I am taking the encounter rate into consideration when I reevaluate the * rating I have given for each area, but not mathematically; I'm not fitting it into the equasion, I'm not exactly sure how.
Since the higher the encounter rate the longer between encounters, it could just be divided by the total: ( [equation] / (formation_encounter_rate / lowest_encounter_rate) ). Then it's relative to the most frequent encounter rate. 12 seems to be lowest on the WM and 24 in the fields.
Anyway, I was trying to figure out exactly how the World Map averages differ from the field map averages; I concluded that if there is a difference, that it was probably minute, but I couldn't quite work out how the formula differs from the current formula; by my reckoning, the functions were different, but the end result was the same. Then someone sent an email this morning offering a World Map formula:
(650*(8/64)) + (4000*(2/64)*(56/64)) + ((800*(22/64)) + (1000*(21/64)) + (1700*(21/64)))*(1 - (8/64) - (2/64)*(56/64))
equals = 1174.7009
Red = shouldn't the first part of the formula be (650*(8/64)) + (4000*(2/64))*(10/64)?
Blue = This seems to make sense, given the fact that 2 checks are taking place. Can you confirm/deny?
Those are all wrong. The World Map does use moderately different calculations, but none of those are right. This is what happens:
Pre-Emptive materia (PEM) grants, at most, 85 / 256 to the pre-emp rate. It also prevents back attacks and side attacks. We'll call its rate PEMr which has a minimum of 16.
If PEMr is greater than 16, we
double it.
If the PEMr is greater than or equal to [0..255] then we skip special formation battles entirely.
Special battles:
A: [0..63] is used to determine if either back-attack formation1 or formation2 are used. Somehow, having a mastered Pre-Emp materia affects this rate (either halves or doubles)
B: If those fail and we have more than 1 character in our party, a new [0..63] is used to determine if we get a side attack
C: If the above fail, there is a new [0..63] to determine if we get pincered
Normal Battles:
D: We use one [0..63] to determine if we get formation 0 - 5
So:
( 1 - (PEMr / 256) ) * //special formation check
(( (back1 / 64) + (back2 / 64) ) //back attack formation selection chance
+
( ( 1 - ( (back1 + back2) / 64 ) ) * //back attack formation fail
( ( side / 64 ) //side attack formation chance
+
( 1 - ( side / 64 ) ) *//side attack formation fail
( pince / 64 )
) ) ) //pincer formation chance
+
( PEMr / 256 + //special formation fail
( (1 - (PEMr / 256) ) * ( 1 - ( (back1 + back2) / 64 ) ) * ( 1 - ( side / 64 ) ) * (1 - (pince / 64) ) ) * //special formation pass, but formation selection fail
( ( form0 / 64 ) + ( form1 / 64 ) + ( form2 / 64 ) + ( form3 / 64 ) + ( form4 / 64 ) + ( form5 / 64 )
) //normal battle selection
This is particularly ugly for several reasons. First off, the percentage chance trickles down into the next checks
sometimes. Not all the time, but I'm going to assume that it will. If we only have one party member then the formula changes. Secondly, the chances that a normal battle occurring are greater than just the inverse of the chances a special formation is CHECKED for. We also have a variable that we have control over. The PEMr can make a drastic difference.
Pincer attacks are pretty rare being a success of "special battle check" and failing both pre-emp and side attack battle checks.
Let's apply this to a full formation entry with no mastered Pre-Emp and more than one party character (from TFergusson's guide):
Cosmo Area - Canyon
Normal Battle #1: 11/64 Chance Back Attack #1: 2/64 Chance
Row 1: 2x Skeeskee
Row 2: 1x Skeeskee Row 1: 2x Desert Sahagin
Normal Battle #2: 11/64 Chance Back Attack #2: 2/64 Chance
Row 1: 1x Griffin
Normal Battle #3: 11/64 Chance Row 1: 3x Skeeskee
Row 1: 1x Golem Side Attack: 10/64 Chance
Normal Battle #4: 11/64 Chance Row 1: 3x Skeeskee
Row 1: 2x Skeeskee Ambush: 4/64 Chance
Row 2: 1x Griffin Grp 1: 1x Desert Sahagin
Normal Battle #5: 10/64 Chance Grp 2: 1x Desert Sahagin
Row 1: 1x Desert Sahagin
Row 2: 2x Desert Sahagin
Normal Battle #6: 10/64 Chance
Row 1: 2x Desert Sahagin
Skeeskees = 222
Griffins = 260
golems = 300
desert sahagins = 230
Normal 1: 666
Normal 2: 260
Normal 3: 300
Normal 4: 660
Normal 5: 690
Normal 6: 460
Back Attack 1: 460
Back Attack 2: 666
Side: 666
Pincer: 460
Do it:
( 1 - (PEMr / 256) ) * //special formation check
(( (460 * 2 / 64) + (666 * 2 / 64) ) //back attack formation selection chance
+
( ( 1 - ( (2 + 2) / 64 ) ) * //back attack formation fail
( ( 666 * 10 / 64 ) //side attack formation chance
+
( 1 - ( 10 / 64 ) ) *//side attack formation fail
( 460 * 4 / 64 )
) ) ) //pincer formation chance
+
( PEMr / 256 + //special formation fail
( ( 1 - (PEMr / 256) ) * ( 1 - ( (2 + 2) / 64 ) ) * ( 1 - ( 10 / 64 ) ) * (1 - (4 / 64) ) ) * //pincer attack formation selection fail
( ( 666 * 11 / 64 ) + ( 260 * 11 / 64 ) + ( 300 * 11 / 64 ) + ( 660 * 11 / 64 ) + ( 690 * 10 / 64 ) + ( 460 * 10 / 64 )
) //normal battle selection
With no Pre-Emp materia:
0.9375 * ( ( 14.375 + 20.8125 ) + 0.9375 * (104.0625 + 0.84375 * 28.75) ) + ( 0.0625 + (0.9375 * 0.9375 * 0.84375 * 0.9375 ) ) * ( 114.46875 + 44.6875 + 51.5625 + 113.4375 + 107.8125 + 71.875 )
Put it all together and you get
527.5466135 per battle.
With maxed Pre-Emp:
0.3359375 * ( ( 14.375 + 20.8125 ) + 0.9375 * (104.0625 + 0.84375 * 28.75) ) + ( 0.6640625 + (0.3359375 * 0.9375 * 0.84375 * 0.9375 ) ) * ( 114.46875 + 44.6875 + 51.5625 + 113.4375 + 107.8125 + 71.875 )
Put it all together and you get
512.3372760713 per battle.
Please note: These only apply to the World Map formation selections. The field functions exactly like I calculated before.
