Congratulations! Your hero has just finished collecting the thirty-freaking-million gold coins into his savings account...
This is a guide for players to complete the savings goal -- to save a terrifying amount of 30,000,000 coins. The guide aims to provide a general sense on what should be done. Players are expected to develop their own way of saving steadily by mastering this guide. From there, one may look for extra terms that can be optimized by themselves.
This guide is written and maintained by. Please PM her if you have inquiries or suggestions about the guide. Please do not change non-typographical/grammatical errors unless you have her consent.
- 1 Don't push too hard
- 2 Expectation
- 3 The cycle
- 4 Basic factors
- 5 Further Optimization
- 5.1 Effectiveness of voice commands
- 5.2 Towns
- 5.2.1 Good trading vs bad trading
- 5.2.2 Heal faster vs heal slower
- 5.2.3 Better prayer vs bad prayer
- 5.2.4 Cheaper equipments vs Expensive equipments
- 5.2.5 Cheap skills vs expensive skills
- 5.2.6 Good savings (lavish parties) vs bad savings (cheap parties)
- 5.2.7 Choosing the right town
- 5.2.8 Special Towns
- 5.3 Daily forecasts
- 5.4 Miscellaneous
- 6 Mathematics for mechanics
- 7 Log
- 8 References
Don't push too hard
Do not push to hard which causes motivation to burn out. Keep it nice and slow.
You should have already noticed that the savings goal is an unique goal in Godville taking an exceptionally long time -- 2 to 8 years to complete.
Taking a step back to the temple goal, people can be pretty motivated: they take 5.5 arena matches a day, they take a few underground bosses too. Proceeding to the ark goal, they take 5.5 dungeons every day again. They also send them back to Godville properly to squeeze 2 temple logs every day. 5 logs a daily would be so simple.......but they soon left the game just because it is too hard to maintain such pace.
To master this super long term goal, it is better to keep it nice and slow. Don't be frustrated on bad RNG or mistakes because it happens to you all the time. The important thing is, if you stick with the game long enough the goal will be achieved on day.
By mastering this guide, your expected daily saving should be
20-30k per day if you are playing completely free (by gaining charges from temple solely).
35-45k per day with minimum investment (20-50 charges bought per month).
60-80k per day if you are investing heavily (200-500 charges per month).
And that does not mark the limit on what you can save. Aggressive players could save more with more charges burnt (although no one has ever achieved an average rate (over 10+ days) of 75k per day, in English Godville). With luck, it is also possible to save up to 120k in a single day.
With that being said, you can be one of the top players in the server easily with proper plan and investment. There is no secret here in being a top player: understand the mechanics properly, then execute your plan with determination and patience, assisted by the power of money.
The differences between the 3 above classes are:
- The difference between F2P and light payers are, light payers are able to (1) afford actions that takes 0~1 charges usually, like taking him back to town after dungeon, on a regular basis; and (2) afford actions that takes loads(10+) charges at a time to pull the hero out of a difficult situation (dungeon failure, hard treasure boss etc).
- The difference between light payers and heavy spenders are, heavy spenders are able to (1) afford actions that takes 2~3 charges (combine items, vc on epic quest, opening all boxes) on a regular basis; and (2) become a lot more aggressive in dungeon and sails.
The above numbers are what you may expect on a day where you are fully available. You should not push for 365 days a year of course.
The cycle is a set of repeated action aimed to reduce GP usage, ideally below 100% so that no extra charge is needed.
Payers who can afford to burn a charge to pull yourself away from bad situations can avoid this section. For F2P and minimum invested players, you may want to maintain what I call a cycle. The aim to allow maintain players in the state that savings can be done anytime.
To save you need to earn money. To earn money you need to participate in dungeon/sails. To dungeon/sails you need a minimum of 50% GP. To save you need to return to town (manually for efficiency). To go back manually you need GP.
Therefore, to save efficiently you need GP. And...in order to fill GP you want to pray in towns with gold.
Therefore you want to keep yourself filled with GP, and have a proper amount of gold anytime. 15k gold desirable to go through towns with bad prayers.
