[Beta 12] Magic/Shroom

[jolin012]

Magic and Mushroom now have a new concept but when I sugguested the numbers I am sure I made Very Clear that If the pool is 45 and the regen is 5 then level 1 well should grant 9 mana change when casting, lvl 2 should grant 15 mana on casting and lvl 3 should grant 30 mana when casting.

And still, I find that it grants 4/8/30 instead which makes me sad. There is just no reason, those numbers are wrong, mine were even perfectly exact.

[Karawasa]

I double checked the calculations and I believe only your suggestion for level 3 is correct. Allow me to explain:

Level 1:

I divided the tower into two time periods. There are 2 periods with 1000 damage, and 1 period with 3000 damage. I then calculated the bonus that would apply both full (good) and partial (bad). I summed each thing, no buff, full buff, and partial buff and divided by 3 the total number of periods.

The conclusion is that full buff does the full 25% while the partial buff only does 15%.

               FB       PB

2000(2)    500     500

3000(1)    750     250


/3


#          #         #

1666    2083      1916


0%       25%      15%

Since the partial buff does not interact with the ability at all, we can increase the power of the ability without a secondary effect.

I used the two time periods again but used mana fractions instead of integers. I found that a 4 mana increase will produce about a 10% increase in DPS.

30/45 * 1000 = 666

15/45 * 3000 = 1000


#1666


26/45 * 1000 = 577

19/45 * 3000 = 1266


#1843


1843/1666 = 1.1 = 10% increase

Level 2 & 3:

Using the same process I found that a 50% buff would result in a damage difference of 20%. A 8 mana return increases dps by about 20%. This makes sense that it would be double, because lvl 2 is double lvl 1.

The same logic applies to lvl 3. It should be 4x as much as lvl 2, and thus would be 32 mana return. However, 30 mana return results in no rest time. Thus, we have to fudge it by about 8%.

[jolin012]

I didn't yet have time to find where in your thinking process you did wrong, but at least I got some proof for now did a test several times with 4 magics buffed by either lvl 2 well or smith. and when buffed by well the damage count it got always landed around 8-10k higher (around 5-10%). Smith proved too weak every time and here I have saved and uploaded one with well and one with smith. (This is easily tested with the commands for gold lumber and lvl. the replays are around 2 minutes each):

beta 11 127253 smith magic.w3g

beta 11 135524 magic well.w3g

[Karawasa]

Wait, what are you trying to prove? We already know that the bad buff increases dps less than the good buff?

[jolin012]

oh, so why did you cahgne the numbers?maybe i missed something but with the numbers i sugguested both buffs would increase dps by the exactly same amount.

[Karawasa]

I changed the numbers because what you suggested didn't accomplish that.

[jolin012]

ok here it goes. this was how I was thinking:

I count as if the tower regularly had 1000 damage (and 1 attack/sec) and the regular avarage output would be 2000 damage. I decided to divide it into 2 periods, one with the ability on and one with it off. the one on I have divided the damage into 2 parts, one that is the regular damage(always buffable) and one that is the bonus damage(or speed in mushroooms case). I call it 1000+3000 for a regular mush. and the damage that is not with the ability on is just 1000. Then I take the total damages for each side and multiply it with the number of secods they are active. in the regular case (1000+3000)*3 and (1000)*6. I add them together. 12000+6000=18000. After that I divide it by the total time (3+9) to get the avarage damage/second. 18000/9=2000.

This is for the regular non buffed mush or magic.

    3 sec         6 sec 

_____________ + ________

| 1000+3000 | + | 1000 |  = (12000+6000)/9 = 2000

And so I moved on and tested with the good and bad buff on the towers. Good buff always gave the % buff they should, but for the "bad" buff I had to change the time that the non buffed section lasts= aka the ability CD.

Here is for the "Good" lvl 1 buff:

    3 sec         6 sec 

_____________ + ________

| 1250+3750 | + | 1250 |  = (15000+7500)/9 = 2500

for lvl 2 buff I had to reduce the time that the non buffed section is active into 4,2 seconds. that means 9 out of 45 mana less needed.

Here is for the "Bad" lvl 1 buff:

    3 sec        4,2 sec

_____________ + ________

| 1250+3000 | + | 1250 |  = (12750+5250)/7,2 = 2500

as you can see, with a cooldown for "lvl 1 bad buffed" of 7,2 sec (and a lost time of 3 sec so only a 4,2 sec wait) the final dps is as it should. that means 1,8 sec less than regular. and 1,8 sec is 9 mana, therefore the tower bad buffed tower should be granted 9 extra mana when casting it's ability to reduce the time it doen't use ability into 4,2 sec.

