10 Jul 2017

# Calculating the Odds at Gettysburg

### Battle of Gettysburg, GIGO, History, Mathematics, Pickett's Charge

Military historians have long debated whether Lee’s decision to attack the Union center on the third day of the Battle of Gettysburg with Pickett’s Division ever had any chance of succeeding.

Up at Norwich University in Vermont, Michael J. Armstrong (with Steve Sondergen) was the most recent to have a try at settling the dispute.

We used computer software to build a mathematical model of the charge. The model estimated the casualties and survivors on each side, given their starting strengths.

We used data from the actual conflict to calibrate the model’s equations. This ensured they initially recreated the historical results. We then adjusted the equations to represent changes in the charge, to see how those affected the outcome. This allowed us to experiment mathematically with several different alternatives.

The first factor we examined was the Confederate retreat. About half the charging infantry had become casualties before the rest pulled back. Should they have kept fighting instead? If they had, our model calculated that they all would have become casualties too. By contrast, the defending Union soldiers would have suffered only slightly higher losses. The charge simply didn’t include enough Confederate soldiers to win. They were wise to retreat when they did.

We next evaluated how many soldiers the Confederate charge would have needed to succeed. Lee put nine infantry brigades, more than 10,000 men, in the charge. He kept five more brigades back in reserve. If he had put most of those reserves into the charge, our model estimated it would have captured the Union position. But then Lee would have had insufficient fresh troops left to take advantage of that success.
Ammunition ran out

We also looked at the Confederate artillery barrage. Contrary to plans, their cannons ran short of ammunition due to a mix-up with their supply wagons. If their generals had better coordinated those supplies, the cannons could have fired twice as much. Our model calculated that this improved barrage would have been like adding one more infantry brigade to the charge. That is, the supply mix-up hurt the Confederate attack, but was not decisive by itself.

Finally, we considered the Union Army. After the battle, critics complained that Meade had focused too much on preparing his defences. This made it harder to launch a counter-attack later. However, our model estimated that if he had put even one less infantry brigade in his defensive line, the Confederate charge probably would have succeeded. This suggests Meade was correct to emphasize his defense.

Pickett’s Charge was not the only controversial part of Gettysburg. Two days earlier, Confederate Gen. Richard Ewell decided against attacking Union soldiers on Culp’s Hill. He instead waited for his infantry and artillery reinforcements. By the time they arrived, however, it was too late to attack the hill.
Was Ewell’s Gettysburg decision actually wise?

Ewell was on the receiving end of a lot of criticism for missing that opportunity. Capturing the hill would have given the Confederates a much stronger position on the battlefield. However, a failed attack could have crippled Ewell’s units. Either result could have altered the rest of the battle.

A study at the U.S. Military Academy used a more complex computer simulation to estimate the outcome if Ewell had attacked. The simulation indicated that an assault using only his existing infantry would have failed with heavy casualties. By contrast, an assault that also included his later-arriving artillery would have succeeded. Thus, Ewell made a wise decision for his situation.

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I’m afraid I do not buy the analysis on Ewell’s decision one bit. The Union 1st and XIth Corps were retiring in disorder late in afternoon having been beaten in a hard fight west of Gettysburg. Ewell’s Corps was arriving from the North, on the right flank of the collapsing Union line. What do you suppose would have happened to the Union Army if Stonewall Jackson had survived the Battle of Chancellorsville, six weeks earlier, and been commanding that corps instead of Ewell? Those computer simulations up at Norwich are clearly not accurately calculating for momentum and morale.

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For every Southern boy fourteen years old, not once but whenever he wants it, there is the instant when it’s still not yet two o’clock on that July afternoon in 1863, the brigades are in position behind the rail fence, the guns are laid and ready in the woods and the furled flags are already loosened to break out and Pickett himself with his long oiled ringlets and his hat in one hand probably and his sword in the other looking up the hill waiting for Longstreet to give the word and it’s all in the balance, it hasn’t happened yet, it hasn’t even begun yet, it not only hasn’t begun yet but there is still time for it not to begin against that position and those circumstance which made more men than Garnett and Kemper and Armistead and Wilcox look grave yet it’s going to begin, we all know that, we have come too far with too much at stake and that moment doesn’t need even a fourteen-year-old boy to think This time. Maybe this time with all this much to lose than all this much to gain: Pennsylvania, Maryland, the world, the golden dome of Washington itself to crown with desperate and unbelievable victory the desperate gamble, the cast made two years ago.

—William Faulkner, Intruder in the Dust, 1948.

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