# A math lesson and a discussion of game mechanics

okay i’m writing this so that the less mathematically inclined have an idea of how gear stacks.(I use a calculator for the actual number crunching and I recommend you do the same to keep it easy) and I implore anyone who knows the math for other mechanics to post here so more people can see how things stack.

i’m taking most of my information for base character stats straight from the battleborn bible:

and for helix choice planning I use this:

now. i’m using this so that people can have an idea of how their gear and helix choices interact since it’s multiplicatively(the bonuses are multiplied rather than added.

using phoebe as an example(just her attack speed for this) i’ll use a common attack speed item at max roll(8.4%) and her level 7 helix mutation “Flurry”(20% attack speed boost)

phoebe has a base attack speed of .4 or 2.5 attacks per second, so take 2.5 and multiply that by 1.084(8.4% above 1 which is your normal attack speed). then you take the value from that and multiply that by 1.2(same as the last one but 20% boost instead of 8.4)

written out like a math problem it becomes
2.5x1.084=2.71
2.71x1.2=3.252

now for the last part is something extra I do, but I check the actual boost over base attack speed by dividing 3.252 by 2.5
3.252/2.5=1.3008

so instead of a 28% attack speed increase it’s actually a 30% increase in reality.

and if you want to find a DECREASING VALUE(reload speed) this is how you do it

easiest way I’ve found is to simply take the 21% and subtract it from 100(79%)

multiply 1.2 by .79(this is how 79% is actually written)
1.2x.79= .948

then at level 7 marquis gets a reload speed and attack speed boost(25%)
.948x.75= .711
divide that by 1.2 to see what your
the actual reload speed bonus is .5925

that’s almost a 60% difference in actual reload times.

I’ve seen all of you being extremely helpful to less experienced players on the forums(myself included) so here’s my attempt to give you guys a resource to help people with questions

8 Likes

@loving-hatred

Excellent and dedicated work!

Thanks for doing this!

I’ve seen this topic on another post but i’ll repost it here because it’s another people might like

next one I’ve tinkered with is build cost reduction, this is taken to the Nth degree(using no flaws, with flaws it actually pays beck faster)

using max roll gear all the way(and one of them is a shard generator)

an epic shard generator with max roll is: 2.1 shards per second with a -14% build cost reduction, cost 1050 shards

A rare wrench with max roll is -21% Buildable Cost, -14% Buildable Cost for 30 seconds after buying a buildable at 924 shards

then the third item can either be shield recharge or delay, but max roll will be another 14% reduction at another 1050

build cost reduction isn’t multiplicative so the math itself is a lot simpler.

21+14+14= 49% for the INITIAL PURCHASE

for how that looks in effect we’ll use a turret(300 shards, then 400 then 500)

300x.51=153 for the first level turret.
but after buying a buildable the next 14% kicks in which makes your bonus 63%
400x.37=148
then 500x.37=185

that’s a total of 486 shards to buy a level 3 turret. that’s a 714 shard discount.

now for the part I hear some people worry about “how long until the gear pays for itself?”

well adding up the cost of the gear
1050+1050+924=3004.

so by the time you by your 5th turret from scratch and invested 2430 shards you’ve actually broken even and are slightly ahead investment wise

1 Like

@loving-hatred

That’s mental!

one thing I’ve been wondering that I hope someone can clue me in on though. does damage resistance provide diminishing returns?(only speaking of the mathematics and the theory, not of viability in an actual match) so if anyone has that answer please clue me in on it!

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I loooooooooooove how much you maths

2 Likes

next post is going to be long, but it’s going to be buff/debuff interactions from ambra and reyna(me and some friends actually did this but now i’m going to math the anecdotal evidence minus the gear for simplicity sake(then probably add in crazy gear further in to show people what’s technically possible if you let it happen)

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now this one is purely what is possible, not necessarily what is likely. please don’t take this as me endorsing one build over another

