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.

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.