Lancer Knightz (Guild)/Punch 1-UV Tickets
From SpiralKnights
This page is part of the data collection project run by the guild Lancer Knightz. Here, we estimate the rates of getting various results from 1-UV tickets at Punch. These data were collected by Donkeyhaute.
Methodology
The methodology is pretty simple. Just before buying a 1-UV ticket from Punch, you decide that you are going to record the result, whether good or bad. What's recorded is
- the date
- type of item: helmet, suit, etc.
- the kind of UV: shock, CTR, etc.
- the level of the UV: +1 (Low), +2 (Medium), +3 (High), or +4 (Very High or Maximum!)
Data
Currently our data set consists of 388 1-UV tickets, mostly for helmets and bombs. Here is a summary of the UV levels obtained from those tickets.
| Item | +1 | +2 | +3 | +4 | Total |
| Helmet | 160 | 36 | 5 | 4 | 205 |
| Suit | 15 | 3 | 2 | 0 | 20 |
| Shield | 0 | 1 | 1 | 0 | 2 |
| Sword | 1 | 0 | 0 | 0 | 1 |
| Handgun | 0 | 2 | 1 | 0 | 3 |
| Bomb | 121 | 26 | 4 | 6 | 157 |
| Total | 297 | 68 | 13 | 10 | 388 |
The possible kinds of UV vary by item, although helmets and suits have the same kinds, and swords and handguns have the same kinds. Here are the helmet UV kinds that we obtained.
| Normal | Piercing | Elemental | Shadow | Fire | Freeze | Shock | Poison | Curse | Stun | Total |
| 28 | 15 | 18 | 19 | 10 | 23 | 19 | 25 | 30 | 17 | 205 |
Here are the bomb UV kinds that we obtained.
| Beast | Slime | Construct | Gremlin | Fiend | Undead | CTR | Total |
| 26 | 21 | 24 | 21 | 22 | 15 | 28 | 157 |
We could list the other items, but we'll wait for more data. Also, we could present the data in greater detail — the number of fiend+1 UVs, the number of fiend+2 UVs, etc. — but let's not.
Results
High UV levels are clearly rarer than low UV levels. Here is a table of frequencies based on all 388 data. For each level, the table shows our best estimate of the frequency and a 95% confidence interval for the frequency. (The confidence interval was constructed by bootstrapping the data set 1,000,000 times and, for each level, taking the middle 95% of the bootstrapped frequencies. Disclaimer: Donkeyhaute is not a statistician.)
| +1 | +2 | +3 | +4 | |
| Estimate | 76.5% | 17.5% | 3.4% | 2.6% |
| Confidence Interval | 72.2%-80.7% | 13.9%-21.4% | 1.8%-5.2% | 1.0%-4.4% |
Are all kinds of UVs equally probable? As far as we can tell, yes. The data above suggest that fire UVs might be rarer than other UVs on helmets. However, a statistical test of uniformity (using chisq.test in R) produces a p-value of 0.057. So we cannot conclude, with 95% confidence, that the kinds are not equally probable. (The p-value for the bomb data is 0.581.)
Basic probability theory lets you derive more results from these. Suppose that you want to obtain CTR+4 on your sword. The chances of getting +4 are about 1/40, and the chances of getting CTR on a sword are 1/8. Assuming that they're independent, your chances of getting CTR+4 are 1/320. So you expect to try 320 times on average, for a total cost of 6,400,000, to get that UV.
