I summarized some practical morale mechanics, feel free to add your own
In Rome Total War, morale is the true health bar. Basic factors that provide a steady boost or penalty include the presence of a general for encouragement and ensuring proper flank security. Tactical pressures like being under missile fire, enduring fire arrows, or facing artillery and cavalry charges also play a significant role. Additionally, fighting from a higher elevation provides a clear advantage for your troops.
The most significant drains on morale come from high casualties and extreme fatigue. Taking heavy losses in a short period or letting your soldiers become exhausted will almost certainly lead to a rout. Having a clear numerical advantage also helps break the enemy, although this can be more difficult to achieve in balanced engagements.