Note: this comes from an obscure technical thread that most might not otherwise notice, started by an excellent 1.5 strategy summary of Sep_18th_480BC, here.

Quoted from asked about computing the odds:

The odds are the ratio of raw units of your units the the enemy's.
Example. You have a total of 499 units attacking 1000 enemy. The odds are 499/1000 = .499. Tweaking these settings in 1.5/1.6 will affect certain strategies, including my own that I have posted about in regards to creating generals and getting experience. These are the source of how certain things are computed, and why it can be advantageous to go into battle facing certain odds. Or not.

---------- SUMMARY OF CHANGES FROM PATCH 1.2 to PATCH 1.5 -------------

export_descr_character_traits.txt

NOTES:
1. Summary of relevant changes of traits, from Patch 1.2 to patch 1.5... line by line.
2. Changes in trait naming conventions (e.g., plurality) are not included. If it is not mentioned below, then no changes occurred.
3. The unaltered 1.2 and 1.5 were compared character for character, and all data files in RTW 1.2 and 1.5 were searched for relevant additions...

 =================

1.2:
Trait GoodCommander
    Characters family
    AntiTraits BadCommander

    Level Great_Commander
        Description Great_Commander_desc
        EffectsDescription Great_Commander_effects_desc
        GainMessage Great_Commander_gain_desc
        Threshold  8 
        Effect Command  4 
    Level Legendary_Commander
        Description Legendary_Commander_desc
        EffectsDescription Legendary_Commander_effects_desc
        GainMessage Legendary_Commander_gain_desc
        Epithet Legendary_Commander_epithet_desc
        Threshold  16 
        Effect Command  5 
        
1.5:  Changed(for Great_Commander):         Threshold  10 
1.5:  Changed(for Legendary_Commander):     Threshold  18  
 =================
Trait BadConspirator
    Characters spy, assassin
    AntiTraits GoodConspirator
1.2:
    Level Very_Lively
        Description Very_Lively_desc
        EffectsDescription Very_Lively_effects_desc
        Threshold  2 
        Effect Management  2 
        Effect MovementPoints  4 
        
1.5:  Changed:        Effect MovementPoints  3 
 =================
1.2:
Trait BadConspirator
    Characters spy
    AntiTraits GoodConspirator
    
1.5: Changed:   Characters spy, assassin
 =================
1.2:
Trait IndecisiveAttacker
    Characters family
    ExcludeCultures barbarian
    AntiTraits GoodCommander, GoodAttacker
1.5: Changed:    AntiTraits GoodRiskyAttacker, GoodAttacker
 =================
1.2:
Trigger V0020_Standard_Battle_Attacker_Crushing_Loss_VnV_Trigger
    WhenToTest PostBattle
    Condition WasAttacker
          and IsGeneral
          and not WonBattle
          and BattleSuccess = crushing
          and I_ConflictType Normal
          and BattleOdds >= 0.5
          and BattleOdds < 1.5
    Affects BadAttacker  2  Chance  50 
1.5:  Removed  and BattleOdds < 1.5
 =================
1.2:
Trigger V0040_Standard_Battle_Defender_Crushing_Loss_VnV_Trigger
    WhenToTest PostBattle
    Condition not WasAttacker
          and IsGeneral
          and not WonBattle
          and BattleSuccess = crushing
          and I_ConflictType Normal
          and BattleOdds >= 0.5
          and BattleOdds < 1.5
    Affects BadDefender  2  Chance  50 

Trigger V0060_Standard_Battle_Attacker_Clear_Loss_VnV_Trigger
    WhenToTest PostBattle
    Condition WasAttacker
          and IsGeneral
          and not WonBattle
          and BattleSuccess = clear
          and I_ConflictType Normal
          and BattleOdds >= 0.5
          and BattleOdds < 1.5
    Affects BadAttacker  1  Chance  50 
1.5:  Removed  and BattleOdds < 1.5
 =================
1.2:
Trigger V0080_Standard_Battle_Defender_Clear_Loss_VnV_Trigger
    WhenToTest PostBattle
    Condition not WasAttacker
          and IsGeneral
          and not WonBattle
          and BattleSuccess = clear
          and I_ConflictType Normal
          and BattleOdds >= 0.5
          and BattleOdds < 1.5
    Affects BadDefender  1  Chance  50 
1.5:  Removed  and BattleOdds < 1.5
 =================
1.2:  Did not exist
1.5:  ADDED (Totally NEW!):
Trigger V0095_Standard_Battle_Clear_Victory_VnV_Trigger
    WhenToTest PostBattle
    Condition IsGeneral
          and WonBattle
          and BattleOdds >= 1.6
          and BattleOdds < 2.1
          and BattleSuccess >= clear
    Affects GoodCommander  1  Chance  100 
 =================
1.2:
Trigger V0190_Withdraw_Before_Battle_Even_Odds_VnV_Trigger
    WhenToTest PreBattleWithdrawal
    Condition IsGeneral
          and I_WithdrawsBeforeBattle
          and BattleOdds > 0.8
          and BattleOdds < 1.5
    Affects IndecisiveAttacker  1  Chance  50 
1.5:  Changed  and BattleOdds < 3
 =================
1.2:
Trigger random_birth12
    WhenToTest CharacterComesOfAge
    Affects BadBuilder  2  Chance  2 
    Affects Feck  1  Chance  2 
    Affects SmoothTalker  1  Chance  2
    
