ADC first crit item DPS research for 3rd and 4th slot

Hello's all, as most people on the discord may have noticed I have been doing stuff. For all the people curious what this stuff was. Well, I decided to sorta dive into crit and DPS. In the end, it ended up a bit of a deep dive (deeper then I would have liked maybe) then expected. That’s why this is going to be quite a long post as I present to you this mini research (while also practicing some of my report skills as in this case I don't need to follow some rules like using the word I, we etc.). However before we start I did this small research fairly quickly because of my low amount of time. I did the calculations in ~4.5 hours however I didn't want to spent that time on the write-up also. So grammar-wise mistakes will be their or badly worded sentences

Introduction

So why did I start this (small) research anyway you might ask? Well, the first reason hast to do with the fact that I have been away for a while. During this time part of the items in smite has changed significantly. During my “prime” time there were only 4 crit items (from which 3 remained in the game, although changed), which were:

• Deathbringer (which passive stayed sort of the same. It was 50% in S1 if memory serves me well
• Malice (which gave a bleed instead of the CD refund. Can’t remember stats)
• Rage (which gave stacks that resetted on a crit. Kinda the same, but not fully as it gave way more crit chance during the time)
• Golden Bow (which got deleted after a buff made it the 1st rush item in the game since it gave a small AoE splash)
  

So there are 2 other items that are new for me, namely Poisoned Star and wind demon. Which I gave a small test spin in jungle practice.
The second reason is that crit builds have changed a bit. The first crit item sometimes is grabbed 3rd over The Executioner (which is not horribly broken anymore, as it doesn’t give a flat and % reduction on stacks).
And lastly, because I have been playing LoL and there infinity edge, which is similar to Deathbringer in passive, is rushed over other crit items (Infinity edge is first item rushed See the end for the reasons).
This all made me curious as to how all the items stacked up to each other in DPS increases when build as 3rd item or as 4th item (or better said before or after The Executioner.

Methods

To simply answer this questions I did some calculations. However, this won't be a proper research if I don't tell you how I did these calculations or which rules I used.

Let's start by talking a little bit about crit. I haven't spend the proper time researching the exact mechanics behind it in smite. Mostly because “The word of Thoth” didn't include it. From a small search about it I saw people saying it was actual random chance, while most other MOBAs use pseudo random.
The difference between these too is that actual random can be seen as rolling some percentile die every basic attack and hope these die land on the numbers 1-X. X being the amount of crit chance you have. Pseudo crit uses the same mechanic however it starts of lower then the given crit chance and goes up like the old Rage on every non crit and down on a crit. This effect makes crit a bit more predictable and makes sure you don't have long crit droughts or sprees.
During my calculations and because of how the used calculator works, these systems fall away. The thing with chance is that the more simulations you run the closer you get to the % of the chance it happens. While on 100 basic attacks hitting 20 crits with 20% will be significantly different, on 100M hitting 20M is a lot less significantly different. Or in more common term the more simulations the closer you get to the actual percentage of your results (for people that haven't had this or need a reminder just google probability).

All of the DPS calculations have been done by using DV-8's & Branmuffin's hunter DPS calculator. I used this tool for the following reasons
It allowed me some insight on how certain calculations were done.
It seemed up to date for the calculations I wanted to run.
A lot of edit ability in stat numbers like protections, hp unevolved evolved items
Base damage increase and actual increase
Direct contact to at least 1 of the makers
And most importantly the DPS calculation for crit assuming “unlimited” basic attacks eliminating (look at the calculation of how crit is added). Also we will need to assume the player is god like in hitting his attacks or is hitting a standing target. With this I of course mean that all basic attacks fire as soon as they can and all hit with the same travel time.

Before I go into how I did the calculations it may be useful knowing which gods were used and why. Staring with the used gods, these were Ah Muzen Cab, Medusa and Neith. The reason for using these isn't really there, since no one has something like Artemis old passive. Also steroids/ability like Jing Wei (add in ability) or bee hive use isn't counted. This means the gods have been selected on random.

The first calculations that I will be showing you (even though i did them quickly at the end because it wouldn't take as much time) will be the DPS boots would give you at which spot in the build order. For these calculations it was placed as first item after the blessing and second item after the blessing for if you wanted to rush stacking. Further spots haven't been calculated as generally you don't want to pick up your boots later in the game.
For these calculations only Ah Muzen Cab has been used at lvl 1, mostly because this was a small side project and certain results showed that god base stats didn't have a significant impact on the results. Both the base DPS and actual DPS versus 68 protections were calculated for getting boots after Hunter's Blessing (unevolved and evolved), Devourer's Gauntlet and Transcendence (both unstacked).

