An Analysis of Crits (OUTDATED, Move Along Now)

EDIT: They changed it such that upgrades add 2 crit and LB adds 5. This is now outdated, and I'm not updating it. If you want to read about how OP crits were for the first 4 days of atWar, go right ahead.

Hey guys, Mathdino here, some of you may have remembered my In Depth Analysis of ARB. This is the equivalent for crits. Back then, I was trying to show that ARB actually does a little more than we think, and that stuff like Lucky Militia really isn't useless. However, now I'm going with the crowd in that crits are incredibly OP, and Lucky Bastard kinda breaks the game.

Wall of text and tables ahead. If you don't care about the Math, just skip down to the results. Don't bother going 'tl;dr hurr durr'.


Now first let's start off by calculating average attack from attack points (for the sake of simplicity, 'attack' will refer to attack and defence). Average attack is the average of all possible attack point values, so if I have 8 attack, I can get 1, 2, 3, 4, 5, 6, 7, or 8 attack, as 0 attack is not possible as confirmed by the admins. This makes the average attack for 8 points, 4.5. Average attack is as such determined by a1(p)=(p+1)/2 or just a1=p/2 + .5, where a1 is the average attack and p is the number of attack points. The table of average attack is below. Just remember that I'll be calculating stuff in average attack; to get the scaled attack points, you just multiply by 2 and subtract 1, so p=2a1(p)-1.

P	1	2	3	4	5	6	7	8	9	10
a1(p)	1.00	1.50	2.00	2.50	3.00	3.50	4.00	5.00	5.50	6.00

What critical chance does is it gives you anywhere between 1% and 100% extra attack to a unit, c% of the time, where c is the critical chance. For example, say I have a marine on None strategy, with 7 attack and 5 crit chance. 7 attack means 4 average attack, and to get the average attack added by crits, we multiply average attack by c%, because crits can add any attack between minimum and maximum. So 5% of 4 is .20, making the average attack 4.20, and the scaled attack points 7.4. This is a large difference.

The function of average attack to P and C is then a2(p,c)=(p+1)/2+c(p+1)/2=(p+1)(c+1)/2. However, we read scaled attack points a little better than average attack, so let's make that p2=2(p+1)(c+1)/2-1=pc+p+c+1-1=p+pc+c.


Now I can't make a 3D table, but I can show you tables for the standard units with different modifiers involved. For those of you who scrolled straight down here, the modified att/def points is just what the new attack or defence score is with crits factored in. In the tables below, None means no upgrades, just what you see in the units FAQ and what the neutrals get. Lucky _ adds 10 crits for infantry, marines, and militia. Lucky Bastard adds 10 crits. Lucky General will take into account that the unit is in a general stack, and thus gets all bonuses that may apply (General Infantry Attack, General Defence, General Tank Attack, etc.).

Modifiers:	None	Lucky Militia	Lucky Militia with LB	Lucky Militia in Gen Stack	Lucky Militia in Gen Stack with LB
Modified Attack Points	3	3.4	3.8	3.8	4.2
Modified Defence Points	4	4.5	5	6.2	6.8

Modifiers:	None	Lucky Infantry	Lucky Infs with LB	Lucky Infs in Gen Stack	Lucky Infs in Gen Stack with LB
Modified Attack Points	4.25	4.75	5.25	6.5	7.1
Modified Defence Points	7.4	8.2	9	10.25	11.15

Modifiers:	None	With LB	In Gen Stack	In Gen Stack with LB
Modified Attack Points	8.45	9.35	10.5	11.5
Modified Defence Points	4.25	4.75	5.9	6.5

Modifiers:	None	Lucky Marines	Lucky Marines with LB
Modified Attack Points	7.4	8.2	9
Modified Defence Points	3.2	3.6	4

Modifiers:	None	With LB	In Gen Stack	In Gen Stack with LB
Modified Attack Points	6.35	7.05	8.2	9
Modified Defence Points	6.35	7.05	8.2	9

Modifiers:	None	With LB	In Gen Stack	In Gen Stack with LB
Modified Attack Points	9.5	10.5	11.65	12.75
Modified Defence Points	7.4	8.2	9.35	10.25

I mean seriously, look at this stuff. Using LB in a general stack, your infs aren't 4:7, they're 7:11. Lucky _ adds a whole attack/defence point to most troops. This is absurd, and has infantry more powerful than PD and IF, tanks more powerful than TG, marines more powerful than MoS, and militia more powerful than GW. Really?

