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Tentatively (needs more testing):
Tentatively (needs more testing):
* Encumbrance allowance (A): 4 x Strength
* Encumbrance allowance (A): 4 x Strength (Wong FAQ, not verified)
* Encumbrance (E) is calculated as a weighted sum: the listed weight is multipled by the number of squares of the item.  I'm not sure how items in the hand work yet, tentatively assuming same as elsewhere.  Contrary to appearances, each armor unit only has one square.
* Encumbrance (E) is calculated as a weighted sum (?): the listed weight is multipled by the number of squares of the item.  I'm not sure how items in the hand work yet, tentatively assuming same as elsewhere.  Contrary to appearances, each armor unit only has one square.
** Ahem...Apoc'd comes through.  There is a total encumbrance field in the Battlescape save.


The scaling factor for actual speed is then the square root of (A-E)/A.  Multiply this by maximum speed, then "do something" (both truncation and rounding are sometimes off by one).
The scaling factor for actual speed is then the square root of (A-E)/A.  Multiply this by maximum speed, then "do something" (both truncation and rounding are sometimes off by one).
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RT speed is simply INT(TB speed/8).
RT speed is simply INT(TB speed/8).
Our interest in this exercise is that in TB the following rules are used:
* aimed fire TU cost is INT((36/RoF)% of maximum TU at start of turn)
** if using Apoc'd, just read off the % from the weapon stats: "Fire Delay".  RoF is calculated in-game from this.
* snap fire TU cost is INT(aimed fire/2)
* auto fire TU cost is INT(snap fire/2)
That is: the cutpoint from 7 to 8 aimed fire TU is incredibly important.  The practical cases that you might actually see with naive loadouts are:
* M4000 transitions at 67 TU.
* The Lawpistol transitions at 45 TU


=== Some examples courtesy of Captain Midnight's editor ===
=== Some examples courtesy of Captain Midnight's editor ===
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This checks in as 85 encumbrance; calculated MP is 66.58, in-game 67.  Oops.  Calculated/actual aimed shot with a Marsec rifle at 67 MP is 8 MP, with corresponding autofire 2 MP/shot.  We'd like 66 MP, for a calculated/actual aimed shot with a Marsec rifle of 7 MP, with corresponding autofire 1 MP/shot.
This checks in as 85 encumbrance; calculated MP is 66.58, in-game 67.  Oops.  Calculated/actual aimed shot with a Marsec rifle at 67 MP is 8 MP, with corresponding autofire 2 MP/shot.  We'd like 66 MP, for a calculated/actual aimed shot with a Marsec rifle of 7 MP, with corresponding autofire 1 MP/shot.
 
* Apoc'd says 73, for calculated speed 69.48.... Oops.
<table {{StdCenterTable}}>
* The starting MP formula may not even be nonstrictly monotone increasing in STR and SPD.  Further investigation warranted.
<tr {{StdDescTable_Heading}}><th align="left">Weight</th><th width="75">MP</th><th width="75">Calculated&nbsp;MP</th></tr>
<tr align=center><td>85</td><td>67</td><td>66.58</td></tr>
<tr align=center><td>86</td><td>66</td><td>66.33</td></tr>
<tr align=center><td>87</td><td>66</td><td>66.09</td></tr>
<tr align=center><td>88</td><td>66</td><td>65.84</td></tr>
<tr align=center><td>89</td><td>65</td><td>65.59</td></tr>
</table>
 
So: the empirical formula is not what Apocalypse actually uses, as rounding the calculated MP at weight 89 gives 66 MP, not 65 MP.
 
Even worse (<i>in vivo</i>):
<table {{StdCenterTable}}>
<tr {{StdDescTable_Heading}}><th align="left">Speed</th><th align="left">Strength</th><th align="left">Weight</th><th width="75">MP</th><th width="75">Calculated&nbsp;MP</th></tr>
<tr align=center><td>73</td><td>44</td><td>85</td><td>51</td><td>52.49</td></tr>
</table>
 
=== Quest for the Real Formula ===
 
Consider the thresholds as "pre-squared":
* INT(85*85*135/220) = 4,433
* INT(85*85*134/220) = 4,400
* INT(85*85*132/220) = 4,335
* INT(85*85*131/220) = 4,302
 
It turns out that the truncated arithmetic average of two squares in sequence, is their geometric average.  So neither is being used by Apocalypse (65&middot;66 = 4290, so 89 encumbrance would give 66 MP in this scheme rather than 65 MP).
 
Apocalypse is not using either the geometric or arithmetic averages of the squares as the threshold (both check in around 4,290 for 65&sup2; and 66&sup2;, which would give 66MP rather than 65MP.  Inverting Apocalypse's distance function doesn't work either: INT(85*135/220)=52, calculated MP would be 69 rather than 67.


[[Category: Apocalypse]]
[[Category: Apocalypse]]
[[Category: Agents (Apocalypse)]]
[[Category: Agents (Apocalypse)]]

Revision as of 19:14, 28 December 2009

Empirical approximation

Tentatively (needs more testing):

  • Encumbrance allowance (A): 4 x Strength (Wong FAQ, not verified)
  • Encumbrance (E) is calculated as a weighted sum (?): the listed weight is multipled by the number of squares of the item. I'm not sure how items in the hand work yet, tentatively assuming same as elsewhere. Contrary to appearances, each armor unit only has one square.
    • Ahem...Apoc'd comes through. There is a total encumbrance field in the Battlescape save.

The scaling factor for actual speed is then the square root of (A-E)/A. Multiply this by maximum speed, then "do something" (both truncation and rounding are sometimes off by one).

The real question: how is the square root being approximated with integer math?

RT speed is simply INT(TB speed/8).

Our interest in this exercise is that in TB the following rules are used:

  • aimed fire TU cost is INT((36/RoF)% of maximum TU at start of turn)
    • if using Apoc'd, just read off the % from the weapon stats: "Fire Delay". RoF is calculated in-game from this.
  • snap fire TU cost is INT(aimed fire/2)
  • auto fire TU cost is INT(snap fire/2)

That is: the cutpoint from 7 to 8 aimed fire TU is incredibly important. The practical cases that you might actually see with naive loadouts are:

  • M4000 transitions at 67 TU.
  • The Lawpistol transitions at 45 TU

Some examples courtesy of Captain Midnight's editor

For STR 55, Speed 85 (the theoretical maximum starting STR and Speed for a human):

  • Full suit of Megapol armor: 14+12+10+10+9 = 55 weight/encumbrance
  • Medikit: weight 3 · 4 squares = 12 encumbrance
  • Marsec rifle: weight/encumbrance 7
  • 3 clips: weight/encumbrance 1 each, 3 total (in-game the rifle is weight 8 as the loaded clip counts)
  • 2 frag grenades, 2 gas grenades: 2 weight/encumbrance each, 8 total

This checks in as 85 encumbrance; calculated MP is 66.58, in-game 67. Oops. Calculated/actual aimed shot with a Marsec rifle at 67 MP is 8 MP, with corresponding autofire 2 MP/shot. We'd like 66 MP, for a calculated/actual aimed shot with a Marsec rifle of 7 MP, with corresponding autofire 1 MP/shot.

  • Apoc'd says 73, for calculated speed 69.48.... Oops.
  • The starting MP formula may not even be nonstrictly monotone increasing in STR and SPD. Further investigation warranted.
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