This is not too hard to achieve. Actually this can be maintained naturally by going back to town after a successful dungeon/sail. A few things may disrupt your cycle though:
- Going back too frequently. Normal quests last about 12 hours where dungeon/sails happen for 3~4 times at the most. Returning 3~4 times within a quest is acceptable so that should not be too bad. Be aware when the quest is almost done though.
- During epic quest. The hero is extremely unwilling to listen while the quest is over 2/3 complete. If you are not a heavy spender you can take a break to let him return himself instead.
- Godville sac: it leaves you with below 10k and below 100%GP. One should avoid exp sac at all cost. There are a few methods to return Godville without sacrificing: send to sail, arena and warping items (that sends you to somewhere else).
Arena is extremely risky as you may lose your gold (and breaks your cycle) and coming out with less than 75% GP (50% sending in and 25% for praying with 0 gold). Warping items are not always obtainable. Heavy spenders may try to combine one (bold+bold for activables) while you need one, while light spenders may also try that when they desperately need one.
However, sending to sail is still the most reliable and risk-free method. The only thing is the 9/12 hours cooldown. The wonderful thing is, quests are done in a 9~15 hours frame [depends on RNG as well as how much time you have wasted outside of questing]. That being said, you can send him to sail every single time when the quest is completed.
So a complete cycle looks like this:
Begin questing -> dungeon-town cycle -> quest completed -> warped back to Godville -> new quest
Of course you don't always complete your quest while you are awake. That's fine - try not to think too much what happens with your hero while you are sleeping. It is easy to enter the cycle when you have full gp -- gp is the core of making any human interference in game. There is nothing that you can do without it.
You start from zero coin. What you can spend is at most what you have gained. More generally, the follow holds
Total coin gained = Total coin used + current coin held
In a long term the amount of coin you have is negligible. Therefore
Total coin gained ~= Total coin used
Now we can break the formula down into various terms. We either lose coins by wasting coins (W), sacrificing coins in godvile (SC), skill upgrades (SU), money saved (MS), dungeon/sail failure (DF) and other negligible terms (OU). We either gain coins from dungeons (D), sails (S), activables (A) and other negligible sources (OG). Therefore we have
W+SC+SU+MS+OU = D+S+A+OG
Neglecting small terms and rearranging gives
MS = D+S-W-SC-SU
Right hand side are the terms we want to optimize: we want to maximize dungeon/sail gains, and minimize coin wasted, sacrificed and use to upgrade skills.
Small terms can also be optimized. One simple example is to remember to open free good boxes -- this is an easy optimization with strictly positive outcome. Others like increasing gain by allowing tribbles to grow bigger -- might be hard and costly to perform, and the return is simply small. That may violate my golden rule of not to push too hard, but if you are happy to try those make sure you can optimize the big terms first.
Primary goal: survive and come out with treasure
Secondary goals: extra boss fights, remove afks, nooks bonus
Other uses: gain/loss HP for manipulation outside, delay cycle
Dungeon is all about gold, right? Treasure gives at least 8k, so this is the main reward unless you fight bosses and kill afks. Any failure would end up in losing half the gold, so if you are carrying a lot with you, always avoid losing. Or at the very least, be the only survivor in a quitting team full of afks.
There are various dungeon guides around (like Kingdada's) so I would skip the job writing one here.
Primary goal: survive and come out with treasure OR sending back to Godville
Secondary goals: extra gold by opening loots
Other uses: delay cycle
Sailing is a huge source of gold that it may spit up to 40~60k steadily from 2 treasures. Of course F2P should not aim for 2 treasures every time: 50% is usually enough for 1 loot but not 2. On the other hand, since it sends you back to Godville, it is worthy to stack the sail cycle with the quest cycle to avoid exp conversion.
Here are some simple sailing tips:
- Although drowning would not result in a death now, you will still receive a penalty of losing half the gold and items so be very cautious not to get sunk.
