[1.1b] Terrible new formula for Chance to Hit

[alpaca]

Cross-post from the bug reports forum.

I ran some tests with 50 corvettes of one weapon type against 50 with another at different evasion and sensor levels. All ships were as barebones as possible (3 weapons of the same type and reactors only in addition to the thrusters, etc). I cheated to get all technologies, enough minerals and credits, instant build, then set fleets to attack each other. Here are the results

Test #  Weapon 1    Weapon 2     To Hit Mod  Evasion  To Hit W1  To Hit W2  Comments
1  Laser (82%)    Mass Driver (76%)       0    5%    94%    93%   Base scenario
2  Laser (82%)    Point Defense (40%)     0    5%    94%    87%   Base scenario

3  Laser (82%)    Mass Driver (76%)       0   20%    74%    74%   Thrusters lvl 4
4  Laser (82%)    Point Defense (40%)     0   20%    75%    48%   Thrusters lvl 4

5  Laser (82%)    Mass Driver (76%)       0   40%    50%    47%   + Precog Interface
6  Laser (82%)    Point Defense (40%)     0   40%    51%    0%    + Precog Interface

7  Laser (82%)    Mass Driver (76%)       6   40%    54%    51%   + Sensor lvl 4
8  Laser (82%)    Point Defense (40%)     6   40%    55%    14%   + Sensor lvl 4

Frankly, I don't see a scenario where these numbers make sense, so there is clearly something very wrong with the calculation somewhere. In the base scenario, there is no significant difference between mass driver and lasers, even though the latter is 10% more accurate. Point defense, which is half accurate, only has a small difference of 7%pt when compared to lasers.

Adding evasion and looking at the point defense numbers indicates that chance to hit is proportional to (accuracy - evasion), however it seems that actual chance to hit is now (acc - evasion)/acc, which is even worse than before. At least the bug where to hit chance modifiers set accuracy to 100% appears to be fixed.

Predicted by (acc - evasion)/acc:

Test #  Weapon 1    Weapon 2     To Hit Mod  Evasion  To Hit W1  To Hit W2  Comments
1  Laser (82%)    Mass Driver (76%)       0    5%    93.9%    93.4%   Base scenario
2  Laser (82%)    Point Defense (40%)     0    5%    93.9%    87.5%   Base scenario

3  Laser (82%)    Mass Driver (76%)       0   20%    75.6%    73.7%   Thrusters lvl 4
4  Laser (82%)    Point Defense (40%)     0   20%    75.6%    50.0%   Thrusters lvl 4

5  Laser (82%)    Mass Driver (76%)       0   40%    51.2%    47.4%   + Precog Interface
6  Laser (82%)    Point Defense (40%)     0   40%    51.2%    0.0%    + Precog Interface

7  Laser (82%)    Mass Driver (76%)       6   40%    54.5%    51.2%   + Sensor lvl 4
8  Laser (82%)    Point Defense (40%)     6   40%    54.5%    13.0%   + Sensor lvl 4

As you can see, the model fits the observed data almost perfectly (with some small deviations that are to be expected in a random experiment), as such, we can conclude that the formula is very likely correct. This new formula is terrible, however, as it almost eliminates any difference between weapon types until you get close to the evasion threshold. This makes evasion the only relevant number and even more overpowered.


Edit: It appears that the above formula is not actually the one used for damage calculation. According to grekulf (a PDX dev), the formula hasn't changed in the 1.1 patch, i.e. it is still given by accuracy - evasion. This seems to agree with tests of actual damage dealt by ships in controlled set-ups other posters have reported on. I did not look at actual damage, only at what the game displays as "hit ratio" and "evasion ratio".

