A mathematical study claims to have proven the long-held belief that the Battle of Britain could have easily been won by the Germans if not for tactical ineptitude.

University of York researchers have created a computer model that uses a statistical technique called 'weighted bootstrapping' to re-imagine the 1940 battle under different circumstances.

It identifies two enormous blunders by notorious Nazi commander Hermann Goering - a trained fighter pilot - who led the assault that crippled the Nazi effort and helped Britain win.

The first mistake was not launching an attack immediately after Winston Churchill's famous 'Battle of Britain' speech on June 18, rather than three weeks later on July 10.

This is because an early strike would have given Britain less time to prepare a coordinated response and train up pilots, giving Germany a significant tactical advantage.

The second major blunder from Hitler was not persisting with concentrated attacks on British airfields after striking a huge blow on August 13.

These attacks lasted just five days but destroyed radar systems used to track German planes. Experts say that had this phase been longer it would have paved the way for a naval and land invasion.

The study provides statistical backing to many historians' belief that if Germany had done these two things differently, it would have stood a much better chance of winning the Battle of Britain.

'Weighted bootstrapping is a bit like taking a ball for the events of each day of the Battle of Britain and placing them in a lotto machine,' the researchers say.

Balls are then drawn, read and replaced to create thousands of alternative sets of days' fighting, but in a different order, and perhaps with some days appearing more than once or not at all.

The researchers then repeated the process to test out the Battle 'what ifs', making some days more or less likely to be chosen, depending on how a protagonist (such as Hitler) would have changed their decisions had they been using different tactics.

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Fighter pilots took up the call to arms in the British spitfires (pictured) and hurricanes, with replacement pilots and planes in shortage due to the severe loss of life. But the British ultimately defeated the Germans

British heroes in Spitfires and Hurricanes defeated the German Messerschmidt planes (pictured) at the Battle of Britain, helped enormously by the tactical failings of Herman Goering

KEY DATES OF THE BATTLE OF BRITAIN June 18 - France seeks an armistice June 18 - British Prime Minister Winston Churchill gives his famous speech declaring the 'Battle of Britain' July 10 - Germany launches its first aerial attack on Britain Luftwaffe Phase 1 July 10 - August 12 - Germany focuses its attacks on shipping conveys in the English Channel. There were widespread night-time raids all along the coast. July 16 - Hitler issued the famous directive number 16, stating his intention to wage battle with Britain's 'hopeless military situation'. He added: 'I have decided to begin to prepare for and, if necessary, to carry out an invasion of England.' August 1 - Germany airdrop leaflets over Britain entitled 'A Last Appeal to Reason' August 13 - Germany lands a huge blow when it hit vital radar masts at key airfields in the South. Known as Eagle Day’ (Adlertag) Luftwaffe Phase 2 August 13 - August 18 - Airfields and radar stations became the focus of German bombing as it focused on destroying the aircraft of Fighter Command. Airfields in the south east of England suffered the heaviest attacks. Luftwaffe Phase 3 August 19 – September 6 - The Luftwaffe continued to bomb towns and cities and turns its attention away from airfields August 20 - Churchill gave one of the most famous speeches of his premiership when he said: 'Never in the field of human conflict was so much owed by so many to so few' August 24 - Luftwaffe , under clear orders not to bomb London, mistake the capital for military targets August 25 -Churchill retaliates and sends 40 planes to bomb Berlin The hero pilots of the Battle of Britain became known as 'the Few'. August 31 - British fighter command suffers its heaviest losses yet. It activates squadron 303 of Polish aces. September 15 - The RAF destroy a huge formation of Luftwaffe over London and forced Hitler to abandon the battle and shelve his plans for invasion. It is henceforth known as 'battle of Britain' day September 17 - Hitler postponed the invasion of Britain (Operation Sealion) following heavy Luftwaffe losses September 26 - The Spitfire factory at Southampton was attacked and destroyed. Advertisement

The real statistical chances of a Luftwaffe victory in July 1940 are a mystery, as there will never be enough data to create an accurate model.

But the study suggests that an earlier start and a focused targeting of airfields would have shifted the battle significantly in the Germans' favour.

For example, had the likelihood of a British victory in the actual battle been 50 per cent, these two tactical changes would have reduced it to less than 10 per cent.

If the real probability of British victory was 98 per cent, the same changes would have reduced this to just 34 per cent.

The Battle of Britain featured a reluctant Hitler drawn into a duel he seldom showed interest in.

The Fuhrer expressed little emotion towards the British Isles, as the Reich was preoccupied with an imminent war with Russia's Red Army on the Eastern front.

Hitler pushed for a deal with the British and tried to intimidate the nation into submission.

