Base Medal chance is just the term given to the chance for each army to get a medal. Eg. for Elephants it's 30% and for Peasants it's 40%. As you note, the bigger the better.

Here's how the awarding of medals works:

1) After a successful battle the victorious side has a chance for 1 unit to receive a medal. This unit is selected at random from the stack of regulars units (ie. No Mercs, Allies, Summoned units or Raised units can be selected by this random chance). If there are no regular units then there is no medal roll made. So as Wooger noted, any unit can get the medal.

2) The base medal chance for the randomly selected unit is taken and various modifiers are added. These modifiers include the heroes medal chance (if a hero is present), the number of units in your stack compared to the other stack and a couple of others. I mention the number of units in your stack compared to the other stack because this is a big modifier. For example if your stack contains 8 units and you kill a single unit you will receive a big negative modifier to your base medal chance due to vastly outnumbering your opponent. On the other hand if you have a stack of 8 and hit a city with 32 men you will have a big positive modifier due to facing overwhelming odds. For this reason, esp in Email games it makes sense to kill a scout unit not with your big hero 8 stack but merely with the hero (for the xp and his modifier) and a single unit from your regulars (esp elephants due to the big medal chance they have). I can often generate a bunch of medalled units this way.

3) The roll is made after all modifiers are added. If the roll is less than the medal chance then the unit gets a medal. If the medal chance was less than 0 after modifiers then no medal is possible.

Notes:

1) There is a bug in the game that works like this. If you summon a unit it normally gets no medals or medal chances. BUT, if you have that unit in your regulars then the summoned unit CAN get medals as you saw with your Wraith.

2) Also, summoned units move into your regular fight order if you have that unit in your regulars, mercs or allies. Otherwise they always fight up front. This is how your wraith went to the back of your stack cause it was in your regulars. Note that armies raised from Necromancy do NOT get this bonus nor can they go into your fight order.


Unit Strength                          Hit Chance
                0 medals    1 medal     2 medals    3 medals    4 medals
     1          0.0500      0.0817      0.0865      0.0932      0.1028
     2          0.1000      0.1600      0.1692      0.1818      0.2000
     3          0.1500      0.2350      0.2481      0.2659      0.2917
     4          0.2000      0.3067      0.3231      0.3455      0.3778
     5          0.2500      0.3750      0.3942      0.4205      0.4583
     6          0.3000      0.4400      0.4615      0.4909      0.5333
     7          0.3500      0.5017      0.5250      0.5568      0.6028
     8          0.4000      0.5600      0.5846      0.6182      0.6667
     9          0.4500      0.6150      0.6404      0.6750      0.7250
    10          0.5000      0.6667      0.6923      0.7273      0.7778
    11          0.5500      0.7150      0.7404      0.7750      0.8250
    12          0.6000      0.7600      0.7846      0.8182      0.8667
    13          0.6500      0.8017      0.8250      0.8568      0.9028
    14          0.7000      0.8400      0.8615      0.8909      0.9333
    15          0.7500      0.8750      0.8942      0.9205      0.9583
    16          0.8000      0.9067      0.9231      0.9455      0.9778
    17          0.8500      0.9350      0.9481      0.9659      0.9917
    18          0.9000      0.9600      0.9692      0.9818      1.0000