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    Damage Calculation Guide by e.cesare

    Version: 1.0 | Updated: 01/04/17 | Search Guide | Bookmark Guide

    FANTASY DEFENSE
    Max Damage Strategy Guide
    Version 1.0
    Copyright 2011-2016 Kelvin Liu
    
    V1.0 December 28, 2016
    -Added "Going Beyond DPSG" section describing advanced strategies
    -Added "Introduction" section
    -Minor fixes: guide name, description, DFC>DPSG, formatting
    
    V0.2 January 19, 2011
    -Corrected attack speeds using data
    -Updated DPS using new attack speeds
    
    V0.1 January 19, 2011
    -Started guide
    
    =======================
    Introduction
    =======================
    
    The table below shows the DPS (Damage per Second) and the DPSG (Damage per
    Second per Gold) of the classes available in Fantasy Defense. A class with
    higher DPS is stronger, but that still doesn't mean it's better. Instead
    you should look at DPSG, which is the bang for your buck. If you want the
    simplest strategy, just build units with the highest Damage per Second per
    Gold (see the table). If you want the advanced strategy, keep reading.
    
    The main purpose of this guide is to present the statistics I've collected,
    not to cover comprehensive gameplay. The strategies presented here are
    simple ones that work, but you may know better ones. Feel free to email me
    about them. There's also no guarantee that I've covered all the factors
    that make units better or worse. My hope is that these numbers and
    discussions help improve your understanding of tower defense strategy.
    
    =======================
    Damage per Second (DPS)
    =======================
    
    DPS is used to compare the strength of units because comparing damage alone
    isn't useful. Why? Because a 200-damage unit is actually worse than a 100-
    damage unit that fires three times as fast. So we calculate DPS by dividing
    attack damage by the time it takes to attack, giving us the average amount
    of damage dealt each second. A minor detail to remember is that a unit that
    deals infinite damage is no better than a 1,000,000-damage unit. Since
    overkill damage does nothing, it counts against DPS, so the faster unit
    with same DPS is always technically stronger. We won't go further into this
    because it's hard measure and not that important.
    
    If you're an advanced player, you know that DPS (and even DPSG) are only
    half the story. DPS doesn't take into account unit placement, the
    usefulness of Range/Slowing/Stunning, or the chance to do extra damage with
    Multishot/Splash/Pierce. I tried my best to fix this by adjusting the DPS
    (eg. by doubling the DPS of Blaster assuming it hits two enemies on
    average), but of course this really depends on the level and unit
    placement. I discuss advanced strategies for using DPSC to compare classes
    in the "Going Beyond DPSG" section.
    
    =================================
    Damage per Second per Gold (DPSG)
    =================================
    
    DPSG measures how much damage you're getting for gold spent, so the basic
    strategy is to build units with the highest DPSG. So build only Holy Eyes
    (or Warriors if the enemies have less than 400 HP) and don't upgrade. This
    strategy might not always work, so see the next section (Going Beyond DPSG)
    for the advanced strategy.
    
    DPSG is a better way to compare classes than DPS, for the same reason that
    comparing DPS is better than just Damage. You can build three Level 3
    Wizards (831 total DPS) for the price of one Sky Arrow (280 total DPS) and
    get more than double the DPS. So DPS isn't everything. On the other hand,
    if there isn't enough space to build three Level 3 Wizards, then you DO
    want to pick the unit with higher DPS.
    
    =================
    Going Beyond DPSG
    =================
    
    Slowing, Stunning, and Range, along with good unit placement all improve
    the effectiveness of units. A high DPSG unit is useless if it's too far
    away to hit enemies. The amount of time a unit spends doing nothing hurts
    its DPSG, so increasing Range and putting the unit in a better spot help.
    Slowing and Stunning help in the same way by keeping the enemies in range
    of your towers. If you use Slowing and Stunning, you should always group
    your other units around these "chokepoints" to improve their "effective"
    DPSG.
    
    This effective DPSG changes depending on the unit's range, location, enemy
    speed, etc., so there's no way to measure it overall. I'll give you two
    ways to measure it yourself. Here's the hard way: Look at a particular unit
    in a particular spot on a particular level and count (in your head) how
    many seconds it actually spends attacking. Then multiply this by the DPSG 
    Damage per Second per Gold) to get DPGL (Damage per Gold for the level).
    Short of doing a bunch of math, DPGL is the best possible way to measure
    unit effectiveness.
    
    Now let me explain the much easier but less accurate way: The greater
    length of path (taken by the enemies) that the unit can reach, the longer
    it'll stay active. Since spots that can hit two (or more) different enemy
    paths essentially multiplies your active time by two (or more), that ends
    up being the most important factor. Hairpin loops (spots the path doubles
    back on itself) count too. (So it's much more important to use range to
    reach more paths or hairpins, than just hitting enemies earlier.) So count
    the total number of paths or hairpins in range and multiply by DPSG to get
    DPGL^ (relative DPGL). DPGL^ is very different from DPGL, but luckily you
    don't need DPGL if you just want to compare which unit is better!
    
    For those interested in the math, here's the formula:
    multiplier = num_paths_or_hairpins x (length_wave + length_range) / speed
    The actual amount of time spent attacking is related to the number of paths
    or hairpins, the length of the wave (total distance, let's say in squares,
    from the first to last enemy), the length of path covered by the unit's
    range (in squares), and the speed of the enemies (in squares per second).
    Since length_range is very small compared to length_wave, we can ignore
    it, giving us:
    multiplier ~= num_paths_or_hairpins x length_wave / speed
    Now, since length_wave and speed are going to be the same for every unit
    (except Slowing or Stunning, to some extent), and we just care about
    comparing the units, we can just divide those out. This leaves us with
    multiplier ~= num_paths_or_hairpins, like we discussed above!
    
