![]() So, for instance, if the median displayed is 9000 orbs, in reality it's probably a little higher, maybe 9050 (yes, it's over 9000). Note that the estimates tend to be slightly more optimistic than they should be. At some point, it makes sense to stop calculating each chromatic orb exactly, and just start estimating. The median and '% after NChr' calculations are made exactly so long as the result is less than 5000 chromatic orbs. Mean calculations are made based on an absorbing Markov chain (Thanks to MantisPrayingMantis for pointing this out). Of course, we can always use more data, so feel free to submit your own using the link in the footer!Īll calculations are made as exactly as possible. Certainly, the model even with just a single parameter is able to account for the data we've collected so far without any real trouble. We find that the expected results are not significantly different than the observed results (p=0.9168, chi2=0.1736, df=2). Because there's a lot of randomness involved in rolling chromatics, we run the model 5000 times (for X=12) and then average the results. ![]() We then see how many we would have expected if the statistical model was true. Here we measure how many red, green, and blue sockets occur in the data we've collected. ![]() Below are three model predictions that I've tested. Essentially, if the test is significant, the model's predictions are wrong, and if it isn't significant then we can't conclude the model is wrong. We'll use that to measure the goodness of fit between the model's predictions and the actual empirical data. The way I've chosen to address this issue is using a statistical test called the Pearson's Chi-Squared test. The model is extremely simple, but it's not of any use if it doesn't actually explain the data that we've collected so far. Basically, I've used a Metropolis-Hastings algorithm, which although inefficient, gives me a probability distribution over X rather than a point value (also I know how to code them up easily.). If you're interested in details about how I have estimated X, I suggest you take a look at my forum post. More data, however, is of course always better. But because our estimation task is simple (there's only one variable, X, to learn) and because the value of X plays a role in the process multiple times per roll, this turns out to be more than enough to get a rough estimate. Right now we're sitting around 1600 chromatic orbs used! That might not seem like a lot, especially when you think about how 1600 orbs isn't necessarily enough to get a good 6 off-color Shavs. For that purpose, I opened up a Community Log where people could enter in data. OK, so how do we figure out what X is? First we needed to collect some data. This type of rejection sampling is inefficient, but should provide us with the same end result as whatever (hopefully more efficient) process GGG is actually using. If we ended up with the exact same item, we just repeat the process. This takes care of the relationship between an item's stat requirements and the probability of rolling specific colors.īut what about not allowing the same colors to appear? To take care of this, a check is performed after all the rolls occur. This means that the probability of getting a specific color socket on an item is a simple formula: We need the variable X because even though a pure strength item has zero DEX requirement, it can still roll green sockets, they're just less likely than red ones. That weight is the stat requirement plus some number (we'll call it "X"). ![]() There's an integer weight for each color, one each for red, green, and blue. So if 6 sockets is represented by 1 and all other sockets are represented by 305, the probability of a 6 socket is 1 out of 306.Īpplying this logic to chromatic orbs, I proposed the following: Every time you roll a chromatic orb, the color of each socket is rerolled independently of the other sockets. During closed beta, Chris confirmed that for jewelers, the probability of rolling a specific number of sockets can be represented by an integer value. One clue would be to look at how other orbs are rolled. If this is true, how exactly does a stat requirement influence the color of an item? But let's assume for now that stat requirements are all that matter. We don't, for instance, have confirmation that other factors like item level or item type don't play a role in the process. The colors you roll are related to the stat requirements of the item, and lower requirements make rolling off- colors easier.Just like jewelers and fusing orbs, chromatic orbs never return your item in the exact same state, i.e.Let's start first with some facts about chromatic orbs:
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