[MECHANICS] Data on Accuracy Versus Deflection

[arkane83]

This is a work in progress. Something randomly inspired me to make a table to see what the real value of accuracy and deflection are. This table is just designed to illustrate how much deflection and accuracy effect each other. 

 

This is a tool to help understand the power of stacking deflection and/or accuracy. In the actual game, you are probably not going to ever experience the extremes unless you severely out-level or are out-leveled by the content. That being said, I found it useful when deciding on how much resolve to take on one of my characters (20). 

 

Keep in mind, that the value of deflection and accuracy are enemy dependent. The more of the opposite stat your opponent has, the more you need and the more/less valuable they can become. Also, PoTD and scaling will both make it much harder to stack deflection. The difficulty you plan on should effect your build. Furthermore, deflection has some relative breakpoints depending on your opponents accuracy:

• 70 Point Deflection Advantage = Immortality (cannot even be grazed). 
• 50 Point Deflection Advantage = Hit Immune (can only be grazed). The time to kill you is about 6x as long as even deflection/accuracy
• 30 Point Deflection Advantage = My calculations have this lasting about 2x even deflection / accuracy. About 333% effective health
• Even deflection = Critical Strike Immunity (can only be hit or grazed). Your effective health is around 167% just from deflection
• 30 Point Accuracy Advantage = Enemy will never miss. It will take someone about 60% of the time to kill you as even deflection/accuracy 
• 50 Point Accuracy Advantage = Enemy will never miss or graze. My calculations have this at 53.3% TTK
• 100 Point Accuracy Advantage = Automatic crit. My calculations have the TTK at 48%

 

This is all based upon the attack rolls that the game uses, which should be:

0-30 MIss

31-50 Graze

51-100 Hit

101+ Crit

 

 

DPS Modifier: The amount that the attack roll theoretically reduces your potential Damage Per Second (DPS). All physical attacks are primarily gated by attack versus deflection and penetration versus armor. All of my calculations are based upon adequate penetration and a steady stream of auto attacks . There are a ton of other factors in figuring out how much damage you will actually do per second; however, we can estimate (over time) how much DPS you will lose due to the attack rolls. I calculated this factor using a weighted average:

 

(%Miss / 100% x 0 Damage) + (%Graze / 100% x 0.50 Damage) + (%Hit / 100% x 1.00 Damage) + (%Crit / 100% x 1.25 Damage)

 

Effective Health of Target: Again, there are other factors (Armor, hit to graze, etc) which will factor into this figure. However, the attack roll will have a major impact on this figure. To estimate the effect the attack roll on "effective health" we can use the reciprocal of the DPS Modifer. Essentially, as time progresses, the negative impact on your damage becomes exponential on how long you survive. Simply put, reducing your damage output by 50% (1/2) results in in 200% effective health (2/1). 25% DPS (1/4) becomes 400% effective health (4/1) etc.

 

 

Relative Time to Kill: This number gets a bit more complex. The number you see here relates the effective health of that point differential to the "standard" of having equal accuracy and deflection. When accuracy = deflection the attacker loses 40% of their potential auto-attack DPS which results in 166% effective health.  If you give the defender 10 more deflection, 10% more DPS is lost. This results in a 200% effective health versus the 166% baseline or 120% relative TTK. This number is:

 

Effective Health @ X Acc-Def / Baseline Effective Health

 

Put another way, if you see a 1000% here, that is 900% harder to kill than my "baseline". Conversely, a 50% here means that the defender (theoretically) dies twice as fast!

 

Value of Point: This is the rate of change of relative time to kill as a percentage of the last points time to kill. I multiplied this by 100 for ease of understanding the relative value of each additional point of accuracy and deflection. 

 

abs(x-y)/x * 100

 

X = Relative TTK of the previous point (the point closer to the baseline)

Y = Relative TTK of the current point (the point further from the baseline)

 

The first point in either direction will be the exact % different from baseline. As you progress up or down the chart, this number relates the change in TTK relative to the previous point. I came up with this value to illustrate that each point of deflection you move towards -70 on the attack roll gets better and better (with some breakpoint exceptions). 

