Tree of Savior Forum

Let's Discuss the Math of Enhancement

She won enough money scamming people to gamble as much as she wants :slight_smile:

Yes. :haha:

I bet she would destroy a Solmiki Pike to apply its weapon skin on her PR Pike if she could. They’re the richest guild on Silute and the biggest guilds there looove to brag on the shout.

Apparently the AA isn’t a troll. It’s indeed effective.

Not uncommon to see elemental line stacking + blessing to deal with hard content.

and it’s not even an idea, it’s already proven.

Thanks for the thread, hopefully this will be helpful to other players. As for me, I will never go beyond +11 because it’s more than enough, and after that come transcendence and attributes, skill gems and other nifty stuff. Wasting money to reach a very high level of upgrade is something that, as a free player, just looks like a waste of precious silver to me…!

Well, I really hope that ping and fps do not count for enhancement. If it really does, it is unreasonable and should be adressed as far as possible.

Looking at the actual system we have, what I miss here precise information: Maximum level, % of success, this whole uncertain question about ping/fps.

It would be more healthy for the game if the developers redo the Enhancement System and follow some basic rules of general games:

  1. Maximum level - set a maximum level and let we be aware of this cap. This will benefit the players (so we can be aware of where we are and how far from the limit our weapon is) and the overall balance for content creation (cause you can easily set weapon predictions for damage outputs when developing content). Also, make it reasonable and reachable (see below)

  2. Clear Success Rate - It doesn’t matter if armor will have a different success rate than weapons, even if equipment will have different rates between their grades. But make them clear, and let we aware of them. Also, make the dificulty progression reasonable, to not end like a cap of +25 but with 0,5% sucess rate. It is not rewarding, just frustrating.

  3. Remove any other factor that influences enhancement besides a Success Rate - again, if FPS/ping or any other unreasonable factor influences it, remove. Enhancement should be affected only by ingame items/buffs and your own luck towards a reasonable success rate table.

  4. Penalty, not Frustration - instead of reducing to +10 regardless of the level, reduce 1 or 2 levels of enhancement. The developers probably never tried to enhance anything upon a higher level and see it faling and going all the way down to +10.

And, finally, the items that we have so far. They sould be reprogramed to properly follow the logic you created for Enhancement System (help me if I forgot any):

  • Anvil - follow regular success rate
  • Silver Anvil - regular success rate, no silver spent
  • Golden Anvil - 0 potential items, regular success rate
  • Shining Golden Anvil - 0 potential items, regular success rate, no silver spent
  • Platinum Anvil - Extra success success rate (the actual reverse system is unreasonable)
  • Diamond Anvil - Extra sucess rate, no potential penalty
    (item distribution should be revisited)
    (new ones can be created for more combinations of no silver spent, success rate and 0 potential)

Not sure how to approach an implementation for the weapons that can potentially be with a higher level of enhancement than the maximum level defined. But we need a more clear enhancement system than what we have right now.

EDIT: Talking about features, the Gems EXP table should be revisited. Also, bonus of Identification should be refined to more logic ones based on the equipment. But I guess this is for another topic.

Nice script. Am I allowed to refactor it in WPF for public use?

I don’t mind if you use or edit that code.

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Lel. My 0 trans SR always outdps those with high refine+trans in stage 6-7 CM boss. You clearly lack experience in high def content where AA>raw dmg.

0 trans sr doing cm7

:thinking:

Frieno+aoe gear ez carry before boss. AA build + add line vs stage 6-7 boss killer. Explore other build first before you even condemn other. So many ktos build doing AA build for end content cos it’s cheaper.

Sorry for off topic.

2 Likes

I think that the reason why the current enhancement system is unsatisfying because the distribution of possible results has high variance no matter how much investment you put into it. It doesn’t help that this variance is accompanied by skewness in the distribution; sometimes good results are exceptionally good, putting them leaps and bounds above the typical result.

I went an ran a modified version of my previous script. I took a hypothetical situation similar to the previous (having 8 potential available for use and starting at +5) and created three sub-scenarios. In all cases, the simulation kept on trying to enhance until it either ran out of potential or ran out of special anvils. The enhancement level at the end was then recorded.

The first is a scenario where the simulation just tries to use normal anvils until the potential runs out.

The second scenario is if somehow there were 30 diamond anvils available and nothing but diamond anvils were used from +5 onward.

The third and final scenario is if 375 golden anvils were available. Assuming diamond anvils were worth 50m and golden anvils were worth 4m, this is the number of golden anvils that could be bought. In all cases the silver cost of enhancing is ignored (so the diamond anvil case should consume the most silver).

Using the data on the final enhancement levels collected from the simulations, histograms of the final enhancement levels were created and the probability densities were plotted in the figure below. A cautionary note about this figure though; these distributions reflect someone that is enhancing with reckless abandon and doesn’t know when to quit. For example, in the case of normal anvils, the simulation could have gone to +16 then fell back to +11 because it still had potential it had to spend before it stopped trying.