The Lucky Upgrades and Lucky Bastard have become incredibly OP now. I tested this out myself for a bit; 10 infantry and a gen killed 8 neutral infantry with 2 left. Do the Math: that's 71 attack vs 55 defence, when it should be 50 vs 54. That is not a battle I should have won.

Knowing how great these things are, I probably shouldn't be posting this, as I've already bought all the lucky upgrades, but please nerf crits in general. There's got to be some better way to do this than increasing whole attack/defence points for 18k or so SP. Also, I suggest nerfing Lucky Bastard further by removing the view range buff and increasing cost of every unit again.

Frankly, I might be one of the few that actually liked ARB, on account of knowing exactly how it worked. That system was fair, made the lucky upgrades somewhat useful but not incredible, made LB a weak strategy, and made each additional ARB point less powerful. Now, the more crit points you add to a unit, the more OP it gets. Please, either bring back ARB or find a way to nerf crits altogether, so high ranks aren't walking around with infantry 2 points better than a low rank, and so non-premiums are not at a great disadvantage for not having LB. It's getting insane.

Thanks for the guide, mathdino.

This is my conclusion:
Luck became a bigger factor now in game which is not really appreciated on the first view.
However after playing some games I am more than glad Lucky Bastard actually got useful now!

If you compare none and Lucky XY in Gen Stack with LB of course there is a big difference.
But you got to keep in mind that there is only one General for each player and LB is supposed to boost
the unit strength for the higher costs. And unlike other strategies you dont get any range advantages
which can also make a big difference.

So if you just take a look at the first two values none and Lucky XY you get the actual difference
between a player with that upgrade and someone without it and you see that the difference
only is about .5. So not that big after all. But just fine to justify the SP cost of the upgrade.

Math I'm pretty sure its even stronger than that. the 1-100% is just a description of what values the Crit chance can be.

"Critical hit chance can be 1-100%, which is the chance to deal additional damage - in addition to regular attack/defence roll, the unit deals it's maximum attack/defence damage. So, if your Tank (max attack 7) rolls 3, the critical hit would be 10 (3+7). Simple?"

so the Critical hit is always 100%

Read the word chance

Wr1tt3n by Cherse, 03.12.2012 at 08:22

Math I'm pretty sure its even stronger than that. the 1-100% is just a description of what values the Crit chance can be.

"Critical hit chance can be 1-100%, which is the chance to deal additional damage - in addition to regular attack/defence roll, the unit deals it's maximum attack/defence damage. So, if your Tank (max attack 7) rolls 3, the critical hit would be 10 (3+7). Simple?"

so the Critical hit is always 100%

Oh god, I did the Math completely wrong. Thanks for the catch, Cherse. That makes LB even more OP than I thought... I'll have the fixes up by tomorrow, alright?

Lol use nothing but lucky bastard for now

Changed the upgrade bonuses to +2 and LB to +5.

Lucky Bastard wasn't the only thing affected by post merge AW changes. We need to rebalance a lot of strats. Relentless Attack is much stronger than PD now, GC is totally out of use, and Desert Storm could really use the +1 carrying capacity for marines.

Wr1tt3n by Acquiesce, 03.12.2012 at 11:00

Lucky Bastard wasn't the only thing affected by post merge AW changes. We need to rebalance a lot of strats. Relentless Attack is much stronger than PD now, GC is totally out of use, and Desert Storm could really use the +1 carrying capacity for marines.

None of the other mechanics were changed, apart from ARB / Critical hit.