 

Honestly, comparing everything to even deflection and accuracy (the way I did) somewhat understates how amazing deflection can be. For example:

 

-20 Deflection would give the enemy 10% Miss 20% Graze 50% hit and 20% crit. Assuming +25% crit damage that leaves you at:

 

(0.1/1*0)+(0.2/1*0.5)+(0.5/1*1)+(0.2/1*1.25) = 85% reduction in DPS from combat roll 

1/.85 = 117.65% Effective health (from combat roll alone)

 

+20 Deflection would give the enemy 50% Miss 20% Graze 30% Hit and 0% crit. 

 

(0.5/1*0)+(0.2/1*0.5)+(0.3/1*1)+(0.0/1*1.25) = 40% reduction in DPS from combat roll

1/0.4 = 250% Effective health (from combat roll alone)

 

Now when you look at it from an effective health point of view, the 40 deflection swing more than DOUBLES your durability. 

 

Obviously, I am leaving out a ton of other variables, including armor, penetration, and gear/abilities which convert hits to grazes. (By the way, that illusion spell which gives a low amount of deflection and hit to graze conversion is really good...). Another thing to keep in mind is that not everything is "on the bonus side". A -5 to your enemies hit roll is the SAME as +5 deflection. You can make these gaps much larger by using perception afflictions on your enemy, hatchet weapon modal, etc.

 

 

 

 

 

 

Edit: I added some charts.

 

Edit 2: I corrected an error in my value of point calculation. 

POE Hit Table v2.pdf

Edited July 2, 2018 by arkane83

[Kaylon]

The grazes and the criticals aren't calculated like that... Here's how it works:

 

Hit = base dmg * (1 + % total dmg bonus)

Graze = base dmg * (1 + % total dmg bonus - 50%) = base dmg * (0.5 + % total dmg bonus)

Critical Hit = base dmg * (1 + % total dmg bonus + % total crit dmg bonus) = base dmg * (1.25 + % total dmg bonus) assuming no over-penetration and only the base crit dmg bonus.

 

After that the miss/graze/hit/crit distribution is correct.

 

Once you completely eliminate misses (acc-def>30) the gain is 0.75%dmg for +1acc and once you eliminate also the grazes (acc-def>50) the gain becomes 0.25%dmg for +1acc (while +1mig adds 3% dmg). So increasing accuracy has serious diminishing returns unless you have high critical dmg bonuses or a good proc on critical hit (like Frostseeker).

[gkathellar]

Kaylon's notes in mind, this is a really good thing to see from a theorycrafting perspective. Good job.

[arkane83]

Kaylon's notes in mind, this is a really good thing to see from a theorycrafting perspective. Good job.

 

Thank you.

 

My calculations were all based upon no damage bonuses or penalties. Kaylon is absolutely correct about damage penalties and bonuses though, which is why I have a note indicating that I am leaving out a ton of other variables.

 

Also, I may revise the value of the point curve to use a different metric to evaluate how much each point actually helps you. I also am thinking of doing a calculator that incorporates some of the damage formula. Bonus crit chance and damage BOTH will influence how valuable accuracy are going to be.

 

The hit to crit, graze to hit, etc. abilities are a bit harder to estimate because, as far as I am aware, they are checked sequentially.  25% hit to crit and 5% hit to crit should be a net of about 28.75% actual hit to crit. If I were to actually make a calculator I would have to do something that uses the real abilities in-game so it is more useful.

[Boeroer]

The hit to crit, graze to hit, etc. abilities are a bit harder to estimate because, as far as I am aware, they are checked sequentially.  25% hit to crit and 5% hit to crit should be a net of about 28.75% actual hit to crit.

You are correct.

 

Same with proc chances on weapons attacks (a bit offtopic, just fyi ).

Edited July 3, 2018 by Boeroer