But Churchill's inspired speech on June 18 announcing 'the Battle of France is over. The Battle of Britain is about to begin' motivated the county and solidified resolve.

Fighter pilots took up the call to arms in the British spitfires and hurricanes, with pilots and planes soon in short supply due to the severe loss of life.

But, according to the latest research, Allied bravery would have been in vain if the Germans had responded with an immediate attack, which would have led to a Nazi victory.

The researchers tries to keep their predictions within the realms of realism, only making adjustments to the timeline that would have been feasible in real life.

Dr Jamie Wood from the Department of Mathematics at the University of York, said: '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.'

He added: 'We found that the key variable is the number of fighter pilots that the British had available.

'If the Germans did find a way to degrade that number more repeatedly, the less the fighter command would be able to put up a viable defence.

'So what they need to do is to increase the number of battles, to increase the number of pilots being used - and there were fewer trained fighter pilots in the earlier weeks of the battle.

HOW THE STATISTICAL MODEL WORKS The statistical technique used by the researchers is called 'weighted bootstrapping'. It investigates the probability of victory if various 'what-ifs' had occurred. It works in a similar way to a lottery machine, with each day of the battle represented by a single ball. Balls - days - are drawn at random, read and replaced to create an alternate timeline. This is repeated thousands of times in different orders to see what the most probable outcome would be. Some days may appear more than once or not at all. Some days were made more or less likely to be chosen, depending on how a protagonist (such as Hitler or Goering) would have changed their decisions had they been using different tactics. Advertisement

'We can see the airfields that the Germans were targeting and, looking at the impact of those attacks, they were creating the right kind of degradation of the British forces to lay the groundwork for an invasion.'

As it was, the first attack was not launched until July 10, a delay which may have spared Britain from German occupation, according to the study.

On July 16, Hitler issued the famous directive number 16, stating his intention to wage battle with Britain's 'hopeless military situation'.

He added: 'I have decided to begin to prepare for and, if necessary, to carry out an invasion of England.'

This tentative announcement spoke of his reluctance to turn the English Channel into a battleground, as his navy was depleted following a campaign against Norway where it lost two cruisers and 10 destroyers.

Hitler feared the naval might of 1940s Britain, and the war instead took to the skies.

The study suggests that if Germany had launched an attack in June following Winston Churchill's (pictured) famous Battle of Britain' speech and targeted airfields, the Nazis would have probably been victorious, paving the way for a naval and land invasion

Pictured, a colourised image showing Hermann Wilhelm Goering in France in 1941. Goring was commander in chief of the Luftwaffe during the Battle of Britain. His blunders allowed Britain and the RAF to emerge victorious

Goering opted to airdrop leaflets over Britain entitled 'A Last Appeal to Reason' on August 1.

These were resolutely ignored, and the nation dug in for further bombardment as the Blitz devastated the nation.

Despite their scattershot approach, the Luftwaffe came close to overwhelming the RAF on a number of occasions.

One of the most significant successes for the German air force was the attack on visible and vital radar masts at key airfields on 13 August.

The Germans did not realise how crucial and advanced the radar systems were and how central to the RAF they had become.

Had Goering continued with this tactic, he would have almost undoubtedly destroyed the radar system and led the Nazi regime in a historic defeat of Britain.

Instead, the decorated Nazi henchman entrusted with the German military campaign flitted between several different tactics.

He relented his attacks on the airfields and this allowed the English, Polish, Canadian, Czech and New Zealand pilots to regroup and saved the invaluable equipment from destruction.

Dr Wood added: 'In the model, every time we create a coherent strategy for the Germans, the results are better from their perspective.

'We don't want to downplay the British strategy. It was bang on. They did exactly what they had to do.

'The problem was that the RAF had a critical shortage of trained monoplane fighter pilots, which the Germans didn't exploit.'

As the battle waged through the summer of 1940, Churchill gave one of the most famous speeches of his premiership.

On 20 August, speaking in the House of Commons, he said: 'Never in the field of human conflict was so much owed by so many to so few.'

The hero pilots of the Battle of Britain became known as 'the Few'.

After throwing away the initial advantage, Germany never recovered the edge over the RAF and, on September 15, now known as Battle of Britain Day, the RAF destroyed a huge formation of Luftwaffe over London and forced Hitler to abandon the battle and shelve his plans for invasion.

The researchers made their calculations using a mathematical model which investigates the probability of victory if all 'what-ifs' had occurred.

It works in a similar way to a lottery machine, with each day of the battle represented by a single ball.

Balls are drawn, read and replaced to create an alternate timeline.

This is repeated thousands of times in different orders to see what the most probable outcome would be.