I had interpreted the former as "hit ratio" = hits/shots, and the latter as "evasion ratio" = enemy misses/total shots, which is what the game displays in v1.0.3. However, in 1.1.0b it appears that these displayed ratios only pertain to shots that would have hit, had the opposing ship not evaded, rather than to all shots, or "hit ratio" = (actual hits - evaded) / potential hits, and "evasion ratio" = evaded / potential hits. Nothing changed in the actual damage calculation, however. Running a test with equal ship setups in 1.0.3 and 1.1.0b (3 small lasers vs 3 point defense against 10% evasion), I could verify that, indeed, the damage levels are very close, despite completely different "hit ratios"

Therefore, you can safely ignore this post as it pertains to changes in 1.1 that are, in fact, only in re-interpreting what the UI displays.

 

[Soranya]

Very interesting Analysis. Thy.

 

[Monkbel]

I wonder if this can be fixed before 1.1 is graduated from beta.

 

[DaveyDave]

It appears again as though the mathmatical operation related to percentage has been mis-applied. If you notice, it appears rather than a percentage, the percentage (a multiplication operation) has been converted into a subtraction operation. That's why with a base chance to hit of 50% or less, the actual hit rate drops to about zero.

This is the second time I've observed using the wrong operators for percentage operations in Stellaris.

If base chance to hit is 75%, we use a multipliers against this number to modify the percentage hit chance. If evasion percentage is 40%, we do NOT subtract 40 from 75. We multiply 75 by .4, giving us and then subtract _this_ percentage from the base chance to hit, (75 x .4 = 30; 75 - 30 = 45) giving us a base chance to hit of 45% (not 35%) If the base chance to hit is 50%, and evasion is 40%, we multiply 50 by .4, giving us 20, and substract _this_ percentage from the base chance to hit, giving us a base chance to hit of 30%. If we simply did a subtraction alone, the base chance to hit would drop to 10%.

As I mentioned, I've observed various operations in Stellaris involving the manipulation of percentages. In the cases I've looked at, the wrong mathematical operators are being used, generating garbage results.

 

[BrokenSky]

I made a simple test to figure out the weapon to-hit formula. I found that for lvl1 sensors, it appears to be:

[To Hit] = [Weapon Accuracy] - [Evasion of target]

However, when equipping lvl2 sensors, weapon accuracy is always 100% regardless of the weapon, but evasion still applies.

[To Hit] = 100% - [Evasion of target]

My test method was to create a singleplayer game with a blank race, just a single ethos (spiritualism) to keep it clean. I used the following console cheats:

-research_technologies (gives all tech to you)
-minerals (gives 5000 minerals)
-instant_build
-attackallfleets (All fleets and stations will become hostile to each other regardless if friend or neutral)

I then built the following two designs:

Frigate with 60% evasion, plasma weapons (82% listed accuracy):
http://images.akamai.steamuserconte...922/6A620A73679360ABAC0701C3A1FD4609902735BC/

Battleship with 7.5% evasion, mix of S/M/L kinetics, (76,72,67% listed accuracy)
http://images.akamai.steamuserconte...534/4750534E551C97EF5389F41119232082272D0907/

Note that it's important to use different weapons in the two test groups because the battlewindow displays both fleets in the same summary, so if you use the same the results get mixed together.

Pitting a fleet of 16 of these battleships against 128 of the corvettes:

http://images.akamai.steamuserconte...096/A526AC72A3E7F4224FE768A347C7AB2A047A2CA5/

If we switch to lvl1 sensors the result is:

http://images.akamai.steamuserconte...957/BB79C936A569F718324F7E780D48A0AF9FC3E28C/

As you can clearly see, using lvl2 sensors the accuracy is always 100%, while with lvl1 sensors it is an the additive formula.

From another thread on Accuracy in 1.0

Edit: said was form 1.1, was mistaken.

 

[beckermt]

It appears again as though the mathmatical operation related to percentage has been mis-applied. If you notice, it appears rather than a percentage, the percentage (a multiplication operation) has been converted into a subtraction operation. That's why with a base chance to hit of 50% or less, the actual hit rate drops to about zero.

