Loyalty store boosts analysis (warning maths)
Erik_Killmonger1001
Member Posts: 427 ★★★
Loyalty store analysis:
so I have never really seen anyone crunch the numbers on the loyalty store so thought I might give it a go, I hope it makes sense and helps you understands the best way to spend your loyalty. Feel free to correct my maths or ask question any questions.
hasty citation-I tried to crunch some numbers on the AW boosts but with diversity of defenders and nodes I found it an absolute nightmare to attempt to standardise their value, instead just buy them is if the will save you from using AW potions and revives, that is all I can say, now enjoy
Attack and health boosts
So first some assumptions, since the lesser attack and lesser health boosts are largely agreed to be the best mainstream boosts in the store we will be using them as a benchmark and calculate the other boosts value relative to them. So lets look at this initially at base you get a 10/15% boost to either base stat for 15 minutes for 8,000 loyalty.
Let’s start with the champion boosts now these are a 10% enhancement for 20 minutes(costing 23,000 loyalty). This minor discrepancy makes comparing them apples to apples difficult so lets scale it up using.. (try not to get too excited) highest common factors. Since the HCF of 15 and 20 is 60 it can reasonably be assumed that you would purchase enough boosts to last you an hour. Now the cost of this is 3 20 minute boosts (costing 69,000) or 8 small boosts. (costing 64,000) So first their is an obvious 5,000 loyalty difference but also take into account the 5% health potency you get by running the two boosts separately. However the cost difference isn’t so divergent it outweighs the advantages that running a single boost can sometimes bring such as scenarios where item use is limited.
Special boosts:
Now the special boosts providing +8% or +12% special attack damage for 45mins/75mins. Unfortunately comparing is still a bit difficult since the flat attack boosts increase all attack including specials and the special boosts just do specials. So to compare we need a compensating multiplier (what enhancement to special attacks is needed to compensate for the loss of basic attack you get by not running an attack boost instead). (I am aware that these boosts are not mutually exclusive but lets use the scenario of you have 8,000 loyalty to spend so do you get the attack or the special boost.)
So in game we have the power shield node that functions as a nice baseline where you do no basic damage but 400% special damage. Therefore the compensating multiplier for the node is 1-->4 for every -1% basic you get +4% special. However this is going in the opposite direction as it is a basic attack punishment for a special enhancement rather than a choice of 2 enhancements so the compensating multiplier will obviously be higher. (If you are going to completely exclude basic attacks you need to provide a higher bonus special damage than you would otherwise to create a balanced node)
So the actual compensating multiplier would probably be around 1-->2, so for the small boosts 20% and the large boosts 30% (double the 10% and 20% boost for base attack) which certainly sounds a lot better than the current measly 8% and 12% available. However the current boosts also have significantly greater duration that needs to be taken into account. The 10% attack boost duration is 15 minutes but the special boost duration is 45 minutes/75 minutes so their is a discrepancy. 20% boost for 15 minutes does scale up to roughly 8% boost for 45 minutes so they are mathematically equivalent if it was just the duration and enhancement. The 12% boost does scale up even nicer for a 40% cost increase you get 50% potency and +66% duration. So if we act as this is the top potency special boost and therefore comparable to the 30% attack boost. With the standard 1-->2 multiplier the expected would be 60% for 15 minutes. If we scale this up to current duration we get exactly 12%.(15x5=75,60/5=12)
However they are also class based which is the main reason they actually work out to be atrocious value.
On any single fight you have ⅙ probability that the champion you use will be of the required class to benefit from the boost and a ⅚ chance that the defender will not nullify the boost with class advantage, since both statements need to be true for the boost to work (if either you use the wrong class attacker or suffer from class disadvantage the boost will have no effect) So multiplying these together to get the probability the boost will be in effect is 5/36.
So the current price has been set at 5,000. Multiply this by 5/36 to get the actual price to get good value is 700 loyalty(1,000 for the 12% boost, also quick citation they have both been rounded because decimals=pain). I’m not kidding because if all the class caveats that is the price that would represent good value when compared to the basic boost. However interestingly if the potency and duration stayed the same and they just enhanced every class's special attacks and had no CD caveat then the current price would actually be an ok deal.
Power boosts:
Now these are a bit more difficult as they don’t boost a stat or attack value in the conventional sense.These are also consistently shown to be high value items by the player base to the point that cost/benefit maths is fairly a moot point. The standard caveat of only working on a single class still applies but since players often use these in conjunction with a synergy team around a single champion such as ghost for entire lane clearing so the standard 5/36 probability does not apply. One interesting mathematical observation while we are talking about them though is that since they are percentage based this gives them a bell curve of effectiveness with direct correlation to opponents health values. In lower HP value content the boosts are often unnecessary since basic combos are often all that is needed to defeat opponents, whereas in high hitpoint fights such as LOL the flat damage dealt is high but the percentage of the opponents health is low. This is in contrast to the base stat boosts where the fact they are percentage based means they have identical effectiveness regardless of the opponent.
Final note-expect a part 2 to this, I am determined to find a way to do some interesting maths stuff with the power boosts it will likely just take a while as I work out how to make it work, I also have some stuff in the works analysing the daily loyalty crystals but since that is crunching numbers on drop rates that may also take some time.
