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5 April 2004 -- The Luck Treatise

Is luck working in the UO world?

Created 5 April, 2004.  All rights reserved.  Copyright 2004, Jonathan Monteleone


 

Everything found in this document can also be found on my webpage and the monster loot/luck project posts over at UOPG. This document is a re-organization of these materials to keep track of all the information.

I also wanted a single post for the UO community and the Dev team so all feedback regarding luck could be in one location, and I figured presenting hard facts would catch everyone’s interest and get the ball rolling!

I would welcome any useful feedback.  All comments can be directed to uomart@ihug.co.nz and please include “[UO] Luck” in the subject heading.

Introduction

Before presenting my monster loot/luck findings, I think it is important to read the official word regarding luck. The current official information regarding luck can be found on Stratics and the UO site. Basically, the higher the luck the better the chance for 1) more items spawning on a monster, 2) spawned items having more properties, and 3) item properties having higher intensity values. These 3 item factors are influenced solely by luck and the monster template.  The monster template is the range of loot that would normally spawn on a monster in template group, but luck has a basic restriction that it cannot make loot on a monster that is better than the maximum allowable loot. See the loot tables for more information about maximum allowable loot and monster-loot templates.

People have posted on the Stratics boards about luck being broken (thread1, thread2, thread3). And over at UOPG, people have some thoughts on luck as well (thread1, thread2, thread3). Since luck has become an integral part of the post-AoS item-based UO, it is important to understand how luck works and indeed if luck IS working. MrTact had this and this to say about luck.

Contrary to popular belief, not all games are created equal.  This is especially true for dynamic worlds such as MMORPGs...the implementation (i.e. programming) of a game design does not equal the actual results of the game design.  Confused?  Think of it this way, just because the code says it should work in a predictable manner does not mean that it will work predictably in the "live" game. Evidence of this is seen in the problems that UO has with random number generation (look for posts by Mulac).

According to OSI, this Figure reflects how luck should be influencing the quality of loot after a monster is killed.  As luck increases, so does the “loot bump chance” (LBC).  The LBC is the percent chance of one, two or all three of the item factors influenced by luck to get an increase in loot quality.

Luck is broken!

This Figure shows how luck is really behaving.  The Figure was generated using actual item statistics from looted corpses for each of the different monsters in the Figure.  The statistics were recorded using a program I wrote to grab the item information for each item on a corpse.  If luck is working as intended, then the basic shape of the curve for each monster should look similar to the first Figure (Predicted effect of luck).  It is clear that the curves do not look anything like the predicted LBC curve.  This may be due to not having enough observations for some of the monsters, but the blood elemental curve has plenty of observations.  It may be due to the units of the y-axis. Instead of LBC, I used a measure of loot quality that reflects the actual number of items, number of properties and value of property intensity. This measure of loot quality is called the Loot Measure (LM) and is a single value reflecting all the statistical information about the magic loot generated after the monster is killed. The higher the value the better the overall loot. The calculation of the LM is based on the change in the number of items, item properties/item, and intensity of item properties compared to these factors at a luck value of 0.

An intensive sampling of blood elemental observations (Figure below) also shows that luck is not working as intended.  The y-axes on the left represent the average number of items and properties on each corpse and the right reflects the average percentage of maximal intensity for items on each corpse. It is very difficult to see ANY trend resembling how OSI describes luck improving the loot spawn.


 

What kind of loot do monsters give?

The histogram below shows the loot measure at 0 luck for a few monsters. This figure shows the kind of loot you get if you use no luck at all.  So, different monsters definitely spawn different quality of loot based solely on the monsters difficulty.  This agrees with what OSI has said in the past regarding monster templates. I wonder why a Vorpal Bunny gives the same kind of loot as a Balron and WW?!?

The same monsters as above were hunted with high luck to compare if the loot was better. Now, does luck really help get better loot? Based on the above histogram, I would say that luck does little to nothing to improve the quality of loot.


 

Putting it all together!

Many people expressed a concern over the validity of my LM measure instead of the OSI LBC measure to reflect the influence of luck on loot quality. I have gone through and recalculated a LBC measure using all the items in my database.  The Figure below is the result. It summarizes the outcome of my research nicely. The Figure is set up with the same axes that OSI uses to explain luck. The solid curve is the increase in getting better loot as luck increases (as defined by OSI). The dots and triangles are from real data I gathered by killing A LOT of blood elementals. Now, this Figure lets us compare real findings with what OSI says should be happening. If luck is behaving as OSI designed it, then the dots and triangles should all be very close to the curve. Overall, that is not the case. I consider this Figure as definitive evidence that OSI needs to take a CLOSE look at luck!

The variability seen in some of the luck values that are close together is most likely due to either 1) luck being broken (this would be my first guess) or 2) other factors influencing the loot quality that may interfere with luck.

The 400 kills/point was to rule out any statistical variability producing outliers. Given that at even the lowest luck levels we should see at least 10 "luck bumps" in 400 kills, I figured that was good enough.

