLoving_Posted 8/7/2013 10:06:53 AM
Han_the_Dragon posted...
Nice job!

I was thinking in not using the free reset, but am starting to get second thoughts..

Anyway I have a question, do I need to recalculate everything if I want to put points into Vigor? Not sure how linear that equation is to make an approximation.. and I don't feel like giving away my 50 Vigor, specially after fighting people with 150+ Vigor and see that I got 0 criticals in the match, while they probably got 100% critical rate..

Edit: The approximation I am talking is a linear one, like finding out what much percent each of those 2 status are (87/240*100 for power), and then use that to calculate the amount of the status with a new limit (190 instead of 240), like just throwing away the amount of points that I want to put into Vigor.


You never get 100% critical rate. Even 200 vigor vs 0 vigor.
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#6IKillFanboysPosted 8/7/2013 10:12:27 AM
_HaradaLoving_ posted...
Han_the_Dragon posted...
Nice job!

I was thinking in not using the free reset, but am starting to get second thoughts..

Anyway I have a question, do I need to recalculate everything if I want to put points into Vigor? Not sure how linear that equation is to make an approximation.. and I don't feel like giving away my 50 Vigor, specially after fighting people with 150+ Vigor and see that I got 0 criticals in the match, while they probably got 100% critical rate..

Edit: The approximation I am talking is a linear one, like finding out what much percent each of those 2 status are (87/240*100 for power), and then use that to calculate the amount of the status with a new limit (190 instead of 240), like just throwing away the amount of points that I want to put into Vigor.


You never get 100% critical rate. Even 200 vigor vs 0 vigor.


Has anybody tested this yet with 200 vigor to see if this is accurate?
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There are so many things you do that make me feel like you crossed the line
But what goes up will surely fall and I'm counting down the time
#7Peng_Way(Topic Creator)Posted 8/7/2013 10:55:47 AM
Han_the_Dragon posted...
Nice job!

I was thinking in not using the free reset, but am starting to get second thoughts..

Anyway I have a question, do I need to recalculate everything if I want to put points into Vigor? Not sure how linear that equation is to make an approximation.. and I don't feel like giving away my 50 Vigor, specially after fighting people with 150+ Vigor and see that I got 0 criticals in the match, while they probably got 100% critical rate..

Edit: The approximation I am talking is a linear one, like finding out what much percent each of those 2 status are (87/240*100 for power), and then use that to calculate the amount of the status with a new limit (190 instead of 240), like just throwing away the amount of points that I want to put into Vigor.


Unfortunately the optimal distribution does not scale linearly (i.e. you can't just use the same ratio of Pow/Total when the total available skill points is 240 versus 100). I'll spare you the mathematical details, but generally, for fewer total skill points, put a greater proportion of them into endurance. The Pow/Total ratio of 87/240 is optimal only when the total is 240; when it's 190, repeating the above calculations will give you an optimal distribution of 62 Power, 128 Endurance.

Some footnotes:
1. For up to 68 total skill points (level 17 if you don't put any point in Vigor), you should put all your points in Endurance; when you have 68 points, putting 1 point into power is optimal.

2. At level 83 (not sure when Namco will raise the level cap enough to allow this), with a total of 332 skill points the optimal point is 133 power, 199 endurance. Since you can't go above 200 in any stat, beyond this point my optimization is no longer applicable. You're either better off having 200 endurance and the remaining points in all power, or some combination of power/vigor, depending on what vigor does exactly.

3. I'm currently at level 51 and the current stats on my Jack-6 (96/108 Pow/End) is not optimal (it should be 69/135); I may have to use another reset drink to tune up my robot.