For the crit analysis the Actual DPS increase the crit item provides on all 3 chosen gods at lvl 20 vs 68 protections has been calculated. For a crit item in the third slot The Executioner (at full stacks) DPS increase was also measured. This is the reason why actual DPS has been used instead of base DPS, since the latter doesn't account for the damage you gain from ignoring protections. The build order used was
evolved Hunter's Blessing
Evolved Devourer's gauntler (during this calculation Transcendence would only put the numbers higher because it provides more power)
Boots (both boots have been calculated)
Crit item (all items have been measured even the crit items you would never get at this spot (or at all).

For 4th item slot crit mostly the same has been done however the item in slot 3 was The Executioner (fully stacked). This was chosen because you don't really want to grab another pen item and you don't want to delay getting some pen at this point. Also calculations have been done for grabbing The Executioner in this slot when you got a crit item in slot 3.

Lastly I calculated the DPS gold cost. This was done by dividing the gold cost of the item with the DPS increase.

As a last note I have been using patch 6.4 darkness falls for anyone that reads this when stats etc. gets changed. The item order may have changed because of the changes to Asi and ichiaval, which I assumed not to be fully in place. This is because these changes are quite major and will shake things “up” or my own expectation. Which is that the changes revert things back to season 1 for Asi which will become the lifesteal pick up for Transcendence. For ichiaval I expect the same to happen (only then we're talking S2 as that's when it became an item) until it at least gets nerfed. Atm I consider ichiaval more broken then as the old The Executioner and a lane winning item. The person that gets it first will win lane until the opponent also gets it. However this isn't about these items look in this thread for (probably) more of my opinion about it here

Results & discussion

Now that the method is hopefully clear and I won't get spammed with questions about how did you do this or that I present to you the results I got and trying to explain why something as well as i can (which can include some mistakes). Starting of course with the boots.



In the above spoiler you can find the graphs for the DPS types. As you can see if you go for boots Warrior Tabi will give a higher DPS. However if you build a stacking item first Ninja Tabi's DPS will quickly overtake Warrior Tabi. The reason this happens has to do with the power-attack speed balance. For more information on this I'm going to refer you to this thread were Branmuffin explains in detail how it works. Briefly, if you are under the optimum point your DPS will favor attack speed or favor power. During the start of the game it will always favor power since it's so low (under 100 while Attack speed is around 1.0). However you can quickly go over this number by grabbing an item that gives power like the 2 used stacking item. Because of this power increase it tips towards favoring attack speed. Taking this balance into account Ninja Tabi is pretty superior over Warrior Tabi as it provides both.

Does this mean you should start building only Ninja Tabi? If you ask me it would be a no. Every god has damaging abilities and they don't scale on attack speed but on power. For basic attack focused gods this means Ninja Tabi will be the better scaling option, which the results below will also reflect.

Crit at 3rd spot

In the spoiler above the actual DPS increase is shown. As already discussed the difference between the 2 graphs is that Ninja Tabi gives the higher DPS increase. So don’t get fooled and look well at the numbers in that Y axis. After that the graphs are quite similar. A thing to note is that Neith is quite a bit higher then the 2 others. This is explainable by the difference in her base stats as she starts with higher attacks speed and power. This effect also shows that if a fully stacked Transcendence was used the gained DPS at the slot would go up, however not show a significant difference.

So since The Executioner isn't a crit item it gets a separate comparison. First of The Executioner DPS increase stacks up quite decently against the other item after you get the full passive. Only Deathbringer and after the first crit wind demon will out damage it. The reason for this is because of the stats it provides are quite similar. However, instead of crit chance it gives pen. This makes it that the DPS increase works differently and is dependent on the target. If you're hitting a person with a lot of protections The Executioner DPS goes down like all other items because of mitigation. However, because of the pen the mitigation is lower creating a bigger gap between the DPS of crit items.
These results point to a reason to grab it over crit in the 3rd slot or delay it to the 4th slot based on which god it a threat or that you’re fighting/hitting mostly

Now the thing everyone came for the crit items. The graph probably says enough. The top 3 crit items at this stage are
wind demon
Deathbringer
Rage
This doesn't immediately mean like with boots you should always rush them. also these calculations don't account for passives that don't affect your own DPS, however i will explain this more in detail at the gold comparison as this is only the DPS it gives you and not the total picture. These 3 items are up so high because their passive provides them with extra stats (apart from Deathbringer that gives you a 30%*crit chance DPS increase).

