Tower damage

[latexpage] Today Dodging Rain posted an awesome spreadsheet, showing a comparison of all towers at level 99. A must read for the experienced Mazebert TD player and a good inspiration for your next trip to Mazebert land ;-) You find the spreadsheet here. Also, there where some questions about the underlying mechanics to calculate the damage of a tower. Hopefully I can shed some light on it with this post.

The basic idea

Alright! The basic idea: When you have n towers on the map, and the sum of their levels is >= the level of the current wave, your towers should be able to clear the wave. This only holds true for the linear part of the creep hitpoint formula. With higher levels of creep waves this linear part becomes more and more neglectable. Also the levelling of your towers will slow down. You need to find other sources to boost your damage and counter the increasing amount of hitpoints.

The damage equation

The final damage equation, where x is the current tower level. Note that the tower level is passed to the linear hitpoint formula \begin{equation} d(x) = 1 + m_{strength} m_{range} m_{basecooldown} \frac{h_{linear(x)}}{h_{reduction}} \end{equation} The strength modifier is a custom factor for every tower, to account for the individual tower skills. When towers are nerfed/buffed this is the first number to look at, unless abilities are completely broken in terms of balancing. The range modifier is a function depending on the tower's range \begin{equation} m_{range}(r) = \frac{3}{2r+1} \end{equation} The linear factor of creep hitpoints, where x is the current round \begin{equation} h_{linear}(x) = 64x + 256 \end{equation} A magic number added to the formula, so that the basic idea works. Note that this number is custom-made for the current layout of the map! \begin{equation} h_{reduction} = 12 \end{equation}