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Playing the numbers game - why Jellicoe got his maths right at the Battle of Jutland

Posted on 23 May 2016

Researchers have used mathematical modelling to re-analyse the Battle of Jutland and help shed new light on the biggest naval engagement of World War One.

HMS Invincible

The Royal Navy's Grand Fleet, based at Scapa Flow in Orkney, clashed with the German High Seas Fleet on 31 May 1916 off the coast of Jutland, Denmark.

Historians largely view the battle as indecisive, with the British left disappointed in their hopes for a decisive victory comparable to Trafalgar, despite their large numerical superiority.

But as the centenary of the battle approaches, researchers have used new mathematical insights to re-examine the behaviour of the commanders and reveal that Admiral Jellicoe – often criticised for his cautious approach – made good decisions, the decisions that the British fleet was built for.

The British Fleet was bigger, faster and had more and larger guns, but the German Fleet was better armoured and highly trained. The British had a total of 151 combat ships compared to Germany’s 99.

Professor Niall Mackay, from the Department of Mathematics at York said: “What the German fleet hoped for was to lure out, isolate and destroy part of the British fleet and tip the overall naval balance in their favour. They would then have a chance to defeat the Grand Fleet and possibly win the war.”

“What we have argued is that Jellicoe realised what he had to do.He needed to fight only when he was perfectly deployed and the Germans were not – so he wasn’t prepared to let his ships go flying after the Germans.

“He always wanted to keep them as this perfect battle line and only fight on his terms. And what we have argued is that mathematically that was the right decision.”

The research team, which also included Dr Jamie Wood,Senior Lecturer in Biological Modelling in the Departments of Biology and Mathematics, and Dr Christopher Price, Lecturer in History at York St. John University, used Lanchester’s Law to analyse the battle, which cost the British 6,000 seamen.

A sea battle involves big naval guns engaging each other directly, often receiving fire from multiple directions. The engineer Frederick Lanchester had determined that the power of such a force is proportional not to the number of units it has, but to the square of the number of units – otherwise known as Lanchester's Square Law.

“Numbers really, really matter and the British realised this. Before the British went for quality they just built lots and lots of ships with lots of guns.” Dr Wood added.

“That meant they were always winning on the numbers game. This is where Jutland is important, because although the British lost more ships and lost more men in the battle, they still had this absolute superiority in terms of numbers and big guns and that’s what the mathematics said you could do.”

Dr Price remarked: “We conclude that the outcome of Jutland, in spite of apparent British tactical and technological failings, was the culmination of a decade of consistent and professionally insightful decision-making by the Royal Navy, which built and correctly wielded its decisive weapon, the Grand Fleet, to achieve the required strategic victory.”

The paper is due to be published in the journal History: The Journal of the Historical Association.

Members of the public are invited to attend a public lecture at the University of York on 5 June about the Battle of Jutland.

The event is a mixture of lecture, wargame and simulation with speakers outlining the tactics involved and some of the mathematics behind them.

The battle will be recreated using scale models on the floor of the lecture theatre, with the speakers and some of the audience taking on roles.

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