Warrior General Games

Originally posted by AirMcMVP
Stopping at 40% may be a waste but going to 50% can be beneficial.

As for asking me to prove something mathematically, sorry, not my game. I've never been a math guy and don't intend to start now. I follow several commonly used plans and alter them here and there. I end up building dots that could play on just about any team in the game. Not always elite but darn close.
Indeed, 30% and 50% are easier to pay off than 40%, that is exactly what we were trying to tell you. 40% is not a good idea!

If you don't want to take the trouble then accept the work of all those that did, ok?

Not sure I'm understanding the logic here. Are you saying that the 40% bonus is subsumed by the 30% bonus because of rounding? These are the training values:

https://sites.google.com/site/glbmandyross/training_hotspots

The only place that 30% subsumes the 40% bonus on 4-way multi-training is above 94.

I may be misunderstanding your point Hag.

Subtract the difference in training between 4 stars and 3 stars. Calculate the training gains from that difference. Make it pay off before 94 (and frankly, who DOESN'T train after 94 nowadays?) without training during inefficient regions (high 50s, 65-68, etc). Remember, it costs 24 BTs, the gain from stars minus the gain from 3 stars has to be bigger than those 24 BTs and the associated lower number of multi-training sessions.

Layman's terms (and not those of the mathematically bent brains) is that sometimes what looks right with the numbers just isn't and that 40% in this case doesn't justify the expense of BT's for the gains you receive. 30%, yes. 50%, yes... 40%, no. And I trust Hag on this cuz I never do 40% anymore.

OK, I did the math. The tl;dr version is that the fourth upgrade will provide a marginal SP value benefit over the third upgrade only if you multi-train that attribute at least 60 times.

The following calculations look only to the multi-training portion of a build, and thus do not consider any non-multi-training issues at the beginning and end of a build. This will not affect most attributes, although there are some important exceptions if you plan to light train the attribute in question for a significant period of time.

First, define the average training return of a single multi-train as Y. In other words, Y is equal to the average increase in SP you will gain to a single attribute when multi-training. Second, define X as the number of times you will multi-train the attribute at issue.

The gross return from the first upgrade is [0.1Y * X]. The gross total return from the second upgrade is [0.2Y * X] and so on.

The cost of an upgrade is a certain number of BTs. But if you assume that you’re going to spend those BTs on extra multi-training (which most people do), you can also state the cost of an upgrade in terms of Y. Each single multi-train costs 3 BTs in comparison to training on light (that is, you get 24 bonus tokens training on light four times compared to 12 BTs for a multi-train, so a difference of 12 BTs per four training days). And on average, a light train gets you about 26% of a multi-train. (You can do the math yourself using the mandyross spreadsheet linked above). Accordingly, the net gain from a single multi-train in comparison to light training is [Y - 0.26Y] or 0.74Y.

For the first enhancement, the 6 BT cost can be treated as 2 fewer days of multi-training, which is a cost of 1.48Y. The benefit of the first upgrade is [0.1Y * X]. We can then determine the net value of the upgrade (stated in terms of Y, that is, units of average SP value of a single multi-train) as [Y = 0.1X – 1.48]. Using this function, the first upgrade provides a net benefit if [X > 14.8]. In other words, the first upgrade is worth it if you multi-train an attribute at least 15 times because this will result in a positive value for Y.

You need 18 total BTs for the second upgrade, which is equal to six fewer days of multi-training, or 4.44Y. The function for the second upgrade is thus [Y = 0.2X - 4.44]. This means that the second upgrade provides a total net benefit if [X > 22.2] or if you multi-train at least 23 times. But, to realize a marginal benefit over the first upgrade, you need to find the point at which the second function intersects the first. That is, you need to solve for X when [0.2X – 4.44] = [0.1X – 1.48], which is [X = 29.6]. This means that the second upgrade is better than the first upgrade only if you are going to multi-train an attribute 30 times.

The function for the third upgrade [Y = 0.3X - 8.88]. It is better than the second upgrade where [0.3X – 8.88] > [0.2X – 4.44], or where [X > 44.4]. So the third upgrade requires 45 multi trains to produce a marginal benefit.