Here is for "good" lvl 2 buff:

    3 sec         6 sec

_____________ + ________

| 1500+4500 | + | 1500 |  = (18000+9000)/9 = 3000

And i found that the non ability period should last for 3 sec on lvl 2 bad buffed ones here at the "bad" lvl 2 buff:

    3 sec         3 sec

_____________ + ________

| 1500+3000 | + | 1500 |  = (13500+4500)/6 = 3000

With a 3 sec shorter nonactive time that means 15 mana should have to be added for a "lvl2 bad buff"ed tower every time it's ability is cast.

and here goes for "good" lvl 3 buff:

    3 sec         6 sec

_____________ + ________

| 3000+9000 | + | 3000 |  = (36000+18000)/9 = 6000

And here is what i calced for the "bad" lvl 3 buff:

    3 sec         0 sec

_____________ + ________

| 3000+3000 | + | 3000 |  = (18000+0)/3 = 6000

With a 6 sec shorter nonactive time that means 30 mana should have to be added for a "lvl3 bad buff"ed tower every time it's ability is cast.

Simple as that.

[Karawasa]

This is for the regular non buffed mush or magic.

    3 sec         6 sec 

_____________ + ________

| 1000+3000 | + | 1000 |  = (12000+6000)/9 = 2000

This is where the problem lies. It would not be 1000+3000 for the non-buffed bonus period. The bonus adds 200% and thus would be 1000+2000.

[jolin012]

Oh, yes. I am an idiot

[jolin012]

I was still curious about why my replay proves lv 2 is 10% wrong, and I wanted to redo my calcs with the correct numbers. but i would find that it was no prob to have the wrong numbers in terms of ability strength.

when I replaced +3000 with +2000 I found that it doesn't make a difference. it doesn't matter how much the ability boosts by, it'll still be the same amount of mana.

I tested the math for your numbers of mana too, and it showed that lvl 1 s about 5% final dps wrong and lv 2 is about 10% final dps wrong.

But these do give the exact numbers. Nothing has been rounded up or down anywhere (except the final outputs 1666,67 and 2083,33)

The regular would now be:

    3 sec         6 sec

_____________ + ________

| 1000+2000 | + | 1000 |  = (9000+6000)/9 = 1666,67

Good lvl 1:

    3 sec         6 sec

_____________ + ________

| 1250+2500 | + | 1250 |  = (11250+7500)/9 = 2083,33

Bad lvl 1. 9 mana added:

    3 sec        4,2 sec

_____________ + ________

| 1250+2000 | + | 1250 |  = (9750+5250)/7,2 = 2083,33

Good lvl 2:

    3 sec         6 sec

_____________ + ________

| 1500+3000 | + | 1500 |  = (13500+9000)/9 = 2500

Bad lvl 2. 15 mana added:

    3 sec         3 sec

_____________ + ________

| 1500+2000 | + | 1500 |  = (10500+4500)/6 = 2500

Good lvl 3:

    3 sec         6 sec

_____________ + ________

| 3000+6000 | + | 3000 |  = (27000+18000)/9 = 5000

Bad lvl 3. 30 mana added:

    3 sec         0 sec

_____________ + ________

| 3000+2000 | + | 3000 |  = (15000+0)/3 = 5000

[Karawasa]

Bad lvl 2. 15 mana added:

    3 sec         3 sec

_____________ + ________

| 1500+2000 | + | 1500 |  = (10500+4500)/6 = 2500

The problem with your calculations is that you keep the ability time constant and instead change the divisor to reflect the difference in time. The above implies that with 15 mana added that half the time is spent in buff mode and half the time is spent in rest mode. When you keep it faithful you get:

    6 sec         3 sec

_____________ + ________

|1500+2000 | + | 1500 |  = (21000+4500)/9 = 2833.33

Thus in the same time period (9 seconds), the level 2 bad buff with your 15 mana increases the overall DPS by 70%.

[jolin012]

Bad lvl 2. 15 mana added:

    3 sec         3 sec

_____________ + ________

| 1500+2000 | + | 1500 |  = (10500+4500)/6 = 2500

The problem with your calculations is that you keep the ability time constant and instead change the divisor to reflect the difference in time.

well, that is exactly how it should be, because the time that the ability lasts doesn't change. only the time it is inactive before turned on again and be changed through the mana gain.