4th item comparison

In the spoiler above you see the graphs for the items on 4th with every 2nd being the DPS increase of getting The Executioner after the crit item.
First some general comments again of Ninja Tabi gives the higher increase and Neith being higher also.
As you can notice the increase is higher than in 3rd slot. For people that don't know the reason, it because of the DPS growth of ADCs being exponential.
Executioner differs a lot depending on item. However, if we go back to the 3rd lvl slot we see a correlation. Every time The Executioner gives a higher DPS increase than the crit item it will also gives this at the 4th slot as you missed this difference in the 3rd and vice versa.

So now again we see sort of the same as with the 3rd item in rankings. The top 3 items are again in the same order:
wind demon
Deathbringer
Rage

However there is one difference I will have to note. The gap of Deathbringer’s damage difference with wind demon (after a crit) became smaller. Especially if you bought Ninja Tabi. Here the difference is only 4 (for Warrior Tabi it’s 12), while at 3rd item the difference is 6 with Ninja Tabi (15 for Warrior Tabi) This is likely caused by the extra AS The Executioner is giving you at this point and wind demon’s passive also giving AS. Tipping the Power/AS balance into the favor of power.

Gold/DPS

So the last part that will finally look at the gold costs and passives. Since gold does determine what item you will have quicker and passives can make a difference.


Looking at the table in the above spoiler the Gold per DPS is calculated when using AMC. During a calculation the difference of initial god power between AMC and Neith was an average of -1.6 gold. The values shown in this table are the amount of gold you’re spending per actual DPS the item provides you. This means the lower the number the higher it ranks.
The Executioner is once again fairly high in here too if you buy it as 3rd item. It almost even with wind demon

The top 3 crit items here are:
Rage
wind demon
Deathbringer
Not all to surprising since they have been dominating the other categories, however there is one difference. Rage is ranked as high as wind demon. Until you trigger the first crit Rage has a lower dps cost after some stacks. If you buy it with slightly more AS ( Ninja Tabi it can even start dipping under an active wind demon because of the crit chance.

Now on passives. Most of the items have their passive already calculated in as they provide extra damage in the form of stats. The only items that don’t have this are Malice and Poisoned Star (and Deathbringer, however that one gives a “flat” increase).
Poisoned Star May have been the 2nd worse DPS increase item after initial Rage, however it has one of the strongest passives. The damage reduction and slow will help tremendously vs someone that picked up another item in the slot. It will also help with getting the hits in, since during these calculations a 100% hit ratio is assumed.

Malice isn’t as lucky with it’s passive compared to Poisoned Star. One a crit every 15 seconds it lowers ability CDs. this will increase your DPS in the way of having abilities up quicker. However, for ADCs it won’t be a pick-up as they rely on basic attacks more as the game does on later. And the CD on the item also doesn’t help as much as it may be 2 seconds once during a fight giving you the chance to use an ability a second time. In cost it aso shows it’s the most DPS expensive item and sadly it’s passive doesn;t help it making it the worse Crit item (like the passive would be more useful on any kind of “caster”, however it would still get outshadowed by CDR).

Concluding statements

So I left a lot open to own interpretation, mostly presenting what I found. This part will mostly be a small recap, while I will also answer my questions that started this lil’ research. (that’s why the typing was rushed and less in depth than I wanted it to be I want to finish this now. I believe I’m on around 10h total now.) the reason for leaving it open for interpretation is because I don’t want this to become dictating and change peoples styles.

So for my own questions. I’m going to answer these sorta backwards. The first question I’m answering is how Deathbringer stacks up against infinity edge. I’m not surprised to find it lower, however it’s still a top 3 item. The only reason to pick up another item is because of their passive. Looking at the gold/DPS table it is actually the lowest as base item. I wouldn’t fully justify it as the first crit pick-up, mostly because timings and the passive of the other items.

The 2nd question was how The Executioner stacks up against the crit items at 3rd slot. Honestly my conclusion would be that it is really game dependent. If you drop behind this would for sure become the 3rd item pick up for me because you’re going to need the pen as teamfights will slowly start starting around your 4th item. If ahead a Shuriken item could be better depending on boxing focus or Rage to start stacking it for when you finish 5th item Deathbringer. All with all it didn't really lose it’s spot for 3rd.

Lastly how do all the crit items stack up against each other? Well this can differ between person however for me from lowest to highest.

Malice
Well who didn't saw this coming? In this state Malice is worthless on ADCs even on more ability based once. It gets heavily out-shadowed by CDR items. To make this item better the passive needs to be either changed or the cost needs to be lowered significantly.

Poisoned Star
So as a first crit item for me Poisoned Star ends up at the lower end as first item pick up. Mostly because of preference and since it’s passive can come into play much later during a fight. 15% is not a lot and the 5% difference of wind demon makes it around an extra 1.6 hit for it to proc. The item is quite strong and I would consider it for a 3 item crit build as last one. For 1st item pick-up I would only consider it to counter Poisoned Star.

