[Mechanics article] Item quality, and its effect on the computation of set bonus value

TheYKcid

Ever noticed something counter-intuitive about the way set bonuses are calculated? For example, adding one piece of gold-quality gear to an otherwise fully-purple set can result—though not always—in ZERO change to the set bonuses provided. It always puzzled me, and a recent bug report (link) reminded me of the issue, so I decided to investigate and post my findings here, in an unnecessarily complicated article that will probably never affect most of the playerbase. But to all those interested—enjoy!

To start off, there are two very clear constants governing the stam/mag provided by a standard 1-4pc set bonus (stam/mag is arbitrarily chosen; you could pick a different stat, eg. weapon damage, but the rules are the same):

1. A fully-purple set provides 1058
2. A fully-gold set provides 1096

It's what happens between those two extremes that gets confusing. In the following example, we start from a baseline of a fully-purple 5pc set, and observe how the set bonus transforms as we add more gold pieces to the set. Notice that at certain intervals, there is no gain in the stat bonus despite the addition of a gold piece, as mentioned in the intro:

• 5 purple pieces - 1058
• +1 gold piece(s) - no change
• +2 gold piece(s) - 1071
• +3 gold piece(s) - no change
• +4 gold piece(s) - 1083
• +5 gold piece(s) - 1096

It gets even more complicated when we include a 2-handed weapon as part of the 5pc set, meaning it now only comprises of 4 individual items. Once again, we see a "null interval" where adding an additional gold piece does nothing, but this time there's only one:

• 4 purple pieces - 1058
• +1 gold piece(s) - no change
• +2 gold piece(s) - 1071
• +3 gold piece(s) - 1083
• +4 gold piece(s) - 1096

What about a 2pc set, you ask? I tested that with the Tremorscale monster set:

• 2 purple pieces - 1058
• +1 gold piece(s) - 1071
• +2 gold piece(s) - 1096

From these examples, we can draw several common observations:

• When wearing a mix of gold/purple, the resultant stat bonus is NOT a numerical average
• When adding more gold pieces, the change in stat occurs at discrete intervals
• There are only 3 such intervals (eg. 1071, 1083, 1096)

Because these intervals occur at different points depending on how many items comprise the set, I suspected there was some underlying proportionality involved. Since there are 3 intervals, the simplest and most likely hypothesis was that they were distributed evenly-apart, at thirds, along the purple to gold spectrum:

• 33.3% - 1071
• 66.7% - 1083
• 100% - 1096

This seems consistent with the first set of data (5pc set consisting of 5 items). With one gold piece, you are 20% of the way towards full-gold and have not passed the one-third milestone, hence no change. You pass this upon adding 2 gold pieces (40%) and thus bump-up the bonus to 1071. 3 pieces, 60%, no change. 4 pieces, 80%, 1083 due to passing the two-thirds milestone. This framework also holds true for the 4-items data, as well as the Tremorscale data.

The final, conclusive way to verify this hypothesis was to test a 3pc jewelry set, since the theoretical intervals coincide precisely with the number of items involved. For this I chose the Ancient Grace set, and yes, I actually purchased gold jewelry solely for research purposes. The result:

• 3 purple pieces - 1058
• +1 gold piece(s) - 1071
• +2 gold piece(s) - 1083
• +3 gold piece(s) - 1096

Bingo!

So to summarize these findings in picture format for easier reference:


Note: just a reminder that these interval values (1058 - 1096) apply to max stam/mag set bonuses. If we were considering a different stat—eg. mag/stam/health regen, spell/weapon damage—they would use a different set of numbers (124, 126, 127, 129) but adhere to the same interval points.

Minno

really effin cool!

Mudcrabber

Did you check your character stats to verify that the tooltip wasn't lying to you? I noticed that issue when I upgraded my bright-throat's necklace from gold to purple. The equipped tooltip didn't change but my stats did, more than the trait/enchant could account for (my magicka recovery went up, though only by 6, and I had a spell damage enchant so that couldn't have caused it, and my total magicka went up by about 100, though the arcane trait value only went up by 30).

Kanar

Good info

TheYKcid

Minno wrote: »

really effin cool!

Kanar wrote: »

Good info

Thanks! I'm fully aware that this might be dreadfully boring to some, but I was really excited while uncovering these details and wanted to share that with the forum, lol.