- Aim for double name(bold) beasties if your ship is hard enough. They are easier to find - usually 2~3 grids away from the outer ring. Be very cautious when fighting them: you will want 90HP against a 60HP two names (or 80HP for 50HP two names), and 120HP if you are on a reef (hence fighting on a reef is strongly discouraged). Needless to say, this method is usually for those with 200% if not 300%+ ark.
Two initial conditions are particularly bad:
- Closed border makes searching at the outer ring extremely difficult, and forces you to take the 9-hour cycle. This is not bad, but you need a lot of food to do it.
- Shuffled beasties completely kills the double-named beasties' distribution, making the treasure hunt a lot more difficult and more luck based.
With these two conditions there is no need to push so hard. Extend your sail by looking for food island (but don't punish much), and if you are not on a great mood that day, just leave it.
Please refer to the Feather Mail page for a complete sailing guide.
Not much to say here. Good boxes should be opened whenever possible. Open 50% mystery boxes when you have spare gp while in town selling etc.
Wasted coins (W)
Primary goal: reduce gold wasted
Secondary goal: manipulate gold count to avoid skill upgrades/exp conversion
The hero will be more likely to waste coins when
- (1) he went back to town with good health
- (2) he is unwillingly to go back.
To avoid (1) you simply send him back when he is in poor form, or basically in red health. Red health means 1/3HP below but one can divide it further.
At an even lower HP(less than 20%) this is the zone where hero might start using recovery items. Players are advised to start monitoring the hero at this stage so that the hero can be sent back in case he did not use recovery items while fighting(that he ended the fight with yellow health instead of red).
With less than 5% HP this is the dying range. He may escape from the fight or even go back to town directly. This is a problem because there is a much higher chance that the destination of an uncontrolled return is Godville. In that case coins will be sacrificed which is bad. Players should send him back immediately in that state. The good thing is, at super low health the hero is likely to listen.
(2) is a more complicated problem. We will cover it in the later section about the use of voice commands.
When the hero is going back with poor health and going back willingly, there is a good chance that the gold will end up in savings (60% is a fair estimate. 75%+ is, not very surprising). In such case, there is not much to do to make hero to save above wasting as the odds is already optimized. Such probablistic coin waste is almost essential.
One thing for sure is that, there is a hidden parameter on how much a hero wanted to save over wasting. The parameter is decided when the hero started going back. What if hero did something else between going back and the waste/save state? What if the hero dungeon'd while going back? Or while recovering health? Or while selling items?
This is unanswered in Godville. Therefore my advice is, try to exit dungeon with low health no matter what, so that the hidden parameter remains at your favour.
It is also possible to completely avoid these mess by entering dungeon only when you are praying, so that the hero will not waste (but also not save) the gold that you earned from that dungeon, and you can regain gp immediately.
Coins sacrificed (CS)
Avoid walking back to Godville, at all cost.
Higher level means tougher hero, but accelerating leveling comes with great cost that you don't want to pay for. 500HP or level 100 is more than sufficient -- not to mention leveling beyond level 100 is also doubly hard.
When a hero returns to Godville for whatever reason, he will first visit his own temple. If he has more than 10k he will sacrifice gold for experience points. Experience received depends on cooldown from the last sac and current level, but that's not important because you simply do not want to sac at all.
You want to minimize the effect of coins sacrificed affecting the amount of coins that you can save potentially.
- The ideal case is to sacrifice nothing. Not only that you lose no coins, you are also eligible for temple bonus. However, unless it is no conversion day, that means you have under 10k coins, that you don't have much to save anyway.
- If you have between 10-30k, that means sanctification is almost unavoidable. What you want to do is to maximize the last 4 digits of your coin count so that you still have something to save. You can micromanage your hero by gaining slightly more or less before returning, but that is often tricky to do. The most viable way is to execute such thing during a dungeon run.
- If you have far more than 30k, then you would actually want as many coins as possible because you will not sacrifice more than 30k coins.
Similar mindset can be applied on skill upgrades in the next section.
Skill upgrades (SU)
Avoid buying skill upgrades, at least the expensive ones.
This is potentially a huge money sink. While the effectiveness of skills are still arguable, they may cost a lot for sure at high levels.