This is the second time I've observed using the wrong operators for percentage operations in Stellaris.

Well, admittedly, it doesn't say "Evades 50% of shots." It says "50% Evasion" which is a mechanic in the game, with a specific definition. In this case, it means that you penalize Accuracy by your Evasion.

The way you expect the formula to be conceived is this:
Acc*Evasion = To Hit
This means an accuracy of 75% vs an Evasion of 50% would be a To Hit of 37.5%.

Instead, the formula is (similar to) the following:
(Acc - Evasion) = To Hit.
Acc 75% vs Evasion 50% gives 25%

However, the 2nd equation is perfectly mathetically valid, because I am subtracting 2 percentages from another. You just need to think of Evasion as percentage point penalty, not a percentage penalty to Accuracy.

 

[beckermt]

From another thread on Accuracy in 1.1

That's not from 1.1.

 

[DaveyDave]

Acc 75% vs Evasion 50% gives 25%

However, the 2nd equation is perfectly mathetically valid, because I am subtracting 2 percentages from another. You just need to think of Evasion as percentage point penalty, not a percentage penalty to Accuracy.

Sorry, wrong.

Another operation which is wrong in the game are the application of percentage discounts to fleet maintenance. If the various discounts total a percentage number above 100, then the fleet pays you. This is a garbage result, because the operation is performed incorrectly. You are redefining the term 'evasion' to defend the game as it is, but the game is generating garbage results because percentage operations are being done in Stellaris incorrectly. The correct way to do multiple modifying percentages is multiplication by a number less than one, and subtract this from the base number. Stellaris is simply skipping multiplication. Violates basic mathematical principles.

AFAIK, Paradox has not acknowledged any problem with these operations, but with every post like this I'm increasingly certain there's a fundamental problem. Since I've seen at least three posts about these things dealing with different areas of the game, with garbage in every one, it suggests their entire table of math functions may be using incorrect operation order.

 

[lebigmac]

indeed, 75 vs 50 evasion is 33% hit chance.

think of like this : 75 hit minus 50 evasion, is 25, wich is 33% of 75, which is your hit chance.

funny little detail with this formula is that 0 evasion will always give 100% hit chance. Even with low hit chance weapons.

 

[EntropyAvatar]

I think I see what they are trying to do with this formula. They want to have low-accuracy weapons that still have a good chance to hit low-evasion targets. However, it's not good since as evasion approaches accuracy, effective hitpoints goes to infinity.

If they want low acc weapons to only be able to effectively hit low-evasion targets, they should make the formula:

hitChance = Accuracy / (Accuracy + Evasion)

That doesn't have nasty asymptotic locations (assuming only positive values allowed) and it's fairly intuitive. When evasion equals accuracy, it's a coin flip. Past that you can stack evasion to drive down the hit chance, but never to zero.

 

[Bob_Herzog]

If they left all modifiers for accuracy in the game this solves nothing about the corvette issue. For some of the weapons that can reach 100% it may be a bit better now for the regular 87-85% corvette but should someone get lucky to get one of the extra boosts needed to reach 90+% ...

In fact on the way to the high values evasion is now even better.

 

[lebigmac]

mm now that i think of it, its a little unintuitive, but I woudlnt discount this formula outright.

It has some interesting consequences when shooting at battleships.

low accuracy weapons like artillery, get a hit chance over their listed chance, vs low evasion stuff like battleships, which i find an interesting consequence...

even though the numbers need tweaking for really high evasion stacking.

 

[Yuifuru]

(posted this in the old thread already, but I figured it needs to be here as well)

Here's what I would propose to calculate hit chance:

Interprete weapon accuracy as "evadability"

hit chance = 1-(1-accuracy)*evasion (accuracy and evasion go from 0 to 1.0 here)

For example, take a weapon with 60% hit chance. It would always have at least 60% real hit chance, only the "inaccuracy" is subject to evasion.