Mudcrabber wrote: »

Did you check your character stats to verify that the tooltip wasn't lying to you? I noticed that issue when I upgraded my bright-throat's necklace from gold to purple. The equipped tooltip didn't change but my stats did, more than the trait/enchant could account for (my magicka recovery went up, though only by 6, and I had a spell damage enchant so that couldn't have caused it, and my total magicka went up by about 100, though the arcane trait value only went up by 30).

Yep, I did, and each interval jump (or lack thereof) was reflected accurately and predictably on my stat sheet.

I'm guessing you forgot to account for regen modifiers. For example, on my Altmer Magsorc, I have a 62% multiplier at baseline (20% from light armour, 10% vamp, 10% Sorc passive, 13% CP, 9% Altmer passive).

Taking a purple 5pc Lich set (with 5 individual pieces), I add 1 gold peice, no change as expected. Adding a 2nd piece, both lines of mag regen go from 124>126, for a total of 4 base regen added. Multiply this by 1.62, and you get 6 (the game engine generally rounds-down), exactly what is reflected on the stat sheet.

This remains consistent all the way to 5pc gold.

Mudcrabber

TheYKcid wrote: »

Yep, I did, and each interval jump (or lack thereof) was reflected accurately and predictably on my stat sheet.

I'm guessing you forgot to account for regen modifiers. For example, on my Altmer Magsorc, I have a 62% multiplier at baseline (20% from light armour, 10% vamp, 10% Sorc passive, 13% CP, 9% Altmer passive).

Taking a purple 5pc Lich set (with 5 individual pieces), I add 1 gold peice, no change as expected. Adding a 2nd piece, both lines of mag regen go from 124>126, for a total of 4 base regen added. Multiply this by 1.62, and you get 6 (the game engine generally rounds-down), exactly what is reflected on the stat sheet.

This remains consistent all the way to 5pc gold.

But my equipped item tooltip didn't change. I had a gold staff and 3 purple jewelry, and when I upgraded the necklace to gold the equipped tooltip didn't change but my magicka and regen went up.

Solariken

I'm gonna drop you an insightful for the work you put in, but man, there are definitely better things to do with your time than this. :P

twofaced

I wonder what was that guy thinking about during coding this tiny part... Hm let's see, I don't like this framework and engine sucks, let's make up something more ridiculous!

Minno

Solariken wrote: »

I'm gonna drop you an insightful for the work you put in, but man, there are definitely better things to do with your time than this. :P

When you think about it, its basically saying "hey, you don't need to fully gold out your gear!"
Like I see a 2pc gold weapon plus 3 purple jewels as the most I would go for that set since it costs WAY too much to gold the jewels but you'll get additional SD/WD out of your weapons.

Flipside, it maybe good to gold 2 or 4 items on light body pieces than to go the full or no gold route (only gaining 13 stats if done this way). But if it was heavy armor, I wouldn't even gold the set (blacksmith materials as really expensive at 6k each but needing 8 for each item for 40 mats needed). and some sets don't even increase the 5pc bonus (like major buffs, or specific buff style sets) so golding out those sets is entirely worthless.

And for 3 set weapons, 3 gold is only 38 difference from 3 purple, but you will probably waste 7k each fragment x 10 frag stack x 4 plates = 280k gold. Really a waste of gold for any gold jewels right now.

eso_nya

And thats why u dont gold out armor

TheYKcid

Mudcrabber wrote: »

TheYKcid wrote: »

Yep, I did, and each interval jump (or lack thereof) was reflected accurately and predictably on my stat sheet.

I'm guessing you forgot to account for regen modifiers. For example, on my Altmer Magsorc, I have a 62% multiplier at baseline (20% from light armour, 10% vamp, 10% Sorc passive, 13% CP, 9% Altmer passive).

Taking a purple 5pc Lich set (with 5 individual pieces), I add 1 gold peice, no change as expected. Adding a 2nd piece, both lines of mag regen go from 124>126, for a total of 4 base regen added. Multiply this by 1.62, and you get 6 (the game engine generally rounds-down), exactly what is reflected on the stat sheet.

This remains consistent all the way to 5pc gold.

But my equipped item tooltip didn't change. I had a gold staff and 3 purple jewelry, and when I upgraded the necklace to gold the equipped tooltip didn't change but my magicka and regen went up.