1.5:  Changed:      Affects BadCommander  1  Chance  2    
 
 =================
 
 1.2:
Trigger harsh_lifestyle1
    WhenToTest CharacterTurnEnd
    Condition EndedInSettlement
          and RemainingMPPercentage = 100
          and SettlementBuildingExists = governors_house
          and RandomPercent > 50
    Affects Austere  1  Chance  2 
    Affects Cuckold  1  Chance  2 
    Affects Ignorance  1  Chance  1 
    Affects Pragmatic  1  Chance  2 
    Affects Stoic  1  Chance  1 
1.5:  Removed:     Affects Cuckold  1  Chance  2 
 =================
1.2:  None
1.5: Added Education (TOTALLY NEW):
;------------------------------------------
Trigger education
    WhenToTest CharacterTurnEnd
    Condition IsGeneral
          and EndedInSettlement
          and RemainingMPPercentage = 100
          and SettlementBuildingExists >= academy
          and Trait Ignorance < 1
          and Trait Insane <= 1
    Affects PhilosophySkill  1  Chance  1 
    Affects NaturalPhilosophySkill  1  Chance  1 
    Affects RhetoricSkill  1  Chance  1 
    Affects GoodEngineer  1  Chance  1 
;------------------------------------------
Trigger education2
    WhenToTest CharacterTurnEnd
    Condition IsGeneral
          and EndedInSettlement
          and RemainingMPPercentage = 100
          and SettlementBuildingExists >= scriptorium
          and Trait Ignorance < 1
          and Trait Insane <= 1
    Affects PoeticSkill  1  Chance  1 
    Affects TacticalSkill  1  Chance  1 
    Affects ArchitectSkill  1  Chance  1 
    Affects Stoic  1  Chance  1 
    Affects LogisticalSkill  1  Chance  1 
;------------------------------------------
Trigger education3
    WhenToTest CharacterTurnEnd
    Condition IsGeneral
          and EndedInSettlement
          and RemainingMPPercentage = 100
          and Trait Ignorance < 1
          and Trait Insane <= 1
          and SettlementBuildingExists = ludus_magnus
          and CultureType roman
    Affects BoringSpeaker  1  Chance  1 
    Affects MathematicsSkill  1  Chance  1 
    Affects StrategicSkill  1  Chance  1 
    Affects PhilosophySkill  1  Chance  1 
    Affects PoliticsSkill  1  Chance  1 
;------------------------------------------
 =================
1.2:
Trigger battle1R
    WhenToTest PostBattle
    Condition GeneralHPLostRatioinBattle > 0.3
          and CultureType roman
    Affects BattleScarred  1  Chance  30 
    Affects RomanHero  1  Chance  15 
    
1.5:  Removed:          Affects BattleScarred  1  Chance  30  
 =================
1.2:
Trigger battle4
    WhenToTest PostBattle
    Condition not GeneralFoughtInCombat
          and PercentageEnemyKilled = 0
    Affects Coward  1  Chance  10 
    
1.5:  Removed:           and BattleOdds <= 1.2 
 =================
1.2:
Trigger family8
    WhenToTest CharacterMarries
    Affects Cuckold  2  Chance  3 
    Affects FaithfulWife  1  Chance  8 
    Affects Fertile  1  Chance  4 
    Affects Infertile  1  Chance  4 
    Affects WellConnectedWife  1  Chance  5 
1.5:  Changed:          Affects Cuckold  2  Chance  4 
 =================
1.2:
Trigger agents2
    WhenToTest SpyMission
    Condition MissionSuccessLevel = slightly_successful
          and Trait GoodSpy = 1
    Affects GoodSpy  1  Chance  10 
    
1.5:  Changed:           and Trait GoodSpy <= 2
 =================