The result would be that a target with 100% evasion would not be completely invulnerable, it just takes the 60% of shots.
A target with 50% evasion would be hit with 80% chance. hit chance = 1-(1-0.6)*0.5
And finally a target with 0% evasion is hit 100%

This is how I thought the game would do it before looking into it, because it made the most sense when I saw missiles always hitting no matter the evasion.

With this, evasion becomes comparable to armor, which is countered by armor penetration, and accuracy would counter evasion in just the same way, and become irrelevant against big targets, just like armor penetration is irrelevant against small ones. It would be easily balanceable and infinitely scalable. There would be no need for limiting evasion stacking or dumb stuff like artificial limiting returns.

 

[lebigmac]

the more i think about it, i think this formula could work.

if one tightened the evasion catagories further, so that battleships were 4-8 evasion, Cruisers around 12-18 or so, destroyers 22-30, corvettes 32-55

then one could revise the "heavy, anti battleship weapons", to have accuracies around 50.
This would make them highly accurate vs their intended target, and unable to hit corvettes at all.

Then make a few other tweaks like not having 100% armor pen weapons, having high armor pen weapons be exclusive to bombers and large mounts, and you d have an improvement to the game I think.

edit: light weapons designed to kill smaller targets could be a bit higher than the 80ish they are now. No reason to limit hit skill to 100 really, with this formula.

some examples:

50 accuracy heavy weapon vs
4 evasion: 92% hit chance (battleship)
8 evasion: 84% hit chance (battleship)
15 evasion : 70% hit chance (crusier)
28 evasion : 44% hit chance (destroyer)
45 evasion: 10% hit chance (corvette)

110 accuracy anti-fighter weapon vs
4 evasion: 96% hit chance (battleship)
8 evasion: 92% hit chance (battleship)
15 evasion : 86% hit chance (crusier)
28 evasion : 75% hit chance (destroyer)
45 evasion: 59% hit chance (corvette)

 

[alpaca]

mm now that i think of it, its a little unintuitive, but I woudlnt discount this formula outright.

It has some interesting consequences when shooting at battleships.

low accuracy weapons like artillery, get a hit chance over their listed chance, vs low evasion stuff like battleships, which i find an interesting consequence...

even though the numbers need tweaking for really high evasion stacking.

The problem is that in the low-evasion regime you get 100% accuracy with any weapon, which makes missiles completely pointless until you see evasion go to 30%-40% or so. To add insult to injury, any point defense will shoot them down unless overwhelmed (missiles do not seem to evade).

We also still have this annoying singularity as evasion goes up towards accuracy. Not sure what max evasion is now, but I think it's something like 70% (40% on ship, 10% from spaceport, 15% from leader, 5% from amoeba). This will still make a lot of heavy weaponry pretty pointless.

It's also extremely counter-intuitive (and would be bad if weapons were more meaningfully balanced) that the accuracy of your weapons barely has any effect in the early game.

 

[FitzOmega]

I don't like the fact that Large weapon needs to be less accurate than Small. I would highly prefer to have the same accuracy on Large but less useful against small ship because of overkilling and less rate of fire. Evasion would still be great against them because missing one shot is really bad for you.

 

[Praetori]

Accuracy should decrease with range IMO. Sure them pesky corvettes dancing around wouldn't be easy to hit at 60 even for lance but that'd be fine. Missiles and torps are made for picking off maneuvering targets at range (which can be countered by PD). This would make destroyer screens sensible (if the tactical combat AI can get an overhaul in positioning etc) since it'd protect your capital-ships from marauding corvette missile-boats.

Also while we're at it, damage should decrease with range as well except for missile and kinetic (as we're in space). Especially plasmas should have a huge drop off (with that I could live with their high armor-pen).

 

[KiwiNoob]

I think I see what they are trying to do with this formula. They want to have low-accuracy weapons that still have a good chance to hit low-evasion targets. However, it's not good since as evasion approaches accuracy, effective hitpoints goes to infinity.