There is a fixed chance where hero purchases a level up for a particular skill. The cost is 500 times level of the skill. Like pet resurrection, the exact amount spend will be slightly above, usually a few hundred more.
Three solutions to reduce the frequency of skill upgrades:
- Carry less coins. If your lowest leveled skill is of level 80, then you will be safe carrying under 40k coins and so on. The chance of triggering a skill upgrade is not a 1/0 switch: it follows a certain distribution. The more skills where level up are eligible, the more likely that skill upgrade will occur. Carrying more coins than that needed to upgrade the lowest leveled skill is not the end of the day. However there is a hidden risk: if skill upgrade still happens, you may be left with extremely low amount of coins, and that obscure your cycle.
- Carry loads of coins. Check your best skill for the maximum possible amount of gold spend on skill upgrades. For example if it is of level 110 then 55k coins will be used at once, for most. Carrying 10k above the threshold would be enough for you to maintain the cycle in the worst case (i.e. with the best skill upgraded).
- Choose the town to save wisely. There are towns where you can upgrade skills cheaply or more expensively. Use these wisely you can avoid skill upgrades to the most.
Here are a few more mechanics that are important.
Effectiveness of voice commands
Do not overuse vcs that reduce the success rate when you need to issue one. Let go when the hero is very likely to ignore your command.
In order for a hero to follow a command, you want the hero to react (i.e. with a diary entry) to and execute your command. These two combine as the willingness to obey. In usual condition the hero is quite likely to listen (taking 1~4 commands) but not when you manipulate him consecutively.
Willingness drops gradually when
- You perform the same action too many times in a short period of time (combine, pray)
- You are halfway through (60%) a quest. The closer to completion the effectiveness drops.
Willingness drops sharply when
- You perform the same action too many times in a day
- You are halfway through (60%) an epic quest. The closer to completion the effectiveness drops sharply.
The last one is the largest problem of all. Not only that it makes vc extremely ineffective (it takes 4~20 charges before they finally obeyed), such state lasts very long (up to 36 hours). Less savings is expected during epic quest.
To avoid such problem, one should either push for completeness of the epic quest (mystery box, do quest commands), or to cancel it at the beginning. However, since epic is a major source of logs such method is not strongly recommended.
Towns are where you go back to save. Each town has their own properties, which are not essentially bad (except for godville with the unwanted sac function), so you should choose wisely on towns you want to go back on.
Erinome does a fantastic job collecting proportion of gold wasted, saved and prayed in different town. One may think the money wasted/saved to be uniform within a range, while amount of gold prayed follows a geometric distribution really. Players may however focus on the simple properties of town since they work good enough, and they are the only thing you can put your hands on -- you can't really control the proportion of gold prayed, right?
Good trading vs bad trading
Items are not your main source of gold so in general that basically does not matter at all. Amount of gold you get by trading is kind of unstable so that does not help in manipulating exact gold count too.
Of course, exception is when you carry valuable items like sailing loots, then trading does matter here.
Importance (out of 5): ☆
Heal faster vs heal slower
That does not affect saving effectiveness at all. If any, fast healing reduces time wasted (by a bit), but slower healing helps by reducing dungeon/sailing cooldown and that makes manipulation a bit more flexible.
Better prayer vs bad prayer
There are two kinds of praying efficiency: - GP gain per coin sacrificed - Amount of coins used for prayers
The first is strictly desirable. The second however, is not. What you want is to fill the GP bar with few coins as possible. Using 4000 coins in a bad prayer town is better than wasting 18000 coins in a good prayer town --- they both fill the bar up to 100%.
Good/bad prayer town as described in game -- means both of them.
That means in a bad town you pray less effectively and sacrificing less coins, so you may not fill up to 100% ( filling up to 80% should be easy), but you potentially waste less coins too. On the other hand, entering a better prayer town means you are almost guaranteed to get 100% but you potentially waste more coins too.
The difference is insignificant anyway.
Cheaper equipments vs Expensive equipments
The significance is more on the non-templer side on gold bricks. Post-temple players don't buy equipments often, and they don't cost much.
