Lt. Commander
Join Date: Dec 2007
Posts: 120
Jedi Counsel: Accuracy Vs. Defense:


Based on the discussions with Al "CaptainGeko" Rivera, in this STOked podcast, and the PDF for 'Accuracy vs. Defense' that can be found accompanying that podcast, I would like to posit a (heavily-tested) theory on how Accuracy and Defense work in relation to each other.


For starters, let's look at what Accuracy and Defense are, and how they are modified:

Accuracy:

Accuracy is the primary factor in determining the effectiveness of the attacks of your ship's weapons.
Accuracy is derived from several sources:
  • The Accurate Trait for Captains (+10% Accuracy to ALL of your ship's weapon attacks)
  • The [Acc] modifier on Uncommon or more rare weapons (+10% Accuracy to THIS weapon's attacks, does NOT apply to any other weapon)


Defense:

Defense is the primary factor in preventing enemy attacks from outright hitting your ship.
Defense is derived from several sources:
  • Your ship's speed - The faster that you travel, the greater your Defense rating, up to a maximum Defense at an Impulse speed of 24.00 (NOTE: Being stopped at Impulse speed 0.00 will give your ship a -15% Defense penalty.)
  • The Elusive Trait for Captains (+10% Defense at all times)
  • Some items (e.g. 2 pieces of the AEGIS set, the Subspace Field Modulator, etc.) - Can be permanent, conditional increases (AEGIS) or temporary boosts (SFM).
  • Some powers (e.g. Attack Pattern Omega, Evasive Maneuvers, etc.)


How do Accuracy and Defense relate to each other?

First, all ships have an inherent 100% Accuracy (1.00 for the STOked spreadsheet) and an inherent 100% Defense (also 1.00 for the STOked spreadsheet).

Second, all weapons calculate their inherent Accuracy bonus independently. Thus, no matter how many [Acc] modifiers one of your weapons may have, they only apply to that specific weapon. The Accurate Trait for Captains, however, applies to all weapons (as if they each were gaining an extra [Acc] modifier). For example: if your ship has 4 Beam Arrays, 1 of them with [Acc]x2, and the other 3 with no modifiers, only the attacks by that one BA with [Acc]x2 will benefit frorm the +20% Accuracy bonus, while the other 3 will use your unmodified Accuracy rating.

Third, the baseline for 'To-Hit Chance' (i.e. how often your weapons will Hit or Miss their targets) is: 100% Chance To-Hit, if your Accuracy = the target's Defense. Therefore, if you are shooting an unmodified attack at an enemy ship that is moving as slowly as possible (to negate the Defense penalty for being stopped, but not enough to gain any bonus Defense), you will hit them 100% of the time.

Fourth, by using the STOked spreadsheet (and, again, assuming that the 'baseline' Accuracy and Defense values for all ships is 1.00, and each +X% is converted to a decimal value, e.g. +10% Accuracy would equate to .1, +50% Defense from speed would equate to .5, etc.), you can see the sliding scale of To-Hit Chance, as the difference between Accuracy and Defense increase. The minimum possible To-Hit Chance is 25%, but the realistic To-Hit Chances are typically in the 40-70% range (Escorts typically have higher Defense bonuses from speed, thus, are a little harder to hit, and Cruisers typically are slower and get hit a little easier).

Fifth, what happens when your Accuracy is greater than a target's Defense (usually only possible if you are able to stop your target, using Tractor Beams or Beam: Target Engines, etc.), well, a few things:
  • You still have 100% chance to-hit your target.
  • You gain a bonus to Critical Chance.
  • You gain a bonus to Critical Severity.
  • The bonuses to Critical Chance and Critical Severity depend on how much greater your Accuracy exceeds your target's Defense (this is referred to as 'Accuracy Overflow') and can be tracked on the STOked spreadsheet (NOTE: The decimal values in those columns work the same as for Accuracy and Defense, and convert to %'s)


Then, just for an example of comparing Accuracy vs. Defense:

Let us assume that you are firing a weapon with no inherent Accuracy modifiers, and your opponent is moving and has a +50% Bonus Defense rating from his ship's speed. On the STOked Spreadsheet, you would enter 1.00 into the Accuracy box in the top-left of the sheet, and you would enter 1.5 into the Defense box.

You will see in the "Diff:" box: -0.5 (because the target's Defense is higher than your Accuracy), and below that, you will see to boxes: "If Diff Negative" and "If Diff Positive" In this case, the difference is negative, so you would look to the right of that box, and see: "0.666666667" which is your To-Hit Chance... Meaning, you have a 66.67% chance of hitting your target with any weapon shot (i.e. 2/3 of your shots should hit the target). (NOTE: This also illustrates that you do not simply subtract your target's Defense score from your Accuracy to determine your To-Hit Chance.)