I realize that but those changes gave a noticeable advantage to some strats. RA gives tanks +2 critical hit and PD gives infantry nothing.

I admit Desert Storm was already in need of a boost.

LB is one of the OPest strategy there is out there. I tried a few days ago and 5 LB Infantry could take on 4 Neutral Infantry. It is amazing Please don't change it!

Wr1tt3n by Acquiesce, 03.12.2012 at 11:18

I realize that but those changes gave a noticeable advantage to some strats. RA gives tanks +2 critical hit and PD gives infantry nothing.

But it is similar to what it was before. Just that now it gives tanks extra critical instead of ARB.

I'm just going by what I've noticed playing. But isn't it correct to say that critical has more of an effect on the outcome of a battle than arb did? Luck is more important now. If so then that might explain relentless attack's strength.

Wr1tt3n by Acquiesce, 03.12.2012 at 11:38

I'm just going by what I've noticed playing. But isn't it correct to say that critical has more of an effect on the outcome of a battle than arb did? Luck is more important now. If so then that might explain relentless attack's strength.

I honestly don't think it makes that big of a difference. We've already lowered the critical bonuses from strategies & upgrades, so it should be quite similar to what it was in Afterwind. Strategies now only add or remove 2 critical, which is a very small amount.

First of all you messed up your first table Math, you put the average attack for 8 points as 5, where it should have been 4.5, and the numbers after it are also off by .5.

Admins, i mentioned this after 2 days in alpha and you said you would do something about this. Extremely bad (or good) rolls are much more common then they should be, getting a max attack point boost 25% of the time is far too much. It doesn't matter if you change the strategies so they are all equal, the main problem is still there and that is that battles are too heavily influenced by luck. Also there is the problem that a crit by a relentless attack tank can give it like 18 attack power, whereas a militia can only deal about 10 on defense, a big difference from 9 vs 5.

I already posted some suggestions on what could be changed here:

http://atwar-game.com/forum/topic.php?topic_id=5759&board_page=2

Whether you follow them or not, it doesn't matter to me, just change something about it to decrease the influence luck has on battles.

Wr1tt3n by Puzzles, 03.12.2012 at 17:20

First of all you messed up your first table Math, you put the average attack for 8 points as 5, where it should have been 4.5, and the numbers after it are also off by .5.

Admins, i mentioned this after 2 days in alpha and you said you would do something about this. Extremely bad (or good) rolls are much more common then they should be, getting a max attack point boost 25% of the time is far too much. It doesn't matter if you change the strategies so they are all equal, the main problem is still there and that is that battles are too heavily influenced by luck. Also there is the problem that a crit by a relentless attack tank can give it like 18 attack power, whereas a militia can only deal about 10 on defense, a big difference from 9 vs 5.

Qu0t3:

Changed the upgrade bonuses to +2 and LB to +5.

They changed it... I have no problem now; no need to change or update the thread. Changing topic title to reflect the outdatedness.

Wr1tt3n by Mathdino, 04.12.2012 at 18:33

Wr1tt3n by Puzzles, 03.12.2012 at 17:20

First of all you messed up your first table Math, you put the average attack for 8 points as 5, where it should have been 4.5, and the numbers after it are also off by .5.

Admins, i mentioned this after 2 days in alpha and you said you would do something about this. Extremely bad (or good) rolls are much more common then they should be, getting a max attack point boost 25% of the time is far too much. It doesn't matter if you change the strategies so they are all equal, the main problem is still there and that is that battles are too heavily influenced by luck. Also there is the problem that a crit by a relentless attack tank can give it like 18 attack power, whereas a militia can only deal about 10 on defense, a big difference from 9 vs 5.

Qu0t3:

Changed the upgrade bonuses to +2 and LB to +5.

They changed it... I have no problem now; no need to change or update the thread. Changing topic title to reflect the outdatedness.

Yep they changed the base Crit rate to 5 as well. I still notice some strange results here and there, but I am oKay with it now.
Thanks Admins.