WARNING: LONG, BORING, NERDY!
(THIS CHAPTER IS OUTDATED SINCE 3.1)
The Basic Spreadsheet:
Ok, Above is a screenshot of the spreadsheet I use for evaluating items on sejuani. This has a lot going on under the hood, I'm not going to explain all of the formulas in detail, but I'll give a rough explanation of how it works. If you have any questions about it or find any bugs feel free to leave a comment. You can download the spreadsheet here and tinker with it yourself here:
http://na.leagueoflegends.com/board/showthread.php?t=3496962
The columns of top grid of the spreadsheet are each items that you could possibly build. The first few rows are the basic stats of the items--Gold cost, health, armor, magic resist, etc. Note that some of the stats on the item are formulas based on other figures in the spreadsheet. For example, warmog's health regen number is based on your current hp, void staff's magic pen number is based on enemy magic resist (since it's a percentage reduction). Spirit Visage HP regen is based off of a percent of your current HP regen.
Note that the spirit items are listed at 1790g not their actual price of 2000g. This is because they build out of spirit stone which you already bought for jungle clearing. If you sold your spirit stone for 490g, you'd have a net loss of 210g. So you save 210g by building your spirit stone into a jungle item rather than selling it mid-late game, which is why I deducted 210g from the price of the spirit items.
More important are the summary rows at the bottom:
- "Stat points": This is the total estimated gold value of all stats on the items, not counting passives or actives or obscure stats like spell vamp% which aren't listed in the top grid. It's just adding up the total gold value of the stats on the item.
- Arbitrary points: this is the total estimated gold value of all actives/passives/auras of the item, plus stats that are not accounted for in the stat points. Some of these are formula's based on the estimated total damage or defenses added by the item--which could vary according to what level you are or what other stats you h ave.
- Scaling Bonus: This is a bonus point added above the stat points based on the benefits of having multiplicative stats on the same item. For example, magic penetration scales with itself, magic penetration scales with AP, armor scales with health, etc. This attempts to account for this by giving a point bonus to items with complementary multiplicative stats based on a formula.
- Total Points/Gold: This is the most important row, so I highlighted it. This is an estimate of the cost efficiency of the item based on all of the above. It takes the total points from the 3 points rows and adds them together and divides them by gold cost. It is also color coded, items in blue are more cost-efficient than items in white, and items in red are generally bad. The bluer the item is, the better I think it is for Sejuani.
At the bottom right are the estimated gold values of each stat (health, armor, etc). This is used to calculate the "Stat Points" above:
The spreadsheet uses formula's to compare the gold values of various stats based on how much they increase your defense or offense as a precentage compared to your current stats. For example, if you currently have 2000 health and zero health regen, and your opponents do not do %health damage, each point of health increases your defenses 1/2000 or .05%. The defensive benefits of health is defined in the spreadsheet at a set value (2.5g by default) and all other quantifiable stats are compared to that. Note that health itself is actually worth more than this, because it adds bonus damage to sejuani's W. So this adds a level of complexity.
Using the % increase of defenses that are gained by increasing health by one point yields a "Gold Factor" which is the estimated value of one gold. So in this example, take .05% and divide by 2.5 to get the gold factor, which is .02% in this example.
Therefore: in this example, a .02% increase in total defenses, whether it comes from health, armor or magic resist, is defined as worth 1g. Note that as you increase your total defenses, the gold factor will decrease as the more defense you have, the more gold it takes to increase your defenses by the same relative %. This will generally decrease the value of defensive items and increase the value of offensive items as you accumulate more defensive items.
The Assassin Factor and Offensive Stat comparison
The "Assassin Factor" is an arbitrary number which is used to compare defensive stats to offensive stats. It's a measure of how much you value offensive stats than defensive stats. I named it the "Assassin Factor" not the "Tank Factor" because originally made the spreadsheet like this for Fizz, who is an assassin.
For example, if you have an assassin factor of 2, that means that you value a 1% increase in your offensive power the same as you would value a 2% increase in your defenses.
This is probably the biggest question mark in any itemization evaluation, and you can enter whatever you want for it. The default is 0.8.
Since Sejuani is a tank I think that defensive stats are more needed, she has a lot of non-damage utility to make her useful and is a very front line champion who is easy to target. So i value defenses higher than i value offenses for her. At the same time, offense is hardly useless, the large aoe damage Sejuani does is one of the reasons I prefer her over most other tanks.
The model input
At the left you have the "Model Stats". These are your current stats before you buy any items. These are used to calculate the value of item stats based on what you need and what helps you. The default values are based on the base health coming from sejuani's base stats and passive and the runes/masteries that I use
The "Your Phys Damage" and "Your Magic Damage" are based on a model of Sejuani's damage that I use, which consists of 3 full damage casts of
, 4 auto attacks times your attack speed bonus, two damaging uses of
, two damaging uses of
and one damaging use of
. You can adjust this model to your liking, adjust the number of points you put in each skill, adjust your level, and all of the other numbers in the spreadsheet will automatically update to reflect your preferences.
The "AP Ratio" figure is the full ap ratio from this combo.