On the flip-side, assume that you still have no inherent Accuracy modifiers, but your target is stopped (and taking a -15% Defense penalty, or -.15), plugging in 1.00 into the Accuracy box, and .85 into the Defense box, you get 0.15 as your Diff score. Since this is positive, you would look in the If Diff Positive box, and get "1.13..." as your result... Meaning you have 'Accuracy Overflow'... You have 100% chance to-hit your target, and, if you look in the lower-right hand portion of the spreadsheet, you can look on the Accuracy Overflow table, and look at the entry for 0.1 (since your overflow is 0.13-ish)... You would gain a little more than 1.25% Critical Chance, and a little more than 5% Critical Severity.


Hope that helps clear up some confusion, and, if you have any questions, I will do my best to answer them here,
-Big Red
Lt. Commander
Join Date: Dec 2007
Posts: 120
# 2
06-06-2011, 02:26 PM
Thanks for spelling this out. I wish they would change the in-game tooltips, as they explain things differently (for instance they describe the default To Hit chance at 95%, and that overflow applies a CrtD, but says nothing about CrtH).

Well done.
Lt. Commander
Join Date: Dec 2007
Posts: 120
# 3
06-06-2011, 02:53 PM
I've always been of the mind the weapons with the [ACC] are more valuable than they show on the exchange. Can't get the CrtD or CrtH if you can't hit the target at all

Thanks you BigRedJedi, I watched that episode, but I appreciate the hard work you put it, especially the testing, so I could understand all the math.
Lt. Commander
Join Date: Dec 2007
Posts: 120
# 4
06-06-2011, 06:58 PM
Jedi Council?! WTF! This is Star TREK not Star WARS.
Lt. Commander
Join Date: Dec 2007
Posts: 120
# 5
06-06-2011, 11:58 PM
Thanks BigRedJedi. This seems to make sense. Understanding the base assumptions behind the chart seems pretty important to get them - and it requires to abandon everything I thought to knew from previous dev comments.

PS: I thought you were on vacation?
Lt. Commander
Join Date: Dec 2007
Posts: 120
# 6
06-07-2011, 12:32 AM
Quote:
Originally Posted by MustrumRidcully View Post
Thanks BigRedJedi. This seems to make sense. Understanding the base assumptions behind the chart seems pretty important to get them - and it requires to abandon everything I thought to knew from previous dev comments.

PS: I thought you were on vacation?

LOL, I am on vacation, but it was a 13-hour drive from where I was visiting, to where I'm currently on vacation, and I occupied my mind with trying to figure out some of this stuff (and listening to the STOked podcast, hooray for iPods)... Had one of those 'Eureka!" moments, when I realized what the spreadsheet was illustrating, and pulled some of my combat logs up, and ran those numbers alongside the newly-assumed base values, and they worked!

What can I say? As my wife would say (as she points at me and giggles): "NERD!"

I'll be back from vacation on June 12th, but I do have some limited 'Net access, so I can 'somewhat' keep up on here. (Just have to wait until everyone else goes to bed. LOL)

-Big Red
Lt. Commander
Join Date: Dec 2007
Posts: 120
# 7
06-07-2011, 09:11 AM
Quote:
Originally Posted by warpseven
Jedi Council?! WTF! This is Star TREK not Star WARS.
Well, obviously BigRedJedi thought BigRedSpock would be a stupid name.

Seriously, I'm sure the OP didn't reply because he felt it wasn't necessary, but I advise repeating the MST3K Mantra.

On the topic (because otherwise it wouldn't be) I admit that it is quite nice that excess Accuracy translates to Criticals. I didn't know that, but it's quite useful.
Lt. Commander
Join Date: Dec 2007
Posts: 120
# 8
06-07-2011, 09:24 AM
I would think defence would be better b/c it helps if your target fired by multiple enemies while acc only helps against 1 opponent at a time.
Lt. Commander
Join Date: Dec 2007
Posts: 120
# 9
06-07-2011, 09:45 AM
Wow this great. Thanks for putting it up.

I did want to have some clarifcation on the defense stat.
It is capped right? Is 100% the max defense you can have?
While you can have an accuracy that is over 100%?

Thanks in advance.
Lt. Commander
Join Date: Dec 2007
Posts: 120
# 10
06-07-2011, 11:11 AM
Quote:
Originally Posted by N_Danger
Wow this great. Thanks for putting it up.

I did want to have some clarifcation on the defense stat.
It is capped right? Is 100% the max defense you can have?
While you can have an accuracy that is over 100%?

Thanks in advance.
Defense from certain sources is capped, like the defense from speed. But otherwise, it's all uncapped AFAIK. The trick is that the final result is not just adding it all together, but subtracting the values and consulting the chart (I tend to assume the chart is actually based on a formula). That one probably provides the cap, like that you can't go below 25 % hit chance. (if you check the excel sheet attached to the podcast BigRedJedi refers to, you should see that there isn't a hit chance below 25 %.)
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