Citation-I am by no means the best at maths, I just went through what I thought made sense and worked to try to standardise the effect of boosts with different potencies effects and duration to properly analyse which ones were the best value, feel free to critique or correct any of my numbers in the comments, thanks
so I have never really seen anyone crunch the numbers on the loyalty store so thought I might give it a go, I hope it makes sense and helps you understands the best way to spend your loyalty. Feel free to correct my maths or ask question any questions.
hasty citation-I tried to crunch some numbers on the AW boosts but with diversity of defenders and nodes I found it an absolute nightmare to attempt to standardise their value, instead just buy them is if the will save you from using AW potions and revives, that is all I can say, now enjoy
Attack and health boosts
So first some assumptions, since the lesser attack and lesser health boosts are largely agreed to be the best mainstream boosts in the store we will be using them as a benchmark and calculate the other boosts value relative to them. So lets look at this initially at base you get a 10/15% boost to either base stat for 15 minutes for 8,000 loyalty.
Let’s start with the champion boosts now these are a 10% enhancement for 20 minutes(costing 23,000 loyalty). This minor discrepancy makes comparing them apples to apples difficult so lets scale it up using.. (try not to get too excited) highest common factors. Since the HCF of 15 and 20 is 60 it can reasonably be assumed that you would purchase enough boosts to last you an hour. Now the cost of this is 3 20 minute boosts (costing 69,000) or 8 small boosts. (costing 64,000) So first their is an obvious 5,000 loyalty difference but also take into account the 5% health potency you get by running the two boosts separately. However the cost difference isn’t so divergent it outweighs the advantages that running a single boost can sometimes bring such as scenarios where item use is limited.
Special boosts:
Now the special boosts providing +8% or +12% special attack damage for 45mins/75mins. Unfortunately comparing is still a bit difficult since the flat attack boosts increase all attack including specials and the special boosts just do specials. So to compare we need a compensating multiplier (what enhancement to special attacks is needed to compensate for the loss of basic attack you get by not running an attack boost instead). (I am aware that these boosts are not mutually exclusive but lets use the scenario of you have 8,000 loyalty to spend so do you get the attack or the special boost.)
So in game we have the power shield node that functions as a nice baseline where you do no basic damage but 400% special damage. Therefore the compensating multiplier for the node is 1-->4 for every -1% basic you get +4% special. However this is going in the opposite direction as it is a basic attack punishment for a special enhancement rather than a choice of 2 enhancements so the compensating multiplier will obviously be higher. (If you are going to completely exclude basic attacks you need to provide a higher bonus special damage than you would otherwise to create a balanced node)
So the actual compensating multiplier would probably be around 1-->2, so for the small boosts 20% and the large boosts 30% (double the 10% and 20% boost for base attack) which certainly sounds a lot better than the current measly 8% and 12% available. However the current boosts also have significantly greater duration that needs to be taken into account. The 10% attack boost duration is 15 minutes but the special boost duration is 45 minutes/75 minutes so their is a discrepancy. 20% boost for 15 minutes does scale up to roughly 8% boost for 45 minutes so they are mathematically equivalent if it was just the duration and enhancement. The 12% boost does scale up even nicer for a 40% cost increase you get 50% potency and +66% duration. So if we act as this is the top potency special boost and therefore comparable to the 30% attack boost. With the standard 1-->2 multiplier the expected would be 60% for 15 minutes. If we scale this up to current duration we get exactly 12%.(15x5=75,60/5=12)
However they are also class based which is the main reason they actually work out to be atrocious value.
On any single fight you have ⅙ probability that the champion you use will be of the required class to benefit from the boost and a ⅚ chance that the defender will not nullify the boost with class advantage, since both statements need to be true for the boost to work (if either you use the wrong class attacker or suffer from class disadvantage the boost will have no effect) So multiplying these together to get the probability the boost will be in effect is 5/36.
So the current price has been set at 5,000. Multiply this by 5/36 to get the actual price to get good value is 700 loyalty(1,000 for the 12% boost, also quick citation they have both been rounded because decimals=pain). I’m not kidding because if all the class caveats that is the price that would represent good value when compared to the basic boost. However interestingly if the potency and duration stayed the same and they just enhanced every class's special attacks and had no CD caveat then the current price would actually be an ok deal.
Power boosts:
Now these are a bit more difficult as they don’t boost a stat or attack value in the conventional sense.These are also consistently shown to be high value items by the player base to the point that cost/benefit maths is fairly a moot point. The standard caveat of only working on a single class still applies but since players often use these in conjunction with a synergy team around a single champion such as ghost for entire lane clearing so the standard 5/36 probability does not apply. One interesting mathematical observation while we are talking about them though is that since they are percentage based this gives them a bell curve of effectiveness with direct correlation to opponents health values. In lower HP value content the boosts are often unnecessary since basic combos are often all that is needed to defeat opponents, whereas in high hitpoint fights such as LOL the flat damage dealt is high but the percentage of the opponents health is low. This is in contrast to the base stat boosts where the fact they are percentage based means they have identical effectiveness regardless of the opponent.
Final note-expect a part 2 to this, I am determined to find a way to do some interesting maths stuff with the power boosts it will likely just take a while as I work out how to make it work, I also have some stuff in the works analysing the daily loyalty crystals but since that is crunching numbers on drop rates that may also take some time.
Citation-I am by no means the best at maths, I just went through what I thought made sense and worked to try to standardise the effect of boosts with different potencies effects and duration to properly analyse which ones were the best value, feel free to critique or correct any of my numbers in the comments, thanks
1