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Holo

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Holo

The Holo tower multiplies the damage of hitscan shots and projectiles -- including those of towers -- that pass through it. Multiple Holo towers can be aligned in order to amplify one shot multiple times, but the damage increase of each successive Holo diminishes significantly. The Holo tower was introduced in the September 26, 2011 update. As of the October 2012 update, projectiles can no longer traverse the Holo. However, this is a bug and will most likely be fixed on the next bug patch.

Because the Amp Field's damage multiplier is applied after the Holo tower's, the two combined can result in staggering damage values; a level 6 Sniper bullet that is boosted by two level 6 Holo towers and a level 6 Amp Field can inflict approximately 37 000 damage.

Attributes Edit

Picture Holo1 Holo2 Holo3 Holo4 Holo5 Holo6
Level 1 2 3 4 5 6
Damage increase 28% 56% 84% 112% 140% 168%
Buy/upgrade price 10 20 40 80 160 320
Total cost 10 30 70 150 310 630
Selling price 8 23 53 113 233 473

Damage increase Edit

For each successive Holo tower that a shot traverses, the effectiveness of the next Holo tower is halved relative to its original damage increase. For example, the total damage increase for a shot that traverses a level 6 Holo (168%), a level 4 (112%) and a level 5 (140%) in that order would be

168% + \frac12 \cdot 112% + \frac14 \cdot 140% = 259%.

Hence, a shot that traverses a row of several Holo towers with the highest-level Holo in front would inflict more damage than a shot that traverses the same row backwards.

In more rigorous terms, the total damage increase from multiple Holo towers is computed with the following equation:

\mbox{Damage increase} = 2\sum_{i=1}^n h_i \cdot 2^{-i}

where hi is the damage increase of the ith Holo tower that the shot traverses, and n is the number of Holo towers that the shot traverses.

Using this equation, the maximum damage increase from a given number of Holo towers can be found by setting each hi to 168%, and then the equation can be simplified to:

\mbox{Max damage increase} = 336% \cdot (1 - 2^{-n})
n 1 2 3 4 5 6 7 8 9
Max damage increase* 168% 252% 294% 315% 326% 331% 333% 335% 335%

* Rounded to the nearest percentage point.

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