The above implies that with 15 mana added that half the time is spent in buff mode and half the time is spent in rest mode.

Correct, when we add 15 mana that makes up for 3sec last 3sec rest, and as you can see in my calculation, that together with a failed 50% boost makes up for a total of 2500dps which is a 50% boost(from the regular of 1666,67).

When you keep it faithful you get:

    6 sec         3 sec

_____________ + ________

|1500+2000 | + | 1500 |  = (21000+4500)/9 = 2833.33

Thus in the same time period (9 seconds), the level 2 bad buff with your 15 mana increases the overall DPS by 70%.

First of all, what do you mean by "Faithful". Why would 6 sec last and 3 sec rest be faithful when the regular is 3 sec last and 6 sec rest?

What has an ability with 6 sec last and 3 sec rest to do with this? You can't change the lasttime. you can only change the rest time. so 6/3 would equal 3/1,5. but what do we want 3/1,5 aka 2833,33 for? isn't it better with the numbers I found that add 25%/50%/200% instead of 70%?

[Karawasa]

You have to keep the time period the same for a fair comparison. While the duration of the ability does not increase, in the same time period a 15 mana increase results in ability going from 3/6 to 6/3.

By reducing the period to 6 seconds, you don't get to see the full result of the 15 mana being added. All the calculations are based off of the same base numbers, and the time period should be considered a base number as well.

How else can we explain the difference between 2500 and 2833.

[jolin012]

You have to keep the time period the same for a fair comparison.

No it doesn't cause at the end of my calculation I divide it by the total number of seconds one round of work and rest takes, to find the dmg/sec.

While the duration of the ability does not increase, in the same time period a 15 mana increase results in ability going from 3/6 to 6/3.

. 15 mana would reduce the rest time by 3, meaning 3 sec work 3 sec rest 3 sec work 3 sec rest etc etc. and there is no reason to find it's avarage damage by taking the first 9 seconds, beeing 3 work 3 rest 3 work, and say that 6/3 is it's avarage. it's avarage is 3/3 when the rest time is 3 sec and the last time is 3 sec. and then i divide it by 6 to find the dmg/sec.

By reducing the period to 6 seconds, you don't get to see the full result of the 15 mana being added.

what? afaik I Do see the full result here:

    3 sec         3 sec

_____________ + ________

| 1500+2000 | + | 1500 |  = (10500+4500)/6 = 2500

in the All the calculations are based off of the same base numbers, and the time period should be considered a base number as well.

No way. Cause by reducing the mana we are reducing the rest period and that reduces the total time of the period it takes to do one work and one rest.

How else can we explain the difference between 2500 and 2833.

How i explain it is cause 15 mana reduce means 3 sec less rest. Not 3 sec less rest and 3 sec more last. Why should there me more last time? There is nothing to increase the time that the ability lasts. How I explain the difference between those numbers is that by not taking for granted that 3 sec less cooldown takes 3/6 to 6/3 but what it does is to make it 3/3 and later I will divide it by 6 instead of 9 as you can see in the calc. And how you get 2833 is by saying that it will last for 6 sec and then rest 3 if i add 15 mana.

I really don't see any problem

[Cisz]

Um, can you at least agree on what the other one is saying?

Could each of you please fill out the following tables:

[pre:2lwcalq2]All towers level 1, damage/second/tower values for b11:

+----------+--------+---------+

dmg/s/tow| no boost | w/well | w/smith |

---------+----------+--------+---------+

mushroom | | | |

---------+----------+--------+---------+

magic | | | |

---------+----------+--------+---------+

Boost towers level 2, damage towers level 1, damage/second/tower values for b11:

+----------+--------+---------+

dmg/s/tow| no boost | w/well | w/smith |

---------+----------+--------+---------+

mushroom | | | |

---------+----------+--------+---------+

magic | | | |

---------+----------+--------+---------+

Boost towers level 3, damage towers level 1, damage/second/tower values for b11:

+----------+--------+---------+

dmg/s/tow| no boost | w/well | w/smith |

---------+----------+--------+---------+

mushroom | | | |

---------+----------+--------+---------+

magic | | | |

---------+----------+--------+---------+[/pre:2lwcalq2]

After that it should be easy to test that on the map, right?