If they want low acc weapons to only be able to effectively hit low-evasion targets, they should make the formula:

hitChance = Accuracy / (Accuracy + Evasion)

That doesn't have nasty asymptotic locations (assuming only positive values allowed) and it's fairly intuitive. When evasion equals accuracy, it's a coin flip. Past that you can stack evasion to drive down the hit chance, but never to zero.

I looked at that but found that it became difficult to get the accuracy down if you wanted to (say if you didn't want a weapon to be able to hit corvettes such as some large mounts). If we go with:

% hit = 1 - tan(evasion / (accuracy + evasion))

then we achieve similar results when accuracy is much higher that evasion but as accuracy drops off to about 1/4 of evasion the chance to hit does reach 0%.

I think one important change to make is to not present accuracy and evasion as percentages but comparable values that are allowed to go above 100 (I.e. a gun has an accuracy of 80 not an accuracy of 80%)

 

[Soranya]

It appears again as though the mathmatical operation related to percentage has been mis-applied. If you notice, it appears rather than a percentage, the percentage (a multiplication operation) has been converted into a subtraction operation. That's why with a base chance to hit of 50% or less, the actual hit rate drops to about zero.

This is the second time I've observed using the wrong operators for percentage operations in Stellaris.

If base chance to hit is 75%, we use a multipliers against this number to modify the percentage hit chance. If evasion percentage is 40%, we do NOT subtract 40 from 75. We multiply 75 by .4, giving us and then subtract _this_ percentage from the base chance to hit, (75 x .4 = 30; 75 - 30 = 45) giving us a base chance to hit of 45% (not 35%) If the base chance to hit is 50%, and evasion is 40%, we multiply 50 by .4, giving us 20, and substract _this_ percentage from the base chance to hit, giving us a base chance to hit of 30%. If we simply did a subtraction alone, the base chance to hit would drop to 10%.

As I mentioned, I've observed various operations in Stellaris involving the manipulation of percentages. In the cases I've looked at, the wrong mathematical operators are being used, generating garbage results.

Paradox math - aka the numbers shown dont work like someone would expect from the given circumstances....
Also it seems to confuse Programmers at Pdx constantly as well and therefor they oftne have inconsitencies in there System. (Aka one Formula uses variant A another uses Variant B. sometimes even within the same system...)

@Paradox
Could you please release the Algorithms for things like "Hit or No hit?" and "Ethic change or no Ethic change?" etc.?
I think that showing us in detail whats happening would prevent alot of confusion of what the numbers presented to us actually mean!

EDIT1:
Just found a Dev Post in the Beta Patch thread that confirms the "Substract Hit from Evasion Number" Formula:
ChanceToHit = (WeaponChanceToHit + SensorModifiers) - (ShipEvasion*EvasionModifiers)

With the ne Evasion "Cap" you can reach around 50%-60% Evasion Value (depending on Admirals and what bonuses you got from Events/Anomaies) and get a total of +6 to hit from Sensors.
As most Weapons are in the 70-80 Hit range this means a minimum ChanceToHit of 15%-20% against Corvets. Unsurpsingly Stacking Evasion is still really really Strong, but no longer breaks the System by getting Evasion rate higher then Hitrates.

Am I correct in the assumption that Rockets and Torpedos seem to have a 100% CtH regardless of Evasion values, so you still need PD for them?

EDIT2:
Link to Dev Post:
https://forum.paradoxplaza.com/foru...not-for-problem-reports.937741/#post-21274147

 

[beckermt]

You're free to complain that the use of percentages is silly in Paradox land, but it's not mathematically unsound. The vast VAST majority of PDX games with percentage modifers use them a PP (Percentage Points) instead of %.

like... every. single. modifier. in. the whole. freaking. game. (excluding flat bonuses)

That's how it has always been.