Cheap skills vs expensive skills
Towns with cheap skills allow you to purchase skills at 50% the price, i.e. 250 per level. An average player with skill levels 60~100 is very likely to have skill upgrades there (as long as they got 15k with them). Therefore if you have lots of coins it's worthy to visit a town with cheap skills so that you can purchase skill upgrades while saving properly.
Towns with expensive skills have skill upgrades costing 150% as usual, i.e., 750 per level. If you have some (30~50k) money it's worthy to go there so that you can't afford for an expensive skill upgrades, hence saving your money towards your shop.
The exact manipulation depends on the amount of coins you have, but both of them can be extremely handy.
Good savings (lavish parties) vs bad savings (cheap parties)
This is the most interesting property of course, because it is directly related to our goal.
Fact: the saving property of a town does not affect the willingness to save.
Given the above fact and that when you send the hero back under appropriate conditions, the chance of saving is larger than the chance of wasting, going for towns that save more is always a good thing. However, I would say there is no need to push hard to towns with good savings -- the expectation is not going to vary much. Also coins that you didn't save/waste isn't going anywhere -- it stays in your pocket till the next chance of visiting towns.
Just a side note, even in good savings town, the hero typically is not going to save more than 75% of the coins (anything over 50% is rare), so there is no need to worry about leaving with insufficient gold that breaks the cycle.
TD;RL it affects the amount you can save in a town, but it does not affect much in a long run.
The town locations are shifting regularly under the townv2 system. However, there are a few positions where good savings towns are usually there, and they are amazingly close to the original good saving towns' positions: 15ms, 33ms, 67ms and 135ms.
Choosing the right town
The choice of town however, is largely out of your control. First the towns are now shuffled (which wasn't in the past). Secondly it is extremely costly to wait the hero to advance to towns two of three up front -- he is very likely to have health depreciated and health potions running out, then he will go back out of your control.
When he goes back autonomously, he may not sell and save (when his bag is filled below 40%), or even worse he may go back to godville, which is known for likely skill upgrade (this is NOT the same as cheaper/more expensive skills. He is just likely to upgrade if possible), and expensive (not effective) prayers. With these properties, Godville is strictly a BAD place to save money (unless you want temple bonuses which is not that great in terms of assisting the savings goal).
So, in order to avoid autonomous return, players are advised to send him back in red health while he is free. There aren't actually many choices for you -- it's either this town or next town, so as long as you avoid towns that may put your into a poor state after skill purchases you will be fine.
The worst town to enter due to exp conversion. They say Godville is fully neutral when it comes to town properties, but that does not seem true. Heroes are quite likely to purchase skills and pray more [up to 1/3 coins] here, which are both bad for savings.
Festive town with all the good properties. Under the townv2 system, this town is good for savings not just because it is a town of good savings (and lavish parties), but it sits right in front of Godville so that you won't return to Godville as far as 2 miles away from it. This is particularly useful because if you send him back by sail upon quest completion, then he will start a new quest without healing, that he is usually injured. That gives you a very good chance to reach town immediately.
[In fact, the chain is very likely to be broken when you start a quest after sailing. There are many reasons for hero to return early: bad injuries and full lootbag. He is likely to return before 15ms, which is the second town. That leaves you very little choice, esp. when the bag is filled.]
The mysterious moving town with properties amplified. This is particularly important when the town allows good savings/lavish parties. It literally allows hero to save or waste all of their gold. Big gamble and may break the cycle -- but like having saving dungeons, this is worth trying.
Heroes aren't able to enter these two towns on a daily basis in the old days so it makes them somehow special. Much easier now of course. Heroes are still advised to pay a visit there if they have not already done so.
The town name suggested by players, and yet to be discovered. For 4 years already. This is really disappointing and I am here to demand devs to put it in >:(
Unlike towns, the effects last for a whole day, so unless the newspaper updating soon, you will have to cope with these.
- Activables cost 25%
This is of course a good thing - aim to activate important items like sea treasure whenever possible.