So, what could be causing the variation? Shard load comes to mind as a potential source of variability. I havent finished with the analysis yet, but it does appear that the amount of people playing on a shard significantly influences the type of loot you get! How did I determine shard load? I based it on known peak playing times and supported this with the %full monitor on the shard list. This allowed me to use the time recorded for each kill and categorize the kill in a shard load list.

As for the variability, it could be coming from luck not working at all. As for consistency, it does show consistently that before 500 luck the loot bumps are above the predicted percentages and after 500 luck the loot bumps are below the predicted percentages.

What you have to keep in mind is that none of what is happening is without error. Even if luck were working according to the distributions that OSI specified, there would still be variability in any actual gathered data. The difference between that situation and now is that the actual gathered data would follow the OSI curve and "wobble" around it within a standard deviation or two. This kind of stuff is ALL about distributions.

The other issue of course is that Im calculating something wrong. Sure, there could be a bug in my code or some assumption I am making is wrong, but given that OSI isnt about to let me see their code I have to work with what I have. I have been analyzing "chaotic" data like this for well over 10 years now, so I have a good feel for handling this type of data.

The luck >=100=0 debate!

Before we discuss what the best luck values to use are, let us look at a common issue often mentioned on Stratics. The dreaded 100=0 issue! People are saying that items having triple digit luck are not registering as triple digits. Instead, a digit is dropping off lowering the effective luck value for the item.

I do not know exactly what is happening, but the figure above has information to explore that issue. The dots represent total luck values where all items had luck < 100, and the triangles represent total luck values where all items had luck > 100. As can been seen, there isnt much difference between the dots and triangles. Conclusion: I do not think the 100=0 is really occurring.

Now, turn your attention to the thick vertical line in the Figure. Notice to the left of the line (lower luck values) the real data shows loot bumps exceeding the OSI defined LBC. To the right of the line (higher luck values) the real data shows LBCs much lower compared to what OSI says should be happening. So, what are the best luck values to use? Based on my findings to date, I would say luck values in the range < 405 would produce the best loot.

How many observations are enough?

Some people have expressed a concern regarding the number of monsters killed and being able to say anything regarding statistically meaningful trends. The Figure below shows how the 3 factors luck influences change as the number of killed blood elementals increases

Notice as the number of kills increases that each of the curves starts to plateau and remain stable. These flat regions tell us enough observations have been obtained to make reasonable statistical inferences from the data. The number of item properties, number of items, and intensity of an item property appear to stabilize around 60, 75 and 50 kills, respectively.  So, 104 kills for this Figure and the 400+ kills used for other Figures should be more than enough observations to make conclusions regarding how luck is performing.

Does gold drop increase with luck?

From my database (400 kills at each luck level):

With 255 luck the gold range was 470 to 723 with an average of 598 gold

With 580 luck the gold range was 446 to 733 with an average of 600 gold

With 971 luck the gold range was 490 to 737 with an average of 611 gold

Yes, it does appear that the average gold is climbing by a few gold pieces but an ANOVA (statistical test to compare for statistically significant differences between groups) says no difference exists. So my data holds with what OSI has said from the onset..."Gold is not influenced by higher luck" This makes sense since gold and "common" items spawn as soon as the monster spawns, while magic items spawn ONLY after the monster is killed. Luck only triggers for the 2nd item spawn cycle.

Posts by others on their luck-loot findings…

Many people have posted snipits of their personal testing of luck and the type of loot they get from different monsters.  I would warn against believing such findings simply based on the memory and relative definition of “best loot” that people use to measure luck and loot quality.

I would have said some of the same things I read in luck posts before I actually started acquiring ALL data. Previously, I would base it on how many "good" (very relative term) items I would get in a span of time. Sometimes it seemed like higher luck gave better items and other times it seemed like lower luck gave better items. That is what started to confuse me and so I dug deeper. If you REALLY want to see for yourself, then how about grabbing my loot recording scripts and gathering some data for the project.

Determining data flucuations

People have been asking to see individual results from the people who have helped with the project so they could see if some kind of consistent pattern can be seen from individual to individual. I did one better.

I took the kill count for luck level 647 to 1,000 kills. Then I used a well-established statistical technique (called bootstrapping) to explore the variability in my data and see if any consistency for loot results exists. The Figure below is the result.

Here is what I did:

1) Number of observations for luck level 647 luck raised to 1,000 kills

2) Randomly picked kills from 1) to create 20 sets, each made up of 400 kills

3) Analyzed each of the 20 sets as if it was a new individual

You can think of it as putting 1,000 pieces of paper in a hat and drawing out 400 pieces of paper, then putting all the paper back in the hat and pulling out another 400 pieces of paper. Did this 20 times.

 

What was found:

The red dashed line shows the "spread" for the result of each of the 20 data sets. The 647 is where the original chance for a loot bump was located (this is the 647 luck point seen in the figure in the first post). The greyish horizontal line is the top of the first Figure of the document.