Deathbringer
Was almost considering placing this one up 1 higher however the middle spot is fine for a 1st crit item Deathbringer pick-up. Maybe on someone with pretty decent AD scaling on abilities it would become the 2nd best item since it gives solid power. For adc it is a must have however as first item you should be able to pick up one of the cheaper items to not get behind for 600 (which is almost a Rage and hidden blade). Must have, not must rush.

wind demon
So I would say for me it’s almost as equal as Rage however it did get 2nd spot anyway. The reason for this is because like the other Shuriken item it’s for a 3 item crit build in my eyes. It’s an incredible strong item on spot 3 in my eyes. It will also counter someone that went Poisoned Star better than Poisoned Star itself. This because it can crit sooner (1.6 basic attack). And it gives you 20% AS vs the 15% I assume lowered basic attack damage (aka physical power not AS) loss. It may still lower your damage output however not your movement speed making it able to dodge better.

Rage
Maybe because it’s an old school item and I liked the S1 builds. Rage is imo the best 1st crit item pickup. It’s cheap and gets quite strong (40% crit chance which is double that from wind demon) after some kills/assists. It can even perform well into a double crit item build, which isn't that possible with other crit items. This item gets even better when you have an AS steroid in your kit as that will make up for the lost AS from Shuriken tree. Going for a 3 crit item build Rage isn’t as strong because of diminishing returns with crit (going from 10 to 20% removes 5 basic attack, while going from 40-50 removes 0.5 basic attacks).

I hope you all enjoyed this little research and find a helpful way in the calculations I have done. Lastly I want to thank Branmuffin and DV-8 for the calculator and Stuke for cleaning up my grammar. For people that want to see the calculations file I made or want to continue with it for more gods. Here you go. Fun fact this thing was 7 pages long and almost 3800 words.



EDIT 19/04: grammar clean up. Huge thanks to Stuke.

Holy wall of text. I looked over it briefly and the math looks solid. Didnt read a lot of the text but just for numbers this should be a good read for all theorycrafters.

at least for as long as their isn't a crit overhaul

I doubt it will be, Vamp. The most that's ever been done to crit items is changing their values.

Crazy writeup, Dev. I can always get behind something that supports 1st crit item as Rage, which is something I often suggest but people tend not to listen to =P

Of course, you can get into other details about build paths for individual hunters, and which ones are best for them. Things to consider:

• Do they have an attack speed steroid?
  
  
• If so, is it high (e.g. 60% or higher) / burst, or low (20-50% max) / constant? High / bursty means you don't necessarily have to build into as much AS (e.g. Shuriken tree), and Rage's higher crit chance can fit better into the burst mentality.
  
  
  
• Enemy comp: more tanky or squishy? Qin's paths are often better against tanky comps...but a late Poisoned Star could help in this tankier meta where fights might be more prolonged.
  
  
• Trans vs. Devo's paths and benefits: This only used Devo's as a base, but right now, from the things I'm calculating, Trans paths w/ Asi are stronger. Devo's means you don't need lifesteal, so you don't have to worry about possibly placing a lifesteal item somewhere in the middle, delaying your main DPS (Qin's or crit), or sacrificing any sustain for more DPS.

I personally like Rage/DB build directions when possible, because it allows for more flexibility due to not needing 3x crit. PS can fit as a late crit item if you DO end up going 3x in that build, because the AS and passive benefits are great and the low PS crit chance fits nicely there.

You never know what will happen. They changed a lot of stuff in the time I was away. some items are so different even though they provide the same function (think chronos pendant, Rod of Tahuti pen items.




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This is a good point. However, I did this research as a more generalized thing. Otherwise it would probably take me really long to finish and a lot of copy pasting values (oh and don't forget the extra pages.

Rage does however get better the more AS someone can gain. also over capping will be less of a problem with Rage



I wonder how much/which parts you read. I stated in my methods I didn't cover the ichival Asi build shifts. So taking that in account, yes Transcendence will be stronger (however no lifesteal) DPS wise. Even if I would only swap Devourer's Gauntlet for Transcendence it will do more damage. I noticed this with Neith DPS being higher than both AMC and dusa. which comes from her higher base power. It's also visible in the boots graph.

Overall this topic can be expended on hugely. However, for the time I had and wanted to use on it this was already quite some big things. Going into a 2nd crit item (even though this would for sure point towards Deathbringer being number 1 (which is without counting the other passives the best DPS/gold item)) would eat up a lot of time.

Also this was harder than the boots one because of the variable of position it's build and which items could be build before it. That's why I chose something more static as to show a difference there can only be one changing variable, which was in this case the crit item (so 1 build path and no steroids (which I mentioned in methods))