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.