The fourth upgrade is [Y = 0.4X - 14.8]. So getting back to the original question, the fourth upgrade will realize a marginal benefit over third upgrade where [0.4X - 14.8] > [0.3X - 8.88], or where [X > 59.2]. This means that you would have to multi-train an attribute 60 times for the fourth upgrade to be worth it.

The fifth upgrade is [Y = 0.5X – 22.2]. It would provide a marginal benefit if [0.5X – 22.2] > [0.4X - 14.8], which is [X > 74]. That means you need to multi-train 75 times to gain a marginal benefit.

In addition to only considering multi-training, there is one other big caveat here. These calculations only reflect SP value benefits. Many builders are willing to sacrifice SP value to get their first and second attributes higher. But in terms of SP value, you can determine how many upgrades to buy as follows:

Upgrades . . . . . Multi-trains needed to benefit
. . . 1 . . . . . . . . . . . . . . . . 15
. . . 2 . . . . . . . . . . . . . . . . 30
. . . 3 . . . . . . . . . . . . . . . . 45
. . . 4 . . . . . . . . . . . . . . . . 60
. . . 5 . . . . . . . . . . . . . . . . 75

Trying to understand that ^ almost killed me

Did you do the math based off of multi training for 4 attributes? If so, you may want to update your table to show those times trained with the days it would take to reach that mark. ie 60 training sessions would take 240 days to reach.

Originally posted by jpjn94
Did you do the math based off of multi training for 4 attributes? If so, you may want to update your table to show those times trained with the days it would take to reach that mark. ie 60 training sessions would take 240 days to reach.

Like so?

(EDIT: Woefully incorrect info removed to reduce confusion.)

Originally posted by Novus
Like so?

You hit Plateau after just 280 days, so...

But there are 16 or so training days per offseason. Those are training days, but not days your player ages.

Using 56 days per season you have 392 training days + the 16 if you create in the offseason, so 408 training days.

I find this thread very interesting. Both for the information it provides and for the lack of understanding it also contains. Not by all mind you.

Originally posted by Novus
Like so?

Upgrades . . . . . Multi-trains needed to benefit
. . . 1 . . . . . . . . . . . . . . . . 15 (60 days)
. . . 2 . . . . . . . . . . . . . . . . 30 (120 days)
. . . 3 . . . . . . . . . . . . . . . . 45 (180 days)
. . . 4 . . . . . . . . . . . . . . . . 60 (240 days)
. . . 5 . . . . . . . . . . . . . . . . 75 (300 days)

You hit Plateau after just 280 days, so...

except not...
there's about 17 days per season not accounted for in player age--there's a 9 day preseason (-8 to 0) and also the off season after the playoffs--which runs day 41 to day 48. There's 8 seasons to get through before plateau, so that adds another 136 days

but there's way more to this issue.

namely 99% of builds will benefit in game performance by doing things that aren't mathematically perfect.

Originally posted by CerNeT
I find this thread very interesting. Both for the information it provides and for the lack of understanding it also contains. Not by all mind you.

So instead of correcting some of that misunderstanding you would rather just make a meaningless post. Your awesome man!!

Originally posted by whodey08
So instead of correcting some of that misunderstanding you would rather just make a meaningless post. Your awesome man!!

* You're

Originally posted by CerNeT
I find this thread very interesting. Both for the information it provides and for the lack of understanding it also contains. Not by all mind you.

Enlighten us then, please.

Originally posted by Plankton
But there are 16 or so training days per offseason. Those are training days, but not days your player ages.

Using 56 days per season you have 392 training days + the 16 if you create in the offseason, so 408 training days.

Originally posted by TJ Spikes
except not...
there's about 17 days per season not accounted for in player age--there's a 9 day preseason (-8 to 0) and also the off season after the playoffs--which runs day 41 to day 48. There's 8 seasons to get through before plateau, so that adds another 136 days.

GREAT catches, both of you!