We also have your current AP, ad, armor pen and mpen values, which in this version of the spreadsheet come from runes/masteries. As we get more items and build more damage, we can add additional stats to the "Bonus" column, which is added together with the base value column to get the total amount of that stat.
Next to this, in the middle of the spreadsheet, are the statistics for the enemy champ who we're trying to kill, including HP, armor and Magic resist. There are also four columns which attempt to estimate what % of the enemies damage is magic, physical, true or % health. These are used to calculate the relative values of HP, armor and MR in relation to eachother. You can adjust these to theorycraft various enemy team comps that could range from anything from entirely physical to entirely magic, or comps that include a lot of %hp damage or true damage.
All of these numbers are crunched together to get a model of sejuani's total damage from the arbitrary number of attacks of each type, which can then be compared to any increase in damage on a percentage basis. The percentage is then compared the gold factor after being multiplied by the assassin factor to determine the gold value of offensive stats.
Note: that any value in white background in a black box is somewhat arbitrary and feel free to adjust these values as you see fit. The values with gray backgrounds are calculated fields where the estimated stat is calculated from elsewhere and these will automatically update as you change other values in the spreadsheet.
Also note: if you adjust the value of "HP Def Value" (near the middle of the spreadsheet), the value of almost everything else in the spreadsheet will change, since most things in the spreadsheet are valued by comparing them to the defensive bonus from hp. The only exceptions are the arbitarily valued actives/passives/auras/unlisted stats (which are included in arbitrary bonus for each item) and arbitrary stats such as tenacity, mana, cooldown reduction, etc.
I don't know how to value CDR, mana and mana regen on a quantitative basis compared to other stats, so i just plugged in 50g for cdr (which seems about right) and .5 per point for mana and 15 per point for mp/5.
If you feel the total value of everything in the spreadsheet is inflated due to your preferences, you could reduce the value of health, thus keeping your calculated stat valuations roughly in line with the arbitrary bonuses and arbitrary stat valuations. (for example, if you set the enemy %hp damage percentage to something absurd like 99%, the value of all calculated stats, including health, will skyrocket as health becomes useless for defense. So in this case it may be a good idea to reset the "HP Def Value" to something proportionally low)
With that in mind, let's take a look at what's on the spreadsheet:
Here's just the Gold efficiency row from the basic spreadsheet:
Since the default version of the spreadsheet uses a no-item Sejuani as a basis, numbers in blue in this spreadsheet are the good first few items to buy. As you can see, the best two items on this spreadsheet, by far, are Spirit of the Ancient Golem and Locket of the Iron Solari. So I buy these first. I didn't bother to put boots in the spreadsheet but I also buy Ionian Boots of Lucidity early.
Now that we've bought those two items, we can update the stats in the spreadsheet as follows to calculate the next best items to buy:
1) under the "bonus" column for "Your HP", type 980. This comes from the hp on locket and golem, plus 180 for its shield.
2) under the "bonus" column for "Your HP5", type 24. The HP5 from locket and golem
3) under the "Armor" colum add the 35 armor from locket.
4) under the "Your AP" bonus column, put -17.46. This is to compensate for the fact that the shield on locket does not add bonus damage to her W unlike actual health would. (it's derived by taking 180 and dividing by the gold value of ap, then dividing again by the "HP dmg Value").
5) Reduce the value of CDR to 0g, because we already are basically capped with ionian boots, locket, ancient golem, runes and masteries. We don't need any more CDR since CDR is capped at 40% and we already have 39.83%.
6) Move the columns for Locket and Ancient golem off the screen to the right because we already bought those already and don't want seconds.
The new spreadsheet can be seen below:
Now let's take a look at this different variation of the spreadsheet:
1) The spreadsheet now thinks Aegis is the most gold efficient item, followed closely by Bulwark. So I usually buy Aegis --> Bulwark next vs typical balanced team comps.
2) Warmogs is blue. Always a good buy on a health oriented champion like Sejuani.
3) Ruby sightstone is blue. You should buy this if you feel there aren't enough wards around for your team.
4) Randuins and Sunfire cape are blue. Buy whichever one of these you like better if you feel you need more armor.
5) Banshee's is blue, but not as blue as aegis/bulwark. So its decent but outclassed for its role as a magic resist item.
6) Rylai's is light blue. Buy this if you really want more slow. Note that the value of the slow on rylai's is pretty arbitrary, I value it at 1200g (as seen in the "arbitrary bonus" row of the rylai's column.) If you think its worth more than this you should probably buy it, I guess it depends on your style of Sejuani.
You could also tweak the Enemy Stats section, particularly the propotion of physical vs magic damage they do. That would be useful if you want to know the proportion of enemy physical/magic damage needed before the spreadsheet thinks randuins is better than warmogs (it's 60/40, fyi, although still arbitrary because the slow on randuins is hard to quantify).
and that's the spreadsheet, you can play around with it however you want, it includes a lot of my arbitrary assumptions that I built into it in an attempt to quantify everything. If you don't like my assumptions you can tinker with it as you please.
http://sh.st/cM6P