Spode's Formula
Be advised that this formula is incorrect and this page do not have other use than historical interest for curiosity. For a correct formula, see Sophawa's Formula |
This formula (created by Spode ) is used to calculate a very accurate estimate of the remaining time your hero will take to finish their Temple. It assumes that the two most important factors are brick gain rate by quests and other random events, and brick gain rate by Arena duel wins. Rate of arena duel wins is extremely important as some players may be very active in the arena and gain bricks many more times faster than other players. For example, someone who achieves 60 wins and 2 losses in 2 months would complete their temple in a significantly less time than a normal player since their history shows that they participate in arena duels a lot and by their method (whatever it may be) have a high chance of winning and thus gaining a brick. Essentially, brick gain by random events is considered highly variable and random (as the name implies) and brick gain by arena duels is considered mostly constant since it is controllable by the player (if you wanted to prove this formulas prediction wrong, you could just win more arena duels, but due to factoring in duel wins, if you then tried to calculate the remaining time with the formula after this, it would not be fooled since it now has extra data and is therefore more accurate). Skirmishes however are not considered but this will be dealt with later in this article.
To summarise, this formula takes account of: random brick gain, [indirectly] players activity on Godville (which affects random brick gain), players activity in the arena, players skill in Arena duels.
If your hero has never duelled before, this formula will not work and you must use Sophawa's Formula instead.
Derivation
First of all, let us calculate the rate at which a hero gains bricks from quests and other random events, not including bricks gained from arena duel wins.
Where A is the age of the hero, T is the percentage of temple completion and W is the number of wins. The number of wins is divided by ten since one win will reward one gold brick and one gold brick equals 0.1 percent of temple completion. We must have conservation of units. The answer from this formula will therefore be measured in temple completion percentage per unit of time used.
Now we need to calculate the rate at which a hero duels. This is the age over the total number of duels as given by this formula:
Where L is the number of duel losses. Notice the total duels is divided by ten to conserve units. The answer from this formula is measured in duels per unit of time used. However, only a certain amount of these duels per unit of time will reward with a gold brick. This amount can be gained from the fraction of wins over total duels. Therefore, the players history is taken into account. This is the fraction:
Now we must multiply the rate of duels with this fraction to give the final rate of duel wins.
Simplified:
Now to get the total brick gain rate we add the two main rates together:
This rate is measured in temple completion percentage per unit of time so if we want to know how long it will take the hero to complete the temple we must use this formula:
However the hero has already taken some time and thus completed some temple so we must subtract the hero's age from this to reach the final formula:
Renormalisation is now needed.
which can be slightly simplified to our final version:
Notice that k is equal to the proper total brick gain rate.
Advantages & Disadvantages
The formula has two main problems which are theoretically unsolvable currently:
- It assumes that all the different rates are constant and not in fact changing.
- The age of a hero is only ever approximate.
The only other potential problem comes in the form of skirmishes. In these types of duels, no gold brick is gained from winning yet the win or loss is still counted in the formula. This is not believed to be a problem since the number of losses and therefore the total number of duels is factored in, but mainly because skirmishes occur so infrequently that they are rare impurities in the win/loss count. This however could be a problem for players who have in fact been through a significant number of skirmishes. No problem is known yet. As for gold bricks gained from coin smelting, this is considered to be a part of the rate of brick gain by quests and other random events since the rate at which a hero gains coins is random.
It is also worth noting that the formula is inherently more accurate for older heroes due to more reliable data having been collected because there is a slight inaccuracy in the rate of total duel participation since heroes can only duel when they reach a certain level (which is reasonably low so this is not deemed too much of a problem).
Despite these niggles, the formula is currently the most precise we have of its purpose. All others so far only deal with the total brick gain rate and are therefore very fuzzy and do not allow for those who participate in the pantheon of gladiatorship, which is frankly a lot of people.
Possible future improvements
- Factoring in the number of deaths per unit of time would make the formula more accurate since every death resets the current quest progress to 50% and therefore slows down the rate of brick gain from quests significantly. The rate of deaths is not the same for all heroes as generally, evil heroes tend to die more and a lot of other factors that control the rate of death like this would then be factored in automatically.