I've been seeing a lot of angst on these forums lately about the RNG. I won't get into a discussion about the advantages/disadvantages of using an RNG system for upgrades as that's a completely separate issue. What I will do is given that the RNG is what we have to deal with is to discuss how to make the most out of the RNG system. By this I mean, how you can determine what you can reasonably expect for a given amount of effort. This does require some basic math for the calculation of probabilities but the calculations aren't that difficult so it should be easy enough to follow. Before we start I'll also mention that I'm ignoring the issues I've noticed previously about the roulette wheel and assume the stated chances of mods are exactly what the blueprints tell us. I will also assume that the randomness in the RNG provides a completely random effect within the modification range. In other words I assume that there are no bugs or other issues affecting the process so if FD subsequently tells us that something about the RNG is broken in some way then obviously these calculations won't be valid as it's based entirely on the numbers they give us. I'll break the discussion up into three basic questions as they seem to be the most common source of frustration and misinformation.
1. "How many rolls should I expect to make to get an experimental weapon effect on my mod?"
This depends on the base experimental mod chance, which is 6% for a Grade 1 mod and increases to 10% for a Grade 5 mod. On average, if you want a specific effect, you just divide this rate by the number of different experimental effects you can get and that is your chance of getting what you want from a single roll. So for a Grade 1 multicannon mod, it's 6%/6 different mods = 1% chance. This means you need to roll on average 100%/1% = 100 times to get a specific mod you want. For Grade 1 beam laser mods it is slightly higher, at 6%/5 different mods, for 1.2% chance which works out to 100%/1.2% = an average of 83 rolls. Keep in mind that this is only an AVERAGE, and you might get it on roll number 1 or you might never get the mod you want no matter how many rolls you make. As the number of rolls increases the closer the results will average out to these numbers. So if you're going to grind enough Grade 1 mats to roll over and over in the hope of getting a specific experimental mod you should expect on average to need this many rolls to accomplish it. This will change dramatically with favors in 2.1.2, but we don't know when that will launch so in the meantime this is how to brute-force the rolls to get an experimental effect.
2. "What are the chances that I grind x number of rolls and don't end up with the special effect I want?"
This is a different question to first one as it's a question of starting with a certain total number of rolls and asking what the chances are of getting what you want are within those rolls. This is a little more complicated as you have to answer this question in reverse, by first calculating the chance of ALL of those rolls in sequence being UNSUCCSESFUL. Then the remaining probability is the chance of one or more of them having been successful in generating the mod you want. Using the example of a specific multicannon mod, you have a 99% with each roll of NOT getting what you want. So you just multiply this together the number of times you will be rolling, i.e., raise this probability to the power of the number of rolls. So (0.99)^x where "x" is the number of rolls. For ten rolls you have a (0.99)^10 = 0.9044 or a 90.4% chance of NOT getting a specific mod with those rolls. This leaves you a 9.6% chance of getting a desired mod within those 10 rolls. As you can see this is NOT the same calculation as the first one because the question is different. To compare these two methods, I stated above that the average number of rolls to get a desired multicannon mod is 100 rolls. But let's say you do 100 rolls. What is your chance of getting the mod you want within those 100 rolls? Calculating (0.99)^100 = 0.3660, or a 36.6% chance of NOT getting the desired mod in those 100 rolls. This gives you a 63.4% chance of those 100 rolls giving you at least one of the mods you wanted. So when I said in the first example that you need an average of 100 rolls, that doesn't guarantee that you will get a particular mod. In fact there is only a 63.4% chance that those 100 rolls will give you the desired mod so it wouldn't be surprising if you made 100 rolls and didn't get the one you want, even though the chances are in your favor. So you would actually have to make hundreds of rolls (far more than 100) to cause this mod chance to hit 90% or higher and this is why some people will need to invest considerably more than the "average" number of rolls to get a mod that they want.
3. "What are the chances of a rolling an upgrade and finding it's worse than what I already have?"
This is a common issue that people are unhappy about, specifically going from Grade 4 FSD to Grade 5 FSD and getting a worse result. The issue here is that if you start with a high result on your Grade 4 you should EXPECT to discard a certain proportion of Grade 5 rolls because of the mod overlap. There are two ways you can answer this question, using either method above. For example let's suppose you get a maximum Grade 4 FSD roll at +35% range increase. The Grade 5 FSD upgrade range is from 15% to 45%. This means that you will only beat your previous 35% by rolling between 35-45% = 10 percentage points out of a 30-point range from 15%-45%, or 10/30 = 33%. So you can look at this result two ways, using either of the above methods. Using the first method tells you that you should expect to make an average of 3 of those Grade 5 FSD rolls to beat your Grade 4 roll, since you would only expect 33% of those rolls to be above the +35% range and would discard the other two rolls. So when someone takes a high-level Grade 4 roll and rolls once on the Grade 5 upgrade, then gets annoyed at the "downgrade", this is actually not surprising. You need to roll 3 times on average to get a better Grade 5 FSD upgrade when starting with a maxed-out Grade 4. Similarly, you can use the second method I described and ask yourself, what is the chance of making those 3 rolls and still not getting a better Grade 5 FSD? Same as above, you take the chance of each of those rolls NOT giving you an improvement (0.66)^3 = 0.296 = 29.6%, so the chance of at least one of those rolls being an upgrade = 70.4%. The chance of getting an upgrade from a maxed-out Grade 4 FSD to a Grade 5 roll doesn't go above 90% until you make a total of 8 Grade 5 rolls, when it hits 91.2%.