• Ambra level 1 left helix "enemies damaged by sunspots take 16% more damage from all sources)
-reyna’s priority target “Fires a homing blast that deals 65 damage (+50% bonus to shields) and reveals the target’s position. The target takes 16% extra incoming damage for 6 seconds.”
-reyna’s level 8 right helix “dogpiler” further increases the damage enemies affected by priority target take by 16%
-rath’s level 10 helix “desperate assault” increases the damage dealt by dreadwind by 45% when shield is broken

now this is going to be interesting and I apologize if i’m wrong in the number of times per second dreadwind hits(I believe it’s four so that’s what i’ll go with, if it’s another value let me know and i’ll correct my math)

now the 3 of them go for say a sentry for a late game hail mary. and i’m not sure how the damage amplification debuffs stack so i’ll do both additively and multiplicatively

now 1.32x1.16=1.5312

so the damage debuff is either 48% or 53%

rath’s dreadwind hits for 146 damage per hit at level 10 base

let’s now see how this number goes
146x1.5312= 223.5552
146x1.48=216.08

now a hit in and raths shield breaks.
217.4304x1.45=323.35(53%)
216.08x1.45=313.316(48%)

per hit. there’s 12 more hits after that,
(four per second for 3 seconds assuming
for the rest of the attack equaling
3,880.2(53%)
3,759.792(48%)

that’s not accounting for any other attacks dealt of gear added in of course. but it is over double effectiveness no matter which way it works out.

@skeksis_SYL
@Ginger_greninja for any one who needs some mathing help

2 Likes

It’s 223.5552, not 217.

Wow! That’s without flaws and discounting the shield benefit too! I tried a similar method with an uncommon wrench (don’t have a rare one), uncommon LLC battery, and epic shard gen on my Miko. Always in combat, always with his shield down. Hit roughly five shards per second

If you wanna math all the way, add in Phoebe’s level ten left helix ult

…Thank you!

1 Like

I appreciate that you’re willing to do the numbers for those who cannot or will not for themselves, but I venture to offer a differing viewpoint. The epic shard and rare wrench should really be compared to zero cost versions of themselves.

In the previous assessment, the player spends 3004 on gear, and gives up his/her entire loadout. With a free shard generator (+2.1 shards/sec) and a free wrench (-21% buildable cost,) the player can upgrade three turrets to maximum

1200 * .79 = 948 * 3 = 2844 < 3004

before he/she would be able to finish paying for the more expensive set, and they both generate shards at the same rate. The free version gives the player shard regen right away, before he/she even leaves the starting room, and there is an open gear slot for something else. Having the shard regen from the get go isn’t gamebreaking, but neither is the extra 14% buildable cost reduction that actually costs 1050 to activate.

Comparing just these two gear pieces to each other, each fully upgraded turret saves

1200 * .14 = 168 shards

Now for this one piece of gear, we’re looking at 1050 cost versus a saved value of 168 shards per full turret upgrade.

This means the player will actually have to buy

1050 % 168 = 6.25

more than 6 turrets before the epic shard generator saves more than its cost to activate.

But before the player can start spending, he/she first must save 1050, which is also before he/she starts generating his/her own shards. Given that the large shards don’t spawn for the first two minutes, it is very unlikely the player will acquire 1050 shards before two minutes and thirty seconds have passed, so the free shard generator earns you at least

2.1 * 150 seconds = 315 shards

more than the full cost version.

With the free shard generator (and the rest of the full gearset,) the cost to fully upgrade a turret is

.21 + .14 = .35 saved (65% initial cost,) + .14 = .49 saved (51% cost for 2nd and 3rd tier)

300 * .65 = 195
400 * .51 = 204
500 * .51 = 255
195 + 204 + 255 = 654

Total gearset cost being

0 + 924 + 1050 = 1974

Whether or not the other pieces of gear are worth it really depends on how long the match goes, but here we’ll show the cost for one to eight turrets for each gearset

1 * 468 = 468 + 3004 (cost of gear) = 3472.
2 * 468 = 936 + 3004 (cost of gear) = 3940.
3 * 468 = 1404 + 3004 (cost of gear) = 4408.
4 * 468 = 1872 + 3004 (cost of gear) = 4876.
5 * 468 = 2340 + 3004 (cost of gear) = 5344.
6 * 468 = 2808 + 3004 (cost of gear) = 5812.
7 * 468 = 3276 + 3004 (cost of gear) = 6280.
8 * 468 = 3744 + 3004 (cost of gear) = 6748.

versus (with free shard generator)

1 * 654 = 654 + 1974 (cost of gear) = 2628
2 * 654 = 1308 + 1974 (cost of gear) = 3282
3 * 654 = 1962 + 1974 (cost of gear) = 3936
4 * 654 = 2616 + 1974 (cost of gear) = 4590
5 * 654 = 3270 + 1974 (cost of gear) = 5244
6 * 654 = 3924 + 1974 (cost of gear) = 5898
7 * 654 = 4578 + 1974 (cost of gear) = 6552
8 * 654 = 5232 + 1974 (cost of gear) = 7206

However, this doesn’t take into account the 315 extra shards the player would earn with the free version before he/she was able to pay for the epic version, so we’ll take that off the total to compare these two on an even footing.