4. I don't know if damage/hp are calculated as integers or real numbers; i.e. "is it possible to have 0.5hp?" Certainly the combo damage display only shows an integer value, and in fact it's only the floor (integer part) of the actual value. As a concrete example: Jack's tombstone throw does 58 pts of base damage; with 96 Power, it should be doing 58 * 1.24 = 71.92 dmg; but, the game only shows the damage value as 71. Did it really just do 71 dmg, or did it actually do 71.92 and the game is just showing 71? This is actually a rather important issue in terms of fine-tuning your own stat distribution.
#8Peng_Way(Topic Creator)Posted 8/7/2013 11:00:49 AM
IKillFanboys posted...

Has anybody tested this yet with 200 vigor to see if this is accurate?


Yes, see the following link:

http://www.tekkenzaibatsu.com/forums/showthread.php?postid=4677080#post4677080

Scroll down that page to see a spreadsheet created by the same person. This is what I referred to in my opening post.
#9Han_the_DragonPosted 8/7/2013 11:20:27 AM
_HaradaLoving_ posted...
Han_the_Dragon posted...


Anyway I have a question, do I need to recalculate everything if I want to put points into Vigor? Not sure how linear that equation is to make an approximation.. and I don't feel like giving away my 50 Vigor, specially after fighting people with 150+ Vigor and see that I got 0 criticals in the match, while they probably got 100% critical rate..



You never get 100% critical rate. Even 200 vigor vs 0 vigor.


As I said, he probably got 100% critical rate, that means he got critical in all critical arts he used in the match, there's no need for something to be 100% to happen all the time in a single match. My main point is that with a big difference in Vigor the difference in the critical rate is also big, to the point of being relevant (in my opinion obviously).

Peng_Way posted...

Unfortunately the optimal distribution does not scale linearly (i.e. you can't just use the same ratio of Pow/Total when the total available skill points is 240 versus 100). I'll spare you the mathematical details, but generally, for fewer total skill points, put a greater proportion of them into endurance. The Pow/Total ratio of 87/240 is optimal only when the total is 240; when it's 190, repeating the above calculations will give you an optimal distribution of 62 Power, 128 Endurance.

Some footnotes:
1. For up to 68 total skill points (level 17 if you don't put any point in Vigor), you should put all your points in Endurance; when you have 68 points, putting 1 point into power is optimal.

2. At level 83 (not sure when Namco will raise the level cap enough to allow this), with a total of 332 skill points the optimal point is 133 power, 199 endurance. Since you can't go above 200 in any stat, beyond this point my optimization is no longer applicable. You're either better off having 200 endurance and the remaining points in all power, or some combination of power/vigor, depending on what vigor does exactly.

3. I'm currently at level 51 and the current stats on my Jack-6 (96/108 Pow/End) is not optimal (it should be 69/135); I may have to use another reset drink to tune up my robot.

4. I don't know if damage/hp are calculated as integers or real numbers; i.e. "is it possible to have 0.5hp?" Certainly the combo damage display only shows an integer value, and in fact it's only the floor (integer part) of the actual value. As a concrete example: Jack's tombstone throw does 58 pts of base damage; with 96 Power, it should be doing 58 * 1.24 = 71.92 dmg; but, the game only shows the damage value as 71. Did it really just do 71 dmg, or did it actually do 71.92 and the game is just showing 71? This is actually a rather important issue in terms of fine-tuning your own stat distribution.


I was thinking it wouldn't be linear nor close to that when I made my post, just wanted to be sure.

Thanks, and thanks to do the math for me for the 190 total!
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#10Peng_Way(Topic Creator)Posted 8/7/2013 3:34:52 PM
Han_the_Dragon posted...

I was thinking it wouldn't be linear nor close to that when I made my post, just wanted to be sure.

Thanks, and thanks to do the math for me for the 190 total!


Sure thing. In fact, it's easy to find the optimal 0-vigor distribution for any level:

let T = total number of skill points you have (or want to allocate among Pow/End);

T < 68: put all points into endurance

68 <= T <= 332: put (T-66)/2 into power, the rest (T+66)/2 into endurance. Works better when T is even.

T > 332: put 200 into endurance, 133 into power, the rest either all into power or some combination of power/vigor.