The following is a description of all the combat result bonuses.
Note that normally all of these bonuses refer to the situation after all the models involved in the fight have finished attacking. The only exception is the extra rank bonus, which instead refers to the number of extra ranks the units had at the beginning of that turn of combat, before any casualties were caused.
Extra Rank
A massed formation of warriors trained to gather their full weight in an irresistible push is often enough to shatter the enemy's will to fight on.
If your unit's formation is at least five models wide, you may claim a bonus of +1 for each rank behind the first that the unit had at the start of that combat turn, up to a maximum of +3. The bonus can be claimed for an incomplete last rear rank, so long as it contains at least five models.
If you have several units fighting in a combat, count the bonus from the unit with the most ranks. Do not add up the bonuses from all the units fighting.
This bonus is lost if the unit is fighting to its flank or rear against an enemy unit with a unit strength of 5 or more. Note that this applies while the enemy unit in the flank/rear is in combat - if the enemy unit breaks and flees, or is reduced to a unit strength of less than 5, the unit regains its rank bonus at the beginning of the following turn.
Skirmishers and fast cavalry never gain a bonus for extra ranks.
Outnumber Enemy
When a group of warriors is facing uneven odds, it is considerably more likely to lose heart. If the combined unit strength of all your units in the combat is greater than the combined unit strength of, the enemy units, you receive a +1 bonus. See the unit strength chart.
Standard
Having the colours of their city or nation flying at the front of a regiment is a great motivator.
If any of your units includes a standard bearer in its front rank, you may add a +1 bonus.
Note that if several units' standards are involved in the combat, you still only add +1, not +1 for each standard. See rules for standards.
Battle Standard
Having the personal banner of their General held high by a great hero is enough to encourage the warriors to even greater deeds of valour.
If the army's battle standard bearer is in the fight, you may add a +1 bonus. Note that this bonus is on top of the bonus for a unit's standard, so a unit with a normal standard and the battle standard receives a +2 combat result bonus.
High Ground
Charging down a hill or mounting a stiff defence at the top of a rocky crag is a great advantage.
If you are fighting from a higher position than your enemy, for example, your troops are occupying the crest of a hill, then you may add a +1 bonus. In the case of a fight involving multiple units, the side that has the fighting rank in the highest position gets the bonus.
Flank Attack
Charging an enemy unit to its flank or rear is lethal, as the enemy warriors helplessly mill around in confusion trying to face the unexpected attack.
If you are fighting against an enemy unit's flank, you may add a + 1 bonus so long as your unit has a unit strength of 5 or more after both sides have attacked. Note that you only count +1 even if both flanks of the enemy are engaged. The bonus is only applied once, regardless of how many flanking units are involved in the combat. If both sides have flanking units, the side with the most flanking units gets the bonus.
Rear Attack
The same rules for a flank attack also apply to units attacking the enemy in the rear, except that a rear attack gives you a +2 combat result bonus. This bonus and the bonus for a flank attack are cumulative, so if you are attacking in the side and rear you will receive a bonus of +3.
Overkill
Seeing the best fighter in the unit cut to pieces does not boost morale among his comrades.
If a character fighting in a challenge kills his opponent and scores more wounds than the enemy has, each excess wound scores a +1 overkill bonus towards the combat result, up to a maximum of +5. This bonus only applies in a challenge as described in the Characters section.