1 * 654 = 654 + 1974 (cost of gear) = 2628 - 315 = 2313
2 * 654 = 1308 + 1974 (cost of gear) = 3282 - 315 = 2967
3 * 654 = 1962 + 1974 (cost of gear) = 3936 - 315 = 3621
4 * 654 = 2616 + 1974 (cost of gear) = 4590 - 315 = 4275
5 * 654 = 3270 + 1974 (cost of gear) = 5244 - 315 = 4929
6 * 654 = 3924 + 1974 (cost of gear) = 5898 - 315 = 5583
7 * 654 = 4578 + 1974 (cost of gear) = 6552 - 315 = 6237
8 * 654 = 5232 + 1974 (cost of gear) = 7206 - 315 = 6891

With the free shard generator, the player can purchase three fully upgraded turrets before another player using the epic version can purchase his second turret. Both versions purchase seven turrets before the epic version starts showing itself as better, and until that point the free version has always been able to purchase turrets much sooner, and thus earn his experience from building (and also, have the benefit of whatever was built,) much sooner into the match.

Based on my recent match history, only Pendles can really be assured of acquiring 6000 shards before the winner is decided. That said, having those buildables up (and that experience earned) earlier goes a long way towards improving your side’s chances of being the winner, so even in that case I feel the free version is better.

tl;dr: If the match goes very long, the epic shard generator is better. If the match is shorter, the free shard generator is better.

5 Likes

So this might not be stat mechanics but it is still in the game. I wanna try and do some math regarding faction loot packs. More specifically, the chance to get a single skin(i.e the white/grey skin) for any given character. Now generally, every battleborn has about 5 skins and taunts, making for a total of 25 total comsetics available from these loot packs. For ease of math, i’m going to say that every faction has 5 battleborn in it, so just keep in mind these numbers’ll change depending on the faction. BTW if my math is wrong feel free to correct me on it

So if we take a guess at the drop rate for skins and taunts, there are a few numbers that stick out. First let’s assume the drop rate for a single cosmetic is 10%.

0.1/0.04(100/25 then turned into a fraction)=2.5
That is to say one in forty packs contains the item you are looking for. Now this is the worst case scenario and not what I believe to be the drop rate.

Now let’s go for 30% drop rate
0.3/0.04=7.5(or just multiply prev result by 3)
So about every 13 loot packs. So theoretically it would take 325 loot packs to get every skin&taunt for a faction. Better but still kinda ludicrous.

Best case scenario imo(that is realistic) is 50%
0.5/0.04=12.5
So this is one in 8 loot packs. Ends up being about 200 packs(theoretically). Even this is quite over the top.

In the end everything is down to RNG and this could take you 25 loot packs(unless I did my math wrong that has a 0.5%chance of actually happening :p). Also kinda hoping the drop rates ARE 50% cos it kinda feels like it imo.

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Apologies everyone, I actually did make that error(it was a late night post I’m about to go through correcting the errors I see

differing view points are completely fine, I was merely pointing out what can be done(using build cost as one example)

[quote=“Japanman15, post:14, topic:1545884”]So if we take a guess at the drop rate for skins and taunts, there are a few numbers that stick out. First let’s assume the drop rate for a single cosmetic is 10%.

0.1/0.04(100/25 then turned into a fraction)=2.5
That is to say one in forty packs contains a cosmetic item. Now this is the worst case scenario and not what I believe to be the drop rate.[/quote]
I don’t understand. What drop mechanics were you assuming?

I think there’s a chance of skin to drop and another chance of taunt to drop. If any or both of them proc, the game then decides what exact skin/taunt will drop. And if you already have it, it is replaced with a credit reward. And those chances are very far from your 50%.

Too many numbers, I’m getting dizzy

An excellent series of posts, @loving-hatred.

No, no, I understand, and I like what you’re doing.

I just wanted to add my two cents to that particular discussionn … people tend to overvalue epic or rares compared to at least one piece of free stuff, and your particular example lended it fairly well to the point I wanted to get across.