    In the table below, I already adjusted DPSG to try and include the value of
    units with special effects (Warlord, Brandisher, Splatter, Holy Eye,
    Sorceress, Blaster, Ice Mage). But these measurements change from stage to
    stage. For example, I assumed Blaster's Splash damage would hit two enemies
    on average, so I multiplied DPSG by two. If you're playing a stage with
    lots of enemies clumped together, maybe you multiply my DPSG by three or
    four instead (and then divide by two because I had already multiplied by
    two).
    
    Now for the strategy: Just always build the unit in the spot that will give
    you the highest DPGL^. Remember the easy way:
    DPGL^ = num_paths_or_hairpins x DPSG (from the table)
    This is much easier than it sounds. Usually it just means putting Holy Eye
    or Ice Mage (if you need range to reach multiple paths or hairpins), or
    Brandisher. If you've made it this far, congratulations! Now you know a
    sure-fire way to build better units. It isn't perfect (since it works
    poorly for Slowing/Stunning, and doesn't consider armor, overkill, and
    other unpredictable factors), but it's a good start.
    
    ==============
    The DPSG Table
    ==============
    
    This table lists the stats for every tower class at each upgrade level.
    Remember that you don't have to upgrade to level 3 to class change. Attack,
    Speed, Range, and Gold (cost) are already given to you in-game. Now, I
    calculated an approximate DPS (damage per second) for each class/level
    taking into account special effects. From this, I also calculated the DPSG
    (damage per second per gold).
    
    You can use this table to find the highest-damaging or most cost-effective
    unit.
    
    cClass           Level   ATT   SPD   RNG   Gold   DPS    DPSG
    ========================================================================
    WARRIOR           1     130   255   100   300    138    0.92
                      2     210   270   104   500    241    0.96
                      3     280   285   108   750    347    0.92
    KNIGHT            1     230   350   108   900    406    0.90
                      2     300   305   112   1400   413    0.59
                      3     380   320   116   2200   567    0.52
    WARLORD           1     450   265   115   2100   755    0.72
    splash damage     2     600   275   119   2700   1059   0.78
    to an area<3x3    3     750   285   124   3900   1393   0.71
    BRANDISHER        1     140   240   111   500    166    0.66
    chance to stop    2     220   255   115   1250   281    0.45
    enemy briefly     3     310   270   119   2250   427    0.38
    ------------------------------------------------------------------------
    ARCHER            1     80    250   230   300    83     0.55
                      2     130   265   260   500    145    0.58
                      3     200   280   280   750    241    0.64
    SPLATTER          1     120   250   250   900    312    0.69
    shoots 3 at       2     180   265   265   1400   503    0.72
    once              3     250   280   280   2200   754    0.69
    SKY ARROW         1     280   290   360   2100   356    0.34
                      2     360   305   400   2700   496    0.37
                      3     450   320   440   3900   672    0.34
    HOLY EYE          1     100   105   220   500    258    1.03
    damages even      2     200   125   240   1250   553    0.88
    after hit         3     300   145   260   2250   891    0.79
    ------------------------------------------------------------------------
    WIZARD            1     120   225   210   300    111    0.74
                      2     180   240   230   500    178    0.71
                      3     260   255   240   750    277    0.74
    SORCERESS         1     240   190   240   900    312    0.69
    attacks through   2     300   210   255   1400   426    0.62
    enemies           3     380   230   270   2200   592    0.54
    BLASTER           1     320   250   280   2100   665    0.63
    splash damage     2     420   265   290   2700   939    0.70
    to an area>3x3    3     550   275   300   3900   1294   0.66
    ICE MAGE          1     140   250   200   500    174    0.70
    chance to slow    2     220   270   230   1250   303    0.48
    to 1/2 speed      3     300   285   260   2250   446    0.40
    
    Note certain units have additional effects (I tried to compensate for these
    when calculating DPS):
    WARLORD - does splash damage to an area slightly smaller than a 3x3 square
              (1.5x DPS)
    BRANDISHER - has about 50% chance of "stunning" the enemy when hit,
                 stopping it in its tracks temporarily (1.2x DPS)
    SPLATTER - shoots 3 arrows at a time, hitting any enemies in range; thus 3x
               DPS unless there aren't enough enemies
    HOLY EYE - marks the enemy on hit; the enemy keeps taking damage for a
               while; this does about 4x DPS
    SORCERESS - pierces the enemy, hitting any enemies behind it (1.5x DPS)
    BLASTER - does splash damage to an area slightly larger than a 3x3 square
              (2x DPS)
    ICE MAGE - has a chance of "slowing" the enemy to 1/2 speed for a while
               (1.2x DPS)
    
    =======
    Credits
    =======
    
    I will credit you if you contribute material, corrections, suggestions, or
    anything else to this guide.
    
    Currently, credit goes to:
    -The GameFAQs forum users for pointing out that Ice Mage and Brandisher are
     great despite low DPS
    -GameFAQs, for hosting this guide
    -And you, for reading this guide
    
    All trademarks and copyrights contained in this document are owned by their
    respective trademark and copyright holders. This may be not be reproduced
    under any circumstances except for personal, private use. This guide may
    not be placed on any web site or otherwise distributed publicly without
    advance written permission. Use of this guide on any other web site or as a
    part of any public display is strictly prohibited, and a violation of
    copyright.
    
    The following websites have express permission to use this guide:
    http://www.gamefaqs.com
    

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