View Full Version : Gem Mathematics

Tony Centers
07-09-2012, 11:18 AM
The mathematics behind Kingdom Age has always intrigued me, so I decided to take a look at the relationship between the cost in gems for an indestructible unit and the total attack + defense points for that unit.

My process was simple. I looked at all of the indestructible units currently available, and found 32 of them. I graphed the cost in gems on the x-axis and the total attack+defense points on the y-axis. I then let Excel fit a curve to those points. What that curve gives me is a way to estimate the approximate gem cost for any given indestructible unit. Here is the formula that Excel gave me ...

gems = 0.1736 x (total attack+defense points) 1.3724

I'll give you an example of how the formula gets used. If the total attack+defense points for a new limited edition unit are 125, I would take 125 to the power 1.3724 (which equals 754.74), and take that times 0.1736, which gives me about 131. This means that the unit should cost about 131 gems. If it costs a lot less than that, it is an opportunity to acquire indestructible points cheaper than other indestructible units. If it costs a lot more than that, the opposite would be true. I'm guessing Funzio has a more complex approach to determining gem cost, but an approimation is all I really need for the level of analysis that I do.

Let's use this analysis on the chests. Right now the three "common" items have total attack+defense points of 52, 51, and 50. The approximate gem cost of those three units should be about 39, 38, and 37. The three "uncommon" units have total points of 145, 150, and 140, with an equivalent approximate gem cost of 161, 168, and 153. The three "rares" have total points of 227, 119, 143 with an approximate gem cost of 707, 339, and 321.

If you buy a three-pack and get three commons, you spent 175 gems for approximately 115 gems worth of value. If you get two commons and one uncommon, the worst combination of items would give you an approximate gem value of 229.

Let's look at one other example ... the first auction-style event. There has been a lot of discussion around how foolish the heavy gem spenders were for chasing the top prize. If we apply the approximation formula to the six prizes that were awarded for finishing in the top 50, the gem value of those six prizes is approximately 4,200 gems. If it took 7,500 gems to get into the top 50, that suggests that the value to those players for the bonus, the ability to upgrade two buildings at the same time, was about 3,300 gems, if they were viewing this purely on the economics. Of course, this ignores the value of all of the honor and gold that they received from opens that didn't give them the red egg. If you were given the opportunity to purchase the ability to upgrade two buildings at once, would you pay 3,300 gems for it? If you use gems to accelerate the build time, 3,300 gems buys you 330 hours of build time, which is a little less than two weeks. For some, this combination of indestructible units and build time is worth it. For others, it isn't. To each their own.

Sorry the the length of the post. I couldn't think of a better way to explain the process and the results.

07-09-2012, 11:34 AM
Nice analysis!!!!!!!!!!

07-09-2012, 01:08 PM
Thumbs up!

07-09-2012, 02:35 PM
Well written!

07-09-2012, 02:44 PM
Only thing I would change is subtract the attack and defence of the unit it is replacing.

For example if you are currently using 20/15 units and you have the option of buying of buying 33/21 at 45 gems or 90/94 at 245

Without subtracting the replaced units you get 11 x 33/21 for a gain of 363/231 vs. 2 x 90/94 for a gain of 180/188 from 500 gems, so the cheaper units always seem better however once you subtract the replaced units the true gain is actually 143/66 for the cheaper units vs 140/158 of the more expensive units.

Then obviously the better your replaced units get the less is gained by cheaper units

07-09-2012, 02:48 PM
Only thing I would change is subtract the attack and defence of the unit it is replacing.

a good defence [sic] is a good offence. [re-sic]

07-09-2012, 06:46 PM
Good work there red 9,9,14,15

07-09-2012, 06:53 PM
Figure these odds red. Told ya I had 10 with 14 hrs left and was happy and would move to the free option as getting 15 was not in the cards. Opened 4 with the free option, one sorry and three eggs to get to13, so I change back to hold option. Get 14 on the last one, go two clicks into ot and get 15. Shut game down after that so 9 ,9,14,15 in these four recent quests for me so I'm not complaining

Tony Centers
07-19-2012, 12:25 PM
I keep coming back to this, to see if I can get a better handle on their approach. I noticed a pattern, and while I haven't solved the riddle, I'm closer. It's apparent from the numbers that they price attack+defense points differently depending on whether the unit is available to everyone or only available to those who've upgraded a certain building to a certain level. When you split the gem units into those two groups, you get a better mathematical fit for each estimation formula than you do in aggregate ... a clear sign that they belong in separate groups for analysis purposes.

FYI, the gem units available from the unit buildings are a better value than the LEs or the "generically available" gem units. It is still the case, though, that the indestructible units from the chests give the highest combined attack+defense for the cost. However, as procsyzarc points out in an earlier post, once you get your armies to a certain level, the "common" chest units may be of no value at all, which means that even though from a pure mathematical sense they are the best value, from an economic sense they are a bad investment (because they will never make it into battle or be used for defense).