- Activables worth as twice/half
Similar to towns with good/bad trading, this does not matter much usually. It becomes slightly more important when you have a sea loot and are deciding to open it or not.
- 70% charge day
Dungeon and sails are now easier. Makes your life easier too.
- Monsters grant artifacts
The player will accumulate loots faster, which puts him faster into the 40% range. The hero will be more likely to enter the waste/save phase during autonomous return to town. Does not matter much during daytime when the hero is closely monitored.
- More likely to lose/destroy/ruin artifacts
No any significant effect. You might be worried that sea loot may be destroyed, but I've never seen that, in contrasts to 10+ times where the sea loot was taken as bait.
- Epic more likely
Epic quest is bad and unwanted as explained. Does not trigger much but you just do not want that.
- All roads lead to Godville
Bad. Damn bad weather.
- Encourages/punishes change personality deepens
Unrelated to savings.
- Encourages/punishes make deeper influences
Unrelated to savings.
- Sending to arena costs 25%
Unrelated to this guide. Arena is not suggested by Saturio since it wastes charges and breaks the coin cycle upon losing a match.
- No skill upgrades
Good that you won't waste coins on skills that day! Just push harder for savings.
- No equipment upgrades
Similar to above but since equipments are not expensive, that does not matter much.
- More efficient prayer
Prayers gives at least 25% more, which is good -- you can safely visit bad prayer towns today.
- Better bingo rewards
You can get 5~10k more from bingo at that day. Not that important but you may make use of that if you used to participate in the bingo game.
- Voice commands more(less) likely to be heard
Lower(higher) costs needed for vcs, but as analyzed above, that does not change the willingness to obey. It is negligible too.
And of course, the most important one:
Heroes and heroines are less likely to spend money in taverns and, if eligible, put into savings instead.
That means the hero will ALWAYS SAVE POST-SELLING.
You should push as hard as possible for savings on that day -- saving above 100k on that day is quite feasible!
- Tribbles are good! They fill up your bag forcing more return with prayers. Tribbles helps by healing the hero, and hungry tribbles are even better because their reproduction rate is faster than the loot drop rate, meaning that you can also fill up your bag faster. They also give coins, which is after all what you need.
Mathematics for mechanics
This is a side talk section: what part of mathematics/statistics is essential for someone to understand the mechanics of Godville, which is basically a black box? Well, we (or our hero) interact with the mechanics (or his world) all the time. That gives us lots of measurements which help us to understand the mechanics.
Do not believe in the so called randomness. Anything with non-zero uncertainty contains randomness. I can flip a coin that shows 99% head and still call it random, it is just not a fair coin. Instead of asking "random or not", we ask "what randomness? Is it uniform randomness, or are there any parameters hidden behind?". And to verify our claim formally, we need statistics, which at the end of the day, is supported by mathematics.
We can reverse engineer the mechanism does not mean we can figure out the codes behind. We cannot give out precise mechanics with exact parameters. What we can do is to set up a model approximating how it works most of the time.
- Investigate and ask question. We want to accelerate progress in Godville. What factors are important if we want to do well? Are there anything we can do to affect these factors? Questions can be pin-pointed to a point where you may found a pattern in it.
- Set models and hypothesis: we find some patterns in the mechanics. Are there any solid description on what is happening there? Can we model that acts as a predictor next time?
- Statistical treatment: to measure how reliable a hypothesis is, we use statistical tools. Common tools include confidence intervals and hypothesis testing, but there are many more...
We give a few examples on how it works.
Example 1. Distribution of treasure location
- Investigation: through countless dungeon trips, heroes found out that the treasure would not be too close to the entrance. It is also known that the treasure will not be too far away from the entrance. It also seems that the treasure is not on the cardinal direction of the entrance.
- Hypothesis: Treasure is in (6,6) diagonal from the entrance?
- Measurement: we collected 3000 dungeon logs and measure the treasure distribution. It turns out that our hypothesis is approximately correct but not fully. The distribution really peaks along the diagonal, not (6,6) but at (5,5). It spreads approximately as a (truncated) 2D-normal distribution centered at (5,5).
