Whether the German Luftwaffe could have won the Battle of Britain in 1940 has been a matter of debate almost from the time the first shot was fired. Now, a team of mathematicians at the University of York has used a statistical technique to determine if Germany could have defeated Britain if different decisions had been made.

The Battle of Britain was one of the decisive battles of the Second World War. Between May and October 1940, Britain was still reeling from the fall of France and the Dunkirk evacuation, while the Luftwaffe, with overwhelming superiority in numbers, fought in the skies over England to destroy the RAF fighter wings and clear the path for a German invasion.

Owing to a number of factors, some of which remained a secret for decades after the war, Britain managed to fight off the waves of German bombers and fighter planes and Hitler had to abandon his invasion plans, but it was a very close-run thing. Since that time, the question remains, if the Germans had made better decisions, could they have won and ended up occupying the British Isles?

Of course, this is a classic example of an unprovable hypothesis because there's no way to replay those times in all their complexity, but the York team has come up with a new computer model that uses "weighted bootstrapping" to calculate the statistical probability of various alternative scenarios.

Essentially, they were looking at things like, what if Hitler had decided not to bomb London? What if Reich Marshall Göring's Luftwaffe had focused solely on knocking out RAF airfields and its fighter planes while on the ground? What if the campaign had begun in full force earlier in the year?

The researchers compare the weighted bootstrapping technique to putting balls representing the event of each day of the battle through a lotto machine. As the balls are drawn out, read and replaced, they calculate alternatives for the battle, but in a different order for events, with some occurring more often and some not at all.

"The weighted bootstrap technique allowed us to model alternative campaigns in which the Luftwaffe prolongs or contracts the different phases of the battle and varies its targets," says Jamie Wood from the Department of Mathematics at the University of York. "The Luftwaffe would only have been able to make the necessary bases in France available to launch an air attack on Britain in June at the earliest, so our alternative campaign brings forward the air campaign by three weeks. We tested the impact of this and the other counterfactuals by varying the probabilities with which we choose individual days."

The results of the study couldn't produce a hard answer, but it did show that if the Luftwaffe had started bombing earlier and stuck to attacking airfields, they would have had a much higher probability of victory. In other words, if the chance of a British victory was 50 percent, these two decisions would have reduced the probability to 10 percent. If Britain was favored at 98 percent, it would have dropped to 34 percent.

Not good odds at all, but it does show the razor's edge that the outcome of a battle can rest on.

"Weighted bootstrapping can provide a natural and intuitive tool for historians to investigate unrealized possibilities, informing historical controversies and debates," says Niall Mackay from the Department of Mathematics at the University of York. "It demonstrates just how finely-balanced the outcomes of some of the biggest moments of history were. Even when we use the actual days' events of the battle, make a small change of timing or emphasis to the arrangement of those days and things might have turned out very differently. This technique can be used to give us a more complete understanding of just how differently events might have played out."

The research was published in the Journal of Military History.

Source: University of York