In this post I will go over the math for why the hound is not overpowered as a tanking troop. I guarantee you will disagree with my method. I guarantee you will disagree with many of the "estimates" and things that I leave out - but there is no easy way to calculate what I am going to calculate, so hear me out:

If youdon't want to readthe entire post, read the paragraph before the conclusion and the conclusion and skip the math.

Otherwise, please read/skimthe entire postso that you can know the extent of my calculations and so that you won't post that I left X or Y out when I didn't. Of course I didn't include everything, but I did include more than just a comparison of HP.

Note: All calculations are made with max troops and defenses.

We can find out whether or not the hound is balanced by comparing it to a similar troop, the golem. No one believes the golem is OP, yet these two troops serve almost identical purposes; the only difference is that one is for ground and one is for air.

Let's start by comparing Lava Hound and Golem HPs. Lava Hounds have 6700, whereas golems have 6300 and two golemites with 1260 HP each, meaning that each golem essentially has 8820 HP.

From the start, we must include one critical difference in ground and air attacks: the seeking air mine. TH10s have 5 seeking air mines, each dealing 2100 damage. It is safe to assume that all air mines will hit hounds, because destroying hounds quickly is an important factor in base design. Since a common number of hounds to bring is 4, this averages to 2625 damage per hound.

Thus, after the air mine, the hound has 3975 HP.

Now, we move to defenses. Excluding X-Bows from the calculation due to their dual nature, and assuming infernoes are set to multi-target, here is the total DPS of all defenses of a max TH10. Using this number, I will calculate how "tanky" each unit is. While you question my use of totaling all DPS, keep in mind that all defenses, other than the x-bow (which we are excluding from the calculation) wizard tower and tesla (both of which can hit ground and air), have about the same range. Thus, range does not play a great role in effective DPS, and if all buildings have about the same range, their DPS can be added together to make an overall DPS of the base.

Buildings which can target both ground and air:

1) Archer Tower: 7 * 98 = 686 DPS

2) Wizard Tower: 4 * 48 = 192 DPS

3) Inferno Tower: 2 * 42 = 84 DPS

4) Tesla: 4 * 99 = 396 DPS

The air defense:

4 * 320 = 1280 DPS

Buildings which can only target ground:

1) Cannon: 6 * 98 = 588 DPS

2) Mortar: 4 * 13 = 52 DPS

Thus, the total DPS for air troops is 2638 DPS. The total DPS for ground troops is 1998 DPS.

A lava hound, with 3975 HP, "scores" 1.507 (3875/2638). This means that it will last 1.507 seconds under fire.

A golem, with 8820 HP, "scores" 4.414.

Now, moving to housing space.

Unquestionably, both units cost 30 housing space. But this is not a complete estimate. In order to get closer to the "true" housing space of each unit, we must consider the hound's pups and the walls which will affect the golem.

Lava Pups: Each pup has 35 DPS and 50 HP. Each minion has 54 HP and 84 DPS. Taking the geometric mean of 35/54 and 50/84, we get 0.621. This means that each pup is worth approximately 0.621 of a minion.

A hound spawns 12 pups, and for simplicity's sake let's assume that 8 survive. This means that 4.968 minions are spawned by the hound, accounting for 9.936 more housing space. Thus, the hound's housing space as a tank is 20.064.

Golem: In order for a golem to function properly, one must bring wall breakers. An estimate of 12 wall breakers for 3 golems is reasonable, so with a golem comes a need to bring 8 more housing space. The golem's total housing space must then be 38.

EDIT: in order for golem to equalize with the hound, 14 wall breakers must be used with each golem. This is more than enough to negate walls.

Now, we will calculate the overall "tankiness per housing space" of each troop. The hound scored 1.507, meaning that its tankiness per housing space is 0.075. The golem scored 4.414, meaning that its tankiness per housing space is 0.116.

Conclusion

It is obvious from the data that hounds are less tanky than golems. Thus, the troop is not overpowered as a tank. I had initially set out to prove with math that the houndwasoverpowered, but I had proved myself wrong and convinced myself that the hound is not in fact overpowered.

Because hounds as a troop are not overpowered, I have come to the conclusion that the combination of balloons and hounds is overpowered. If hounds are not overpowered, then either balloons are overpowered or the combination is overpowered. Balloons are not overpowered; they were there before hounds and no one complained. Therefore, the combination is overpowered and the problem is not in the hound itself, but in this combination of balloons and hounds together which is OP.

So far all the examples of hounds being OP are examples of lava hounds and balloons together being OP. I will take a strong stance on this as because the math shows that hounds aren't OP as a troop, their effectiveness when used in conjunction with balloons is OP, so that can only mean that the combination and not the troop is OP.

If you say that hounds, because they create an overpowered combination, are therefore OP, then you are not considering the scenario where one adds hounds to a strategy that is not balloonion: for example, mass dragons. Because hounds as a troop are not OP, nerfing hounds would nerf combinations such as hound/drag, and would thus be unfair because these nerfs are only targeted as lavaloonion.