 

Now, taking the average of all 20 points resulted in a mean=57 and standard deviation=13. The LBC spread is large and almost all the results are well above the OSI predicted chance for a loot bump. I may go through and perform this analysis at each of the luck levels, but I wanted to get this out so people could see that the loot at 647 (even though an apparent outlier compared to the OSI prediction) does appear to be consistently better than what OSI expected at this luck level.
Future research

1) Continued generation of the database (want to help build the database?)

2) Tabulation of the exact distributions for 1) most common types of items, 2) most common properties, and 3) most common intensity value. These distributions will also be sub-divided by monster and luck value. I have asked on the UOPG boards what people consider the best 5 properties. I will use the answers to isolate how often these best properties spawn? do they spawn more often on one monster than another? do certain types of items or properties spawn more frequently at certain luck levels?, etc.

3) Investigating time-related factors that could influence loot quality. For example, some people say the longer you spend at a spawn, the worse the loot gets. Others think the time of day influences the quality of loot. This issue is more likely related to the shard player load than actual time of day. The monster-loot database can be used to explore these issues.

There is a theory that "camp age" plays a role in the kind of loot you get. As you spend more time at the same camp the quality of the loot decreases. Some say this is a "feature" implemented by OSI to stop people from camping the same monster spawn for too long. OSI has never confirmed this phenomenon, and I believe the rumor of camp age started after OSI released information about their "population" controls for skill gain (Pre-LBR), which BTW was dumped (supposedly) with pub16.

Anyway, I have not really seen this to be the case. What I have noticed after camping the exact same blood spawn for 3,000 kills over a weeks time during different times of the days is that a cyclic nature to loot does seem to be occurring. I have not figured out how to proof this definitively yet. Every 300 blood kills or so I get a few good items that are well above most of the other items I had been getting.


 

GLOSSARY OF LUCK TERMS

Luck - The player’s total luck value at time of kill. I used 4 types of luck including: total luck based on all items > 100 for each piece, total luck based on unknown luck for each piece, total luck based on all items < 100 and total luck based on a combination of luck pieces 100 < item < 100. This breakdown of luck was introduced to investigate if the observation, luck 100=0, is a real phenomenon or not.

KILLS - Number of monsters killed for a level of luck and type of monster. The idea is to generate enough data for each luck and monster to statistically make conclusions about how luck works based on the data gathered. A nice side-effect will be to determine the best monsters to hunt to get the best loot at a given luck level.

GOLD - Average gold for the monster killed. OSI stated that gold is not influenced by luck.

ITEM SPAWN (%) - This is the chance of an item spawning on a corpse. For example, if 100 monsters are killed and only 80 of them had items, then the Item spawn percent would be 80%. I do not believe that this parameter is influenced by luck. A word about how items are dealt with in the analyses. There are two types of items; 1) items that typically spawn on monsters, for example wooden clubs on ogres and ogre lords or scrolls on demons and liches, and 2) magical items that spawn when monster is killed. The Table above only summarizes the type 2) items, which is what we are all really interested in anyway. I do still record the type 1) items, but they are not used for anything at this time.

MAXIMUM ITEMS SPAWNED - This is the maximum number of items that spawned on a corpse at a given luck level and monster. As stated on the official luck webpages, this parameter is influenced by luck. I am not so sure this is the case, but as the database grows we should be able to shed some light on this issue.

MAXIMUM PROPERTIES SPAWNED - This is the maximum number of properties per item that spawned on a corpse at a given luck level and monster. As stated on the official luck webpages, this parameter is influenced by luck.

MAXIMUM INTENSITY (%) - This is the highest relative intensity on all of the properties that spawned on all the items for a given luck level and monster. This parameter is influenced by luck according to the official webpages. Calculation of this paramter is carried out as follow: 65 luck would be a 65% intensity (65/100*100) and a 10% Defense Chance Increase would be a 66.7% relative intensity (10/15*100). Obviously some of the properties are not appropriate to use when calculating this parameter. Take for instance Faster Casting Recovery, which on all items (except artifacts) has a maximum value of 3. So, choices of 1, 2, or 3 produce intensities of 33, 66, and 100% respectively. I chose to use properties that had at least 5 possible values for the property to calculate the relative intensity for comparison to find the maximum intensity. The more possible values for a property intensity, the more accurate the result to the actual maximum intensity used for the monster loot template.

TOTAL ITEMS - This is the total number of items that spawned for a given luck level and monster. This parameter is influenced by luck, and should give some idea about the relationship between luck and its ability to influence number of items that spawn.

TOTAL PROPERTIES - This is the total number of properties that spawned on all items for a given luck level and monster. This parameter is influenced by luck, and should give some idea about the relationship between luck and its ability to influence the number of properties per item.

MONSTER - Type of monster that was killed at a given luck level.

 

 

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