 Rwy'n fwyaf i'n dechrau, rwy'n ddweud i'r ysgolfaeth yma, oeddiwch i'r llunio, yn ymateb, rwy'n ddweud ei bod yn ymddangos, ond mae'r ystod o'r ffordd o'r atryg, a mae'n ffordd o'r rhan o'r ffordd o'r rhan, oherwydd yr oedd yn ymddangos, rwy'n rhan o'r ffordd o'r rhan o'r rhan. Rwy'n ddweud i'r grwp o'r hystoriadau a'r cystafoli ar gyfer y mynd, Ac mae'n gweithio cyd-ddiwyll y meddyliadau yn ymgyrchol hwnnw. Mae'r Hysbeth yn fleeingol, yn hynny yn mynd i'r hysrfa fel Llyfrgell, a mae'n hyn o'n mynd i gweithio'i ddod yn gallu parlwg y cyfenni hysbeth cael ymgyrchu'r hysri a dyfoddau'n dod yn ni. Roeddwn yn dod gan gael gan ymdaith arsig ar ôl, a fydd yn rhan i gael arsig arni arni eich gwaith ymlaen. Mae, oherwydd i'r cerddau'r cyfnod o'r yr ysgrifetau ynghylch yn y dyfedg y Dogwr Bank, wedi'i gwybod y byddai ymlaen o'r cyfrwsau yn 1915, mae'n gweithio'r cyfrwsau peirio'r cyfrwsau a'n fawr amser sydd arall oedd am ymlaen ymlaen i'w ymlaen cyfrwsau o'r cyfrwsau. Yn y ffordd maen nhw'n gweithio'r mathai, rwy'n credu i'w ddweud i'r hynny'n trefynol yw ddau'r cyfrwsau a'r cyfrwsau ar fy mod i'r cyfrwsau sydd eisiau byddai'n gweithio'r cyfrwsau. I hope to spend the first ten minutes also telling you things that will be very unsurprising to you. So if we take the 50 years before the Battle of Doggabank, as you know it was a period of unparalleled perhaps technical development and change without many opportunities to test the results of all those technical changes. So, no. Turn it on, the top right. Yes. Okay, so following the era of oak-built warships, we all know that the first couple of iron clads appeared around 1860, but they still look very much to the modern eye as the earlier wooden warships did. A couple of years later, well, you take the rather lovely frigate Merrimack and you turn it into that, the Virginia. And as we all know, what results is a stand-off effectively in which neither ship is well able to damage the other. So armour has the ascendancy over guns at that particular point. And because of this supremacy of the defensive with new iron armour, you had to think of something else to do. And we had a return briefly to the techniques of ramming, indeed. The affondatore, the sinker, was one of the ships at the Battle of Lissa in 1866, where the apparent lesson was that iron-clad ships could get in close and could sink through ramming. But actually, the story is not quite as simple as that because the guns at the time, well, the British still preferred to use a muzzle-loading rifle. And the point is that without the breech mechanism, you get an immensely strong gun. And although armour progressed so that we had compound armour in which layers of wood and iron were alternated, in fact, the British muzzle-loading rifle could certainly penetrate compound armour. So, although both guns and armour were developing, it's not absolutely clear that the defensive is always in the ascendancy. But we didn't really have tests after the Battle of Lissa. Of course, just to throw in a wild card here, we have the invention of the torpedo in the late 1860s. And I guess the sort of type of ship which is typical of the late 19th century is a battleship like HMS Victoria, in which what you have is mixed armaments, mixed guns. So you see turret guns there, just one turret, and then lots of casement guns here. And of course, nobody really knew what Rangers battles would be fought at. You had a history of battles being fought at very close ranges. You expected that the greatest damage could be done at close ranges, and you could put greater weight of metal on the enemy with those smaller guns very often. If anybody is interested in the development, the article which I like on that is by Carl Lautenschliger in international security from 30 years ago. And he has a nice summary of the development of the various weapons and defences against them through that period. OK, so let's take ourselves to the beginning of the 20th century, and the battle of Tsushima between a Russian fleet, which had just steamed a very long distance, and a very well-trained and effective Japanese fleet. The Japanese one. Bringing things home a little bit. At that time, Commander Bradley Fisk, one of the great figures in the US Navy, wrote a little article in the Naval Institute Proceedings, Why Togo One, and essentially he says Japanese fleet handling was better, Japanese gunnery was better than the Russian. Right, where had we got to in 1905? Well, we had the big gun, and armour had made very rapid progress. We had Krupp's cemented armour, so this