The mathematics of a firefight

When you examine the mathematics of a firefight, it’s easy to see why the big company usually wins. Let’s say that the Red squad with nine soldiers meets a Blue squad with six. Red has a 50 percent numerical superiority over the Blue. 9 versus 6. Or it could be 90 versus 60 or 9000 versus 6000. It makes no difference what the number are, the principle is the same.

Let’s also say that, on the average, one out of every three shots will inflict a casualty.

After the first volley, the situation will have changed drastically. Instead of a 9 to 6 advantage, Red would have a 7 to 3 advantage. From a 50 percent superiority in force to a more than 100 percent superiority.

The same deadly multiplication effect continues with the passage of time.

After the second volley, the score would be 6 to 1 in favor of Red.

After the third volley, Blue would be wiped out completely.

Notice how the casualties were divided between the two sides. The superior force (Red) suffered only half the casualties of the inferior force (Blue).

This result may be just the opposite of what you have been led to believe by all those Hollywood movies-the handful of marines decimating a company of Japanese before the marines are finally overrun.

In real life it’s different. What happens when a Volkswagen Beetle hits a GMG bus in a head-on collision? You wind up with a few scratches on the bumper of the bus and a very thin German pancake. (The bigger you are, the harder they fall.)

The two vehicles have exchanged momentum. It’s a basic law of physics. The larger, heavier vehicle sustains less damage than the smaller, lighter force.

There’s no secret to why the Allies won World War II in Europe. Where the Germans had two soldiers, we had four. Where they had four, we had eight. The skill and experience of an enemy who had practically invented modern warfare and the leadership of men like Rommel and Von Rundstedt could not change the mathematics of the battleground.

In the military, the numbers are so important that most armies have an intelligence branch known as the order of battle. It informs commanders of the size, location, and nature of the opposing force. (The case of General William C. Westmoreland against CBS was based on whether order of battle documents in the Vietnam war were falsified or not.)