- Conclusion: We conclude that the diagonal theory is true with a little tweak. To simplify the model so that the theory can be easily spread out, we usually emphasize the diagonal rule and the point (5,5).
Check User:Saturio for further details on this diagonal rule.
Example 2. Stochastic process - dungeon strategy?
Things often get complicated when we have a stochastic process. i.e., what happens next step depends on decisions made on the previous steps(current step). Stochastic process is extremely complicated and one cannot easily put them into a model. We can however, compare the performance of two algorithms by focusing on a single output parameter.
- Investigation: for whatever reason we want to complete dungeons as fast as possible. Consider two simple strategy: (1) avoid bosses whenever possible and (2) defeat bosses whenever they are on the way to treasure. Which one is better for dungeon speed run?
- Hypothesis: Since I am using strategy (1), the hypothesis should be (1) being faster, while the alternative hypothesis should be (2) being faster. By symmetry that does not really matter.
- Measurement: We cannot really force a scientifically fair experiment as that would be costly and bears the risk of multi suspects. We can however conduct a small scale comparison between two experience heroes running the two sets of strategy. We record the time taken for each dungeon take took to complete, and make sure that the strategy is executed consistently.
- Conclusion: And yes, avoiding bosses is faster if you want to speedrun a dungeon.
Example 3: Unknown parameters - getting famous on newspaper?
In previous examples, there are clear indication on what parameters we should consider as independent variable (input) and dependent variable (output). This is sadly not always the case in a more general setup.
In this example, we shall look at an example where we hope that there is no hidden parameter behind. Here we want to investigate how frequent a hero will have his name mentioned on the newspaper.
- Investigation: Honorable mention only happens for heroes in top 200 in one of the pantheon is picked.
- Hypothesis: Heroes are picked uniformly across the top 200, and across all pantheons?
- Measurement: First of all, we have to make a extra assumption that the distribution is time-independent. i.e., the chance of getting picked will not be affected by the previous picks (and the time itself). The main reason is that we only have two observations per day, and that is simply not enough to make any conclusion should the process is time-dependent.
Using the hypothesis, we calculate the predicted probability for each players and measure the actual count over a long period of time. That gives us a measured proportion. On the other hand, using the top-200 counts we can calculate the expected proportion for each player.
We now have two distributions and we want to check if they are equal, so what we are going to use is the Kolmogorov–Smirnov test. Although we have a categorical domain (which does not take values in numbers), we can map the categories to the real line as a discrete distribution then to a continuous distribution (via kernel density estimation(KDE)). By such we can compare the two distributions.
- Conclusion: and yes. By statistics we confirm our belief that the probability really depends (solely) on how many pantheon top-200 you have.
But the story does not end here...
Example 4: Unknown parameters - traders' orders?
What if you suspect that the distribution is actually dependent of some unknown parameter? Well, the goal is to figure out what the parameter is.
You may notice that traders share an extra slot on the newspaper saying that a certain hero is looking for an item. This is exclusive to traders and they can spend 50% GP to order one of the three given items. Among all the traders who ordered something, the newspaper editor would choose one of the orders and put it on the newspaper.
The parameters on the likelihood of getting onto the newspaper is unknown, but it is absolutely not uniform randomness.
Whaleness? Age of account? If you look into the frequency count, you can see something REALLY strange and does not fit any simple theory (if you know the top players well enough). But this is getting too deep and I shall not talk about that here...
But the procedure is kind of straightforward. If you suspect that the distribution depends on some particular parameter, you may group the players according to that parameter and conduct a test on the whether their likelihood of getting the order delivered being the same.
The difficulty here is that most of the parameters can not be publicly measured...How often does a particular player actually spend 50% for the order? How to measure the whaleness of a player? Unability to obtain complete data has always been a big challenge for statistics.
V1.0 17/02/19: The initial version
V1.1 24/02/19: Formatting revamped
V1.5 19/06/19: Adding new section: mathematics in mechanics
- Uniform distribution, discrete or continuous, over a given domain. The distribution solely depends on the domain and has no extra parameters.