[jolin012]

Thank you for helping us out. I believe that this was exactly what i tried to show through my replays at the top but I wasn't clear enough. Now I'm filling the application to see if I understood K right and if he understood what i meant Everything rounded to no decimals

[pre:s95ylt7t]All towers level 1, damage/second/tower values for b11:

+----------+--------+---------+

dmg/s/tow| no boost | w/well | w/smith |

---------+----------+--------+---------+

mushroom | 1667 | 1982 | 2083 |

---------+----------+--------+---------+

magic | 1667 | 2083 | 1982 |

---------+----------+--------+---------+

Boost towers level 2, damage towers level 1, damage/second/tower values for b11:

+----------+--------+---------+

dmg/s/tow| no boost | w/well | w/smith |

---------+----------+--------+---------+

mushroom | 1667 | 2311 | 2500 |

---------+----------+--------+---------+

magic | 1667 | 2500 | 2311 |

---------+----------+--------+---------+

Boost towers level 3, damage towers level 1, damage/second/tower values for b11:

+----------+--------+---------+

dmg/s/tow| no boost | w/well | w/smith |

---------+----------+--------+---------+

mushroom | 1667 | 5000 | 5000 |

---------+----------+--------+---------+

magic | 1667 | 5000 | 5000 |

---------+----------+--------+---------+[/pre:s95ylt7t]

[Karawasa]

You will notice that the numbers are not that far off with the Beta 11 values. The difference is minute, and does not justify a jump from 4/8/30 to 9/15/30.

Furthermore, I have repeatedly tested the Beta 11 numbers with the new system I have planned for Beta 12. Over a period of 9 seconds, the effective damage output and average dps were quite similar between Shroom+Smith and Shroom+Well.

As such I am keeping the current values from Beta 11. Soon enough you will be able to test this yourself with the system planned.

[Cisz]

Karawasa, I tested magic lv1 with both well lv2 and smith level 2, and they are not equal. Over the time of one wave of evil childs passing, magics do about 1500 less damge with smith lv2.

[Karawasa]

Karawasa, I tested magic lv1 with both well lv2 and smith level 2, and they are not equal. Over the time of one wave of evil childs passing, magics do about 1500 less damge with smith lv2.

Over the course of a wave, placement of tower and position of creeps factors into output dramatically. I think it is better to look at one single time period, in this case 9 seconds. I can tell you that they are equal when placed in the same situation. Perhaps a Shroom with Fire Up should be placed differently than a Shroom with Spring Forward to maximize its damage over the course of the wave.

Hopefully you will all be able to test it yourself tonight.

[Cisz]

To even out exactly those tiny details i suggest to test a mass of towers and devide the result. That's why i used 12 magics and repeated the test for both versions. The numbers varied each time, but never were close to equal.

[jolin012]

but, may i ask, why aren't the current replays/proof enough? Both I and Cisz have tested with Magic+well and magic+smith, and tier 2 well seems stronger with magic every time tested.

But if you really want it it's ofcourse ok with me to keep it the current way for b12, just don't understand why, and run the same test with the new counter, but I can't understand what's wrong with the current, perhaps have a look first? =)

Edit after the light of each the two of yous latest posts:

Karawasa, I tested magic lv1 with both well lv2 and smith level 2, and they are not equal. Over the time of one wave of evil childs passing, magics do about 1500 less damge with smith lv2.

Over the course of a wave, placement of tower and position of creeps factors into output dramatically. I think it is better to look at one single time period, in this case 9 seconds. I can tell you that they are equal when placed in the same situation. Perhaps a Shroom with Fire Up should be placed differently than a Shroom with Spring Forward to maximize its damage over the course of the wave.

Hopefully you will all be able to test it yourself tonight.

That is where you do your mistake I believe. When the total time of the 2 periods (last and rest of ability) change due to mana added, the time you must use is also changed. To find the avarage output, you must add together one of each otehr the 2 periods. Not 9 sec that would in 3last 3 rest take 3 sec last 3 sec rest and then 3 sec last more and add it together. It would give a false avarage of that last is always active twice as much. To find an output that is safe, you must let it work for a longer time, perhaps 30 seconds(that's how i did in my reps. Or else you could let the "last" and the "rest" last once each, and then divide the output by the total numbers of seconds the 2 periods sum together, to get a damage/sec, like I did in my calculations, but in real game it's easier to see the output on an entire wave of many seconds.