Butler has no leaders or units with and siege or engineer abilities. The only things then with him that matter are: 1. his force is stronger, and 2. he has 122 offensive-fire-power from artillery.
Magruder has no leaders with engineer or fort-defender nor an engineering unit, but he does have a supply train and plenty of supply. The only other things with him that matter are: 1. his force is weaker, 2. he has 72 defensive-fire-power from artillery, and 3. he's intrenched in a redoubt at level 4.
In the GameLogic.opt file we find:
// ********************************************************
// ***** SIEGES *****
// ********************************************************
sieValueForSiegeBonus = 18 // How many Artillery Combat Pts needed to get a +1/-1 modifier to siege
sieOutcomeDiceRollSides = 12 // Sides of the Siege Outcome roll / compared to TQ/Discipline
sieWagonDepotProtectChance = 90 // Chance that a non empty depot/wagon protects against surrender
baseProdCoefLocked = 100 // Percent of base supply when under siege with port unblocked
sieExtraModifier = 0 // Extra Modifier (positive: help the besieger)
sieSurrenderModEndangered =- 3 // If structure breached, lack of supply and weaker than besieger, get this penalty to surrender
Magruder's Siege Roll Modifiers:
artillery: 72 / 18 = +4
Fort level 1: +1
sieSurrenderModEndangered -3 (see above)
Total +2
Butler's Siege Roll Modifiers:
artiller: 122 / 18 = 6.7777 = +6
Total +6
Average Discipline: I'm not sure how to calculate this. Magruder himself has Discipline 10, the artillery each have 7, but they're smaller than regiments. Just counting elements I get this:
Discipline ............ number-of-elements(including Magruder)
Discipline 10 * elements 2 = 20
Discipline 9 * elements 9 = 81
Discipline 7 * elements 5 = 35
Discipline 6 * elements 4 = 24
Discipline 5 * elements 5 = 25
Total elements 25
Total discipline 185
185 / 25 = 7.4 = 7 average discipline.
Each side roles a d12 (12 sided die) and modify this with their Siege Roll Modifiers. Subtract the defender's modified roll from the besieger's modified roll to get the SRV (Siege Roll Value).
Results:
SRV > defending units’ average discipline: Defender surrenders and all units are eliminated unless the defending force includes a supply wagon, in which case the result is ignored (90% of this according to "sieWagonDepotProtectChance = 90 // Chance that a non empty depot/wagon protects against surrender".
SRV >= 3 A breach is made. Cities and pre-war forts are breached after a single breach result while permanent fortifications require two breach results to be fully breached.
SRV > 0 5 hits are inflicted on the defenders for each point of SRV.
SRV < 0 The defender has managed to repair a breach.
Magruder's possible dr range is lowest 3 to highest 14
Buttler's possible dr range is lowest 7 to highest 18
So basically, just for determining a surrender, you can add the Magruder's force's average discipline to their dr and if the Butler's dr is greater, the Magruder's can surrender with a 10% chance.
Magruder's possible dr range with average discipline of 7 add is lowest 10 to highest 21
Buttler's possible dr range is lowest 7 to highest 18
I'm not about to calculate that exact probability of Butler attaining the SRV > average discipline, but it is obviously very possible, and the 10% chance of supply not preventing surrender, although small, is still there, and that is probably what happened.
References:
http://www.ageod.net/aacwwiki/Manual:Siege_combat and
http://www.ageod.net/agewiki/Sieges_and_breaches