Looking at this figure the first thing we might glean is where each distribution peaks. Normal anvils peak at +8. Golden anvils peak at about +9 or +10. Diamond anvils peak at about +14. These peaks might reflect the ‘typical’ enhancement level you would achieve using each method, except that our code is a bit stupid. In the case of golden anvils, for instance, a reasonable person might quit at +11, shifting the peak to the right. It might be more accurate to say that the normal and golden anvil curves might better reflect the levels that are typically sampled rather than what is typically achievable. The diamond anvil curve is an accurate reflection of what can be achieved because diamond anvils are affected by an enhance-until-you-can’t attitude.

Unsurprisingly, diamond anvils shift the expected level to the right. They’re just better, and by a lot. You’d expect golden anvils to force clustering around +10, and it does. Interestingly it seems a little more prone to putting you on the +9 side rather than the +11 side if you enhance recklessly. Also interesting is that normal anvils are clearly better at getting to +16 than golden anvils. It’s not actually surprising when you think of how golden anvils force things to +10. If golden anvils were to have the same effect as normal anvils (but can be used at zero potential) then we’d expect them to have much closer distributions.

All the distributions are skewed right (they trial to the right), and this is one of the most unsatisfying aspects of enhancement. Ending up on the right side of the curve isn’t hard, but sometimes you’re only a little bit above the main cluster but at other times you’re very far above that cluster. Those far-above cases are rare, but frequent enough to not seem impossible.

I just wanted to put these distributions out there to get a sense of how different upgrade methods pan out. I also wanted to put this forth first before I started exploring how we might tweak these distributions. I might also think about a way of parsing the information of how the level goes up and down in a more intelligent way in order to better reflect someone that knows when to quit.

As a final remark before I go do other things and come back to this problem later: I think the golden anvil distribution is possibly the most reasonable or satisfying kind. It tails off the least, but offers some room to have better enhancements that can make a person feel special.

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The problem that I see is how any of the anvils % simply disappear for high levels of enhancement. They have huge peaks, premium items are better when the basic items starts to fall down, then all of them scale down a hill wildly, it doesn’t look to be a reasonable scaling. They just tumble down and disappear.

Question: is the level 40 the cap enhancement level?

I don’t understand why they keep some enhancement features like this, in a way that it is so rare and so hard to achieve the maximum amount (even with premium items) that it is simply not worth. They have it with gems and enhancement now, why they don’t address both as they have been doing with Transcendence so far (making it more reachable) and with the card system? It would be more healthy and less frustrating.

I wonder if brave enough players will destroy a lot of masinios 1 hand mace / musket / pistol to use on ichor for belcopter (because of the cost and 5%).
If I happen to use 20-30 diamonds anvils there is still a possibility that I don’t get past +14?
Not long ago my masinios mace went to +5 with 0 potential.

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Diamond anvils aren’t a guarantee. It’s just better odds. Granted, they’re much better odds.

You can upgrade the belcopter gear before inserting the ichor i think?

It has come to my attention that there has been some hot debate over exactly how hard it is to achieve some really high levels of enhancement. So I decided to write some simulations to test the most aggressive upgrade strategy I can think of. Here’s the code. In this case I tested a scenario where all 13 potential was put towards enhancement and all diamond anvils were used. Money is no object in this scenario, and the player would expect to use golden sockets after running out of potential. I didn’t take the time to record how many anvils would be used, and I can if someone is really interested, but the point of this exercise is to answer the question of how unlikely it really is to get certain enhancement levels, even when you throw everything you possibly can at it.

Probability density plot of enhancement levels. Note that the peak is at about +19, so getting about that much is reasonably likely if you use all diamond anvils. However, the distribution starts at +6, so there does exist the extremely unlikely scenario that you just fail 13 diamond anvils. A final thing to note the the distribution is almost bimodal; there’s a local maximum at +40. There exists the possibility of a scenario where the enhancement could go above +40 but it actually hits the hard cap. It’s extremely unlikely, considering how small that area is, but it’s nonzero.

Here is a reverse cumulative distribution plot. Basically, the y-axis can be read as the probability of getting above a certain enhancement level. Here are some typical values of interest:

84.11% chance of getting at least +16
53.41% chance of getting at least +20
19.82% chance of getting at least +25
4.936% chance of getting at least +30
0.128% chance of getting +40

Things in the +20’s are surprisingly likely. Though maybe it’s not that shocking considering we’re using all diamond anvils and 13 potential. +40 is stupidly unlikely as one might expect.

Something to think about.

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I don’t know it will be proved useful or not.

I “destroyed” 7 masinios rapiers I should have recorded them too.

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