TL;DR:
The purpose of these calculations is that it tells you what the odds of obtaining or improving an upgrade actually are and you can decide if that is worth your time grinding for the mats you need to make those rolls. With the FSD example you clearly wouldn't expect a single Grade 5 roll to be an upgrade from a maxed-out Grade 4 as your chances are only 33% for it to be an improvement and 67% for it to be a downgrade. Hopefully this explanation helps people understand how the probabilities work for RNG and takes some of the frustration out of the process.
1. "How many rolls should I expect to make to get an experimental weapon effect on my mod?"
This depends on the base experimental mod chance, which is 6% for a Grade 1 mod and increases to 10% for a Grade 5 mod. On average, if you want a specific effect, you just divide this rate by the number of different experimental effects you can get and that is your chance of getting what you want from a single roll. So for a Grade 1 multicannon mod, it's 6%/6 different mods = 1% chance. This means you need to roll on average 100%/1% = 100 times to get a specific mod you want. For Grade 1 beam laser mods it is slightly higher, at 6%/5 different mods, for 1.2% chance which works out to 100%/1.2% = an average of 83 rolls. Keep in mind that this is only an AVERAGE, and you might get it on roll number 1 or you might never get the mod you want no matter how many rolls you make. As the number of rolls increases the closer the results will average out to these numbers. So if you're going to grind enough Grade 1 mats to roll over and over in the hope of getting a specific experimental mod you should expect on average to need this many rolls to accomplish it. This will change dramatically with favors in 2.1.2, but we don't know when that will launch so in the meantime this is how to brute-force the rolls to get an experimental effect.
2. "What are the chances that I grind x number of rolls and don't end up with the special effect I want?"
This is a different question to first one as it's a question of starting with a certain total number of rolls and asking what the chances are of getting what you want are within those rolls. This is a little more complicated as you have to answer this question in reverse, by first calculating the chance of ALL of those rolls in sequence being UNSUCCSESFUL. Then the remaining probability is the chance of one or more of them having been successful in generating the mod you want. Using the example of a specific multicannon mod, you have a 99% with each roll of NOT getting what you want. So you just multiply this together the number of times you will be rolling, i.e., raise this probability to the power of the number of rolls. So (0.99)^x where "x" is the number of rolls. For ten rolls you have a (0.99)^10 = 0.9044 or a 90.4% chance of NOT getting a specific mod with those rolls. This leaves you a 9.6% chance of getting a desired mod within those 10 rolls. As you can see this is NOT the same calculation as the first one because the question is different. To compare these two methods, I stated above that the average number of rolls to get a desired multicannon mod is 100 rolls. But let's say you do 100 rolls. What is your chance of getting the mod you want within those 100 rolls? Calculating (0.99)^100 = 0.3660, or a 36.6% chance of NOT getting the desired mod in those 100 rolls. This gives you a 63.4% chance of those 100 rolls giving you at least one of the mods you wanted. So when I said in the first example that you need an average of 100 rolls, that doesn't guarantee that you will get a particular mod. In fact there is only a 63.4% chance that those 100 rolls will give you the desired mod so it wouldn't be surprising if you made 100 rolls and didn't get the one you want, even though the chances are in your favor. So you would actually have to make hundreds of rolls (far more than 100) to cause this mod chance to hit 90% or higher and this is why some people will need to invest considerably more than the "average" number of rolls to get a mod that they want.
3. "What are the chances of a rolling an upgrade and finding it's worse than what I already have?"
This is a common issue that people are unhappy about, specifically going from Grade 4 FSD to Grade 5 FSD and getting a worse result. The issue here is that if you start with a high result on your Grade 4 you should EXPECT to discard a certain proportion of Grade 5 rolls because of the mod overlap. There are two ways you can answer this question, using either method above. For example let's suppose you get a maximum Grade 4 FSD roll at +35% range increase. The Grade 5 FSD upgrade range is from 15% to 45%. This means that you will only beat your previous 35% by rolling between 35-45% = 10 percentage points out of a 30-point range from 15%-45%, or 10/30 = 33%. So you can look at this result two ways, using either of the above methods. Using the first method tells you that you should expect to make an average of 3 of those Grade 5 FSD rolls to beat your Grade 4 roll, since you would only expect 33% of those rolls to be above the +35% range and would discard the other two rolls. So when someone takes a high-level Grade 4 roll and rolls once on the Grade 5 upgrade, then gets annoyed at the "downgrade", this is actually not surprising. You need to roll 3 times on average to get a better Grade 5 FSD upgrade when starting with a maxed-out Grade 4. Similarly, you can use the second method I described and ask yourself, what is the chance of making those 3 rolls and still not getting a better Grade 5 FSD? Same as above, you take the chance of each of those rolls NOT giving you an improvement (0.66)^3 = 0.296 = 29.6%, so the chance of at least one of those rolls being an upgrade = 70.4%. The chance of getting an upgrade from a maxed-out Grade 4 FSD to a Grade 5 roll doesn't go above 90% until you make a total of 8 Grade 5 rolls, when it hits 91.2%.
TL;DR:
The purpose of these calculations is that it tells you what the odds of obtaining or improving an upgrade actually are and you can decide if that is worth your time grinding for the mats you need to make those rolls. With the FSD example you clearly wouldn't expect a single Grade 5 roll to be an upgrade from a maxed-out Grade 4 as your chances are only 33% for it to be an improvement and 67% for it to be a downgrade. Hopefully this explanation helps people understand how the probabilities work for RNG and takes some of the frustration out of the process.
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