GGG, keep your RNG, but reduce its Standard Deviation

Probably anyone who's been around PoE forums for a while will have seen multiple threads either complaining or boasting about how many orbs it took to 6-link their item or obtain an off-color socket configuration. I've seen 6L tallies claimed from just a handful of Fusings to several thousands, with many giving up in disgust. One of the common responses to such reports can be summed up as follows:

RNG is RNG. Love it or leave it.

Although this is obviously true in a tautological sense, it's a grossly oversimplified take on statistical probability. A deeper analysis of a sequence of randomized results will reveal not only the probability of a successful result, it will also show the standard deviation of those results over time. For those unfamiliar with this term, here's an intuitive definition:

Standard deviation is the range of variation from the average probability of obtaining an expected result.

More details here: http://en.wikipedia.org/wiki/Standard_deviation

Although GGG have not yet divulged the exact probabilities involved in socket-crafting, player reports appear to indicate the odds of 6-linking an item to be somewhere around 1000:1. Most forum posters seem to feel that's not an unreasonable probability to expect for obtaining optimal results.

What many players object to, however, is the wide range of variance from those statistical odds of success. In probability theory, that variance can be measured as a high degree of standard deviation. What players would prefer to see are results that statistically range much closer to the average odds of success, i.e. a low degree of standard deviation.

The distinction between average chance and standard deviation is the key to understanding how GGG could potentially resolve the chronic controversy over RNG in a manner that would satisfy both players and developers. Each side in this dispute has valid concerns that should be respected:

Developers: Need to insure long-term statistical averages in success rates. Unconcerned with the results of individual cases.

Players: Need to insure high probability of success within a predictable range of results. Unconcerned with long-term statistical averages.

In concise terms, GGG is primarily concerned with statistical success rates, while players are primarily concerned with the standard deviation from the average chance of success. Consequently, there is a solution that could meet both concerns. For each RNG-based decision process in the game:

* Maintain the current average chance of success.
* Reduce the standard deviation from the chance of success.

In the current RNG implementation, there appears to be no correlation among results in long-term sequences of crafting attempts. This results in unconstrained levels of standard deviation, and a great deal of player dissatisfaction. There are a number of practical algorithms that could be used to reduce the standard deviation of RNG-based results without altering the average probabilities of success. I'm not going to presume to advise GGG on the technical programming details involved, as I'm confident they're well equipped to determine that themselves. My view is not that GGG have mismanaged their RNG implementation, rather that they have not yet seen the need to control the standard deviation of its results. From both player responses and my own experiences, I think this is a vital aspect of the game that GGG should take initiative to improve.

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RogueMage wrote:

My view is not that GGG have mismanaged their RNG implementation, rather that they have not yet seen the need to control the standard deviation of its results.

Your post is agreeable, but you'll have to convince Chris that there is a need in the first place -- he's on record as expressing his fondness for high variance.

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ephetat wrote:

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RogueMage wrote:

My view is not that GGG have mismanaged their RNG implementation, rather that they have not yet seen the need to control the standard deviation of its results.

Your post is agreeable, but you'll have to convince Chris that there is a need in the first place -- he's on record as expressing his fondness for high variance.

* I laughed. Hard. At some of the comments in the comment section. Holy crap.

* I like the OP.

One of the things that buggs me the most is that Itemlevel allows for higher stats such as life etc. but it doesn't prevent values such as "1 hp" roll. If that would be altered, i'd have the guts to dump orbs on higher iLevel items for my endgame chars.

When there is no standard deviation, there is no RNG. The higher the standard deviation, the more random the situation is. It's silly to say "keep your RNG but reduce its standard deviation," because what we call "RNG" is standard deviation.

The correct amount of randomness is not too high, and not too low. Imagine a slot machine that had no prize payouts other than 1,000,000,000 USD, but (obviously) a very, very low chance of hitting that one payout; also consider a slot machine that simply gave you a refund every time. Both are horrible. Fun lies in the middle ground.

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ephetat wrote:

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RogueMage wrote:

My view is not that GGG have mismanaged their RNG implementation, rather that they have not yet seen the need to control the standard deviation of its results.

Your post is agreeable, but you'll have to convince Chris that there is a need in the first place -- he's on record as expressing his fondness for high variance.

In that video Chris responded to requests to put a hard cap on RNG-based crafting, i.e. limiting the worst-case results to a fixed maximum number of attempts before success. I agree with his view that guaranteed outcomes of that sort would trivialize the game.

What I'm advocating instead is to narrow the typical range of variation in outcomes by reducing the standard deviation around the average chance of success. This would make both extremely lucky and extremely unlucky results occur much less often, but without any absolute guarantees of success. Players would still have to gauge how many orbs they feel confident will likely produce the desired results.

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ScrotieMcB wrote:

When there is no standard deviation, there is no RNG. The higher the standard deviation, the more random the situation is. It's silly to say "keep your RNG but reduce its standard deviation," because what we call "RNG" is standard deviation.

No, that's not what standard deviation is, and we have an example from PoE that illustrates the difference.

With Evasion, you have an RNG-based percentage chance to evade based on your stats, but the range of variance in results is constrained by what GGG calls "entropy". The game maintains a counter that forces an evasion periodically according to your chance to evade. This is what happens when standard deviation is reduced to zero. The desired result then occurs at precisely the rate of your evasion odds, with zero variation.

By contrast, look at something like blocking, where RNG-based results vary randomly at the average rate of your chance to block, with zero correlation among blocking attempts. This is a case of unconstrained standard deviation, where the range of variance is based solely on inherent properties of the RNG algorithm itself.

What I'm advocating is a balance point somewhere in between these two extremes, with a narrower range of variance than with blocking, but not as strictly deterministic as evasion. It is this range of RNG behavior that is measured by standard deviation.