There's been some discussion around what the "correct" mafia size is. The common school of thought is that you should have the maximum mafia for your level (i.e. maxMafia = level * 5). I somewhat agree with that advice as long two conditions are true:The second condition is my personal opinion. The logic behind it is that the quality of weapons in your inventory degrades rather quickly as you go down the list from best items to worst. For example, let's say I'm at level 100 and have 500 items in each category and 500 mafia members. I have the maximum mafia size and every mafia member is outfitted, so I have the "correct" mafia size, right? Well, not really. If I have been following the storyline, the last third of my inventory is filled with really crappy items; items that have less than 1% of the stats of my best item in the same category. So the 500th mafia member will have less than 1% of the attack/defense of that of my 1st mafia member. So I propose having a mafia size that equips down to your 80% mark, or if you have the idealized case above, 400 mafia (500 * 80% = 400).
- You can outfit all mafia members with items from each category
- All items used are decent (i.e. top 80% of all your items in each category)
If you do this, your stats will be numerically lower than they would be if you had 500 mafia. However, they won't be 20% lower, more like 5% lower because the last 20% have quite poor stats. (5% is an estimate and completely depends on your inventory.) So why would you do such a thing? You're now ~5% weaker. The answer: bracketing.
Bracketing
Through trial and error, it has become clear that Crime City has some kind of bracketing system in place; at least in the low to mid levels. It makes sense considering a player with amazing items and 100 mafia could still get crushed by a player with crappy items and 500 mafia. Brute force will likely rule over grace. To prevent this from happening, brackets are used to group players of the same range. Since bracketing based on stats would make rivals too closely matched and the game dull, Funzio chose to bracket based on mafia size and level.
Normal Distribution
Remember Probability & Statistics from college? Yeah, I tried to forget too. Anyway, you learn about this concept called Normal Distribution. Normal distribution is a probability distribution that produces a bell-shaped curve. That curve, conveniently enough, describes many phenomena in nature, industry, research, and I suspect even mafia size. I do not know this to be true though, but I suspect it’s the case.
What I cannot decide is whether the mean, μ, is the maximum mafia for that level or the maximum overall (500), but I’m guessing it is one of the two. Whether it's advice from the forums or their own conclusions, I've noticed that most players will increase their mafia size to one of those two limits. So it's safe to say the highest density of users hovers around one of the two and tapers outward from there... just like a normal distribution curve.
This is valuable because we can assume one thing to be true: the game adjusts brackets to ensure there are a minimum number of rivals for you to tussle with. We will call that unknown minimum "N" (because it's easier to type). Since the highest user density is in the low to mid levels, you have very narrow visibility to rivals (i.e. your level and/or one below) because N is easily met. As the herd thins into the higher levels, the brackets open up to include many levels and mafia sizes. That's the game adjusting brackets, or turning them off entirely, to ensure N is always met. That is also why the break-over from mid-level to high-level – when the bracket really opens up – keeps increasing; players are leveling up and the game is adjusting brackets to the changing density of users.
It would be valuable to know where the boundaries of your bracket are, wouldn't you agree? We don't know that though, and I strongly doubt Funzio is going to give it up. What we do know is that we can take the integral of the normal distribution equation to find the area under the curve between two limits. That equation is below (good luck):
Hypothesis
I think that the integral of two limits is always the same at a given level. So, if the areas are the same and we know one set of limits, we can approximate the other set of limits. I’m no math expert and this is a big reach, so take this with a grain of salt.
Live Example
I am at level 89 with 280 mafia. I can see other users as low as 240 mafia and as high as 425 mafia currently. Notice the offset? I suspect the software offsets the bracket toward the denser population to keep the bracket as narrow as possible. Anyway, all I know are some theoretical limits found through experimentation. And I do not know what the mean, μ, or standard deviation, σ, are... or if this really is a normal distribution curve, for that matter. Those parameters don't matter much in this case because we're assuming they will be equal throughout our bracket calculations. So plugging our limits into our fancy online normal distribution modeler, we get some area.
Now, let's say we want to find the limits of our rival with the most mafia (425) just to see if they will find me on their rival's list. We know the software offsets the bracket to the denser region, but in this case, it tops-out against the level limit of 445. That forces our lower limit down until we get to the same area.
The Home Run
So according to this, my rival with 425 mafia cannot see me. I can see him, but I am off his radar. If he's meeting my two conditions listed above, he's much stronger than me. However, because I have limited my mafia in order to meet my two conditions, I am out of sight. And because most of my rivals are not meeting those two conditions, I am relatively stronger compared to those in my bracket, maybe the top 5% of my bracket. That means I can no-bank. :-) Yet, if I had maxed out my mafia size, I may only be in the top 30% because I'm using my crappiest weapons just for the sake of using them. And that's assuming I even have enough items to equip all my mafia. I can't no-bank in the top 30%.
Want proof? I've been no-banking for five weeks. I get attack and robbery attempts daily, as I should with over $1 million hanging out in the open. In that period, I have not had a single successful attack or robbery. Just say'n...
Also, here’s my prediction for what the limits will be for a level 100 player with a mafia size of 500. I would love for someone at that level and mafia size to confirm/deny those limits.
Notes:
This analysis applies to CC v2.2.
Bracketing is certainly dynamic and will change as opponent density changes.
I am not a math expert and I do not claim to be one. If I made a goof or am way off base, call me out and I'll either fix it or get educated.
I used the below site for images.
http://davidmlane.com/hyperstat/z_table.html
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Originally Posted by Dravak
