We illustrate the model by considering three arbitrary conflicts between two forces, with the following assumptions:
(Changes to these quantities are easily made via Excel’s Control Toolbox Scroll Bar Properties. For Technical Comments on using scroll bars in Excel worksheets, click here.)
In each of our examples, we assume the initial numbers of troops are 10,000 for the Blue Force and 5,000 for the Red Force. For simplicity, we assume the time step in the discrete model is one day.
We can use the Excel tool provided here to help predict the outcome of each conflict. Click on any of the figures below -- or this link -- to open the active worksheet in Excel or in your browser. You will have to agree to enable macros (if that is not your default setting). Also, if the worksheet opens in a browser window, you will have to agree to let it open an Excel window when you change any of the scroll bars. You may, if you wish, save the Excel file to your own computer. This window will remain open so you can return to the examples.
Conflict No. 1
The warring forces begin battle with one force initially twice as large as the other. Although the larger force also receives reinforcements, 250 per day, it is experiencing combat and non-combat losses at a rate three times greater than the smaller force. Who wins?
BattleFactors |
Red Force |
Blue Force |
Number of Troops (Initially) |
5000 |
10000 |
Combat Losses (%) |
1.0 |
3.0 |
Non-Combat Losses (%) |
1.0 |
3.0 |
Reinforcements |
0 |
250 |
Blue Force wins in 50 days.
Conflict No. 2
Using the conditions in Conflict No. 1, what if the smaller force were able to receive reinforcements, for example, 215 per day? Then who wins?
BattleFactors |
Red Force |
Blue Force |
Number of Troops (Initially) |
5000 |
10000 |
Combat Losses (%) |
1.0 |
3.0 |
Non-Combat Losses (%) |
1.0 |
3.0 |
Reinforcements |
215 |
250 |
Red Force wins in 77 days.
Conflict No. 3
Now assuming that reinforcements for the smaller force were 260 rather than 215 per day, what happens? If the larger force improved their troops’ training prior to fighting, fewer combat losses might occur, while simultaneously bolstering troop morale. How much change would need to occur in combat and non-combat losses to change the tide of the fight?
BattleFactors |
Red Force |
Blue Force |
Number of Troops (Initially) |
5000 |
10000 |
Combat Losses (%) |
1.0 |
0.3 |
Non-Combat Losses (%) |
1.0 |
0.6 |
Reinforcements |
260 |
250 |
Blue Force eventually wins, with the Red Force beginning a steady loss rate in about 58 days.
Journal of Online Mathematics and its Applications