I just replicated your conditions, but using Bone Pirate, which is still an exact comparison anyway since Bright-Throat is literally the magicka copypaste of that set. Yes I have a lot of spare, redundant purple and gold gear in my bank.

When going from 1 gold 2h + 3 purp jewels > 1 additional gold jewel, the two generic stam bonuses go from 1058 > 1071, as reflected from previous data. The special 5pc stam bonus goes from 1930 > 1953. So we have a total gain of 49 stam from this. As my added gold jewelry unfortunately wasn't robust, deduct 840 for a net base change of -791 stam.

My stam multiplier is 1.14x (10% Redguard, 4% Undaunted, no CP as I tested in Sotha). -791*1.14 = 901.74

My max stam changes from 27149 to 26247, a reduction of 902, essentially exactly identical to predicted value.

There's a variable you missed during your example. Perhaps a small modifier was changed somewhere. Also, do note that the 5pc max resource value from Bright-Throat has a proc condition, and thus doesn't benefit from CP modifier (Bone Pirate behaves the same way). So add that to the list of confounding variables that might've skewed your results.

Based on my controlled tests, though, nothing seems amiss so far.

Edit: also do note that sometimes tooltips will not immediately update when you change a piece of gear. Move your cursor away, or perhaps even close and re-launch the window, and it should refresh.

I've also repeated the Bone Pirate test for stam regen, and results were identical to predicted values.

TheYKcid

Solariken wrote: »

I'm gonna drop you an insightful for the work you put in, but man, there are definitely better things to do with your time than this. :P

You are probably right. But hey, someone's gotta do it!

Mudcrabber

TheYKcid wrote: »

Edit: also do note that sometimes tooltips will not immediately update when you change a piece of gear. Move your cursor away, or perhaps even close and re-launch the window, and it should refresh.

I had tried removing and re-equipping the gear, and still got the same stats, but I don't think I tried a /reloadui. I had typed my before-upgrade equipped stats in a text editor, so I know the displayed value didn't change, but I didn't save the file.

Nichts

Great post, based on my thread from yesterday.
https://forums.elderscrollsonline.com/en/discussion/443582/odd-computation-of-purple-and-golden-set-boni-is-not-correct-when-mixed


It is worth mentioning, that the calculation of the maximum magicka works with the displayed value of the tooltip of the sets. See the last part of my Thread.

As it was mentioned in some comments here as well:
Regular boni (like 2 piece Mothers Sorrow) will get two multipliers: CP_multiplier (1.2, if >300) and skill_multiplier (e.g. Race passive), while some other boni (usually 5 piece boni) only get the skill_multiplier.

Lord_Eomer

TheYKcid wrote: »

Ever noticed something counter-intuitive about the way set bonuses are calculated? For example, adding one piece of gold-quality gear to an otherwise fully-purple set can result—though not always—in ZERO change to the set bonuses provided. It always puzzled me, and a recent bug report (link) reminded me of the issue, so I decided to investigate and post my findings here, in an unnecessarily complicated article that will probably never affect most of the playerbase. But to all those interested—enjoy!

To start off, there are two very clear constants governing the stam/mag provided by a standard 1-4pc set bonus (stam/mag is arbitrarily chosen; you could pick a different stat, eg. weapon damage, but the rules are the same):

1. A fully-purple set provides 1058
2. A fully-gold set provides 1096

It's what happens between those two extremes that gets confusing. In the following example, we start from a baseline of a fully-purple 5pc set, and observe how the set bonus transforms as we add more gold pieces to the set. Notice that at certain intervals, there is no gain in the stat bonus despite the addition of a gold piece, as mentioned in the intro:

• 5 purple pieces - 1058
• +1 gold piece(s) - no change
• +2 gold piece(s) - 1071
• +3 gold piece(s) - no change
• +4 gold piece(s) - 1083
• +5 gold piece(s) - 1096

It gets even more complicated when we include a 2-handed weapon as part of the 5pc set, meaning it now only comprises of 4 individual items. Once again, we see a "null interval" where adding an additional gold piece does nothing, but this time there's only one:

• 4 purple pieces - 1058
• +1 gold piece(s) - no change
• +2 gold piece(s) - 1071
• +3 gold piece(s) - 1083
• +4 gold piece(s) - 1096

What about a 2pc set, you ask? I tested that with the Tremorscale monster set:

• 2 purple pieces - 1058
• +1 gold piece(s) - 1071
• +2 gold piece(s) - 1096

From these examples, we can draw several common observations:

• When wearing a mix of gold/purple, the resultant stat bonus is NOT a numerical average
• When adding more gold pieces, the change in stat occurs at discrete intervals
• There are only 3 such intervals (eg. 1071, 1083, 1096)

Because these intervals occur at different points depending on how many items comprise the set, I suspected there was some underlying proportionality involved. Since there are 3 intervals, the simplest and most likely hypothesis was that they were distributed evenly-apart, at thirds, along the purple to gold spectrum:

• 33.3% - 1071
• 66.7% - 1083
• 100% - 1096

This seems consistent with the first set of data (5pc set consisting of 5 items). With one gold piece, you are 20% of the way towards full-gold and have not passed the one-third milestone, hence no change. You pass this upon adding 2 gold pieces (40%) and thus bump-up the bonus to 1071. 3 pieces, 60%, no change. 4 pieces, 80%, 1083 due to passing the two-thirds milestone. This framework also holds true for the 4-items data, as well as the Tremorscale data.

The final, conclusive way to verify this hypothesis was to test a 3pc jewelry set, since the theoretical intervals coincide precisely with the number of items involved. For this I chose the Ancient Grace set, and yes, I actually purchased gold jewelry solely for research purposes. The result:

• 3 purple pieces - 1058
• +1 gold piece(s) - 1071
• +2 gold piece(s) - 1083
• +3 gold piece(s) - 1096

Bingo!

So to summarize these findings in picture format for easier reference:


Note: just a reminder that these interval values (1058 - 1096) apply to max stam/mag set bonuses. If we were considering a different stat—eg. mag/stam/health regen, spell/weapon damage—they would use a different set of numbers (124, 126, 127, 129) but adhere to the same interval points.

So you are concluding upgrading Jewellery (excluding bloodthirsty and infused) or Item sets armor pieces to Gold not worth

TheYKcid

Lord_Dexter wrote: »

So you are concluding upgrading Jewellery (excluding bloodthirsty and infused) or Item sets armor pieces to Gold not worth

Well... not really. Ultimately how worthwhile it is depends on the individual. Someone with 60M in the bank would probably have no qualms spending 1M on upgrading 3 pieces of jewelry to gold and maxxing-out their set.

But for someone who's considering using their last 300K on a single jewelry upgrade, knowing whether or not it gets them past one of the "jump points" could strongly inform their decision.

And then there are traits that benefit more from the purple>gold upgrade, as you mentioned. So it's really a case by case thing imo. I really just posted these findings out of academic interest more than anything, lol.

TumlinTheJolly

These findings bring me joy.

TheYKcid

All I ever wanted, @TumlinTheJolly

Reorx_Holybeard

How I did it for our Build Editor when I looked into how this works a few years ago is that between the white level 1 and the gold CP160 item there are only 86 different "values" a set bonus can take on. So the build editor takes the numerical average of all set items and then rounds it to the nearest (MAXVALUE/86).

This seemed to work well originally (at least with minimal error in most cases) but since One Tamriel and after I haven't gone back to look at how it works now which may well be different.

TheYKcid

Reorx_Holybeard wrote: »

How I did it for our Build Editor when I looked into how this works a few years ago is that between the white level 1 and the gold CP160 item there are only 86 different "values" a set bonus can take on. So the build editor takes the numerical average of all set items and then rounds it to the nearest (MAXVALUE/86).

This seemed to work well originally (at least with minimal error in most cases) but since One Tamriel and after I haven't gone back to look at how it works now which may well be different.

@Reorx_Holybeard I checked your method against my results, and it was almost entirely accurate if you always round-down after calculating the numerical average.

The only anomaly I noted was for 1pc purple + 2pc gold (in a 3pc set), where the average was ‭1,070.67‬, therefore necessitating that you rounded up to get the correct result (of 1071), in this case.

Worth giving it a second look? Btw I love the build editor!

mague

TheYKcid wrote: »

Bingo!

On quite some descriptions you can find this:

5 item bonus was added in Patch V1.1.2
2 & 4 item bonuses were added in Patch V1.3.3.

Initially they all have been sets with 1 and 3 item bonuses. 9 slots allowed up to 3 sets. Hence the remain of 33.3% 66.7% and 100% in the code.