is where you take steel and you treat the outside very differently from the inside. You may treat it with carbon or even just by blowing carbon dioxide over it, and you create a much more effective hardened armour. And the third thing that was a really significant technological development at that time was the possibility of replacing reciprocal engines with the steam turbine. So clearly from the point of view of fundamental engineering, if you try to create rotary motion then a rotary system is likely to be more powerful if you can get it right. And as is common knowledge in this room at least, the idea of putting them together in a single ship, well, came from various places, Italy originally, but the first ship to be built was HMS Dreadnought. So what you have there is a combination of big guns only, turbine propulsion and an appropriate amount of armour. And this was all part of John Fisher's revolution in the Royal Navy. But there was a second idea, which was that perhaps speed could be defence. And I guess the reason I put the three words at the bottom there is because all the careful people at the time, and people afterwards such as the British commander Gellico, made the point that what you really have in building a battleship is a choice in a certain tonnage of what you put into it, guns or propulsion or armour. If you put more of one, you have to put in less of the other. That's one of the others. The battle cruiser, the idea was to have the big guns, to have excellent propulsion, giving the ship great speed, but to be rather light on armour. So a ship like that could very effectively hunt down merchant raiders and raiding cruisers around the worlds, very good for a maritime empire. The ship looks very similar to Dreadnought, but of course what is hidden there is that the armour is very thin, something like four inches as opposed to ten inch or more for Dreadnought battleships. Now, was it intended that this should be used, this kind of ship should be used in the battle line? Well, it's actually never quite clear. This term battle cruiser is really a later one. At the time we would have called this an armoured cruiser, which of course has its own irony. But given that it looks so much like a battleship, that seems like a very naive point, but that does, it seems, affect people's minds and the willingness to put such ships into the battle line. The first time these battle cruisers were used was to do the job for which they were intended. So British light forces suffered a defeat of Coronel, just west of Southern America in autumn of 1914, and battle cruisers were dispatched to destroy the German raiders, which they did. That was, well, they were a bit lucky actually. The Germans only had eight inch guns, but there was one eight inch shell which lodged very close to one of the British battle cruisers vitals. It might have gone differently, but we didn't do a study of that battle. What we did instead was to have a think about the first big clash of dreadnoughts, by which I mean all big gun ships, which happened to be between battle cruisers at the beginning of January 1915. So if you recall the situation in the North Sea in the First World War, the crucial thing for Britain was to blockade Germany. Unlike a hundred years earlier, this was done not through a close blockade, but through the stationing of the Grand Fleet, all of the British big ships, in various bases on the west side of the North Sea. If you're a German, then from the German point of view, of course the British Isles looked like a great big breakwater across your access to the world, which is very much how they were used. The German intention was, with the Tirpitz's notion of the Riscoflotta, to attempt to try to get down to something like numerical parity by breaking off a portion of the British fleet at a point where the Germans had superiority, had advantage of concentration and destroying it. The British politically had a rather difficult job to do, because of course they knew that that was exactly what they had to avoid. What the Germans tended to do was to raid east coast towns in a way that created, so British east coast towns, in a way that created outrage in the British popular press and a lot of popular pressure on the Royal Navy to do something, but of course doing something by displashing a partial force was always going to be rather dangerous. Anyway, to cut the long story short, the first big clash here is between five British battle cruisers, so Dreadnought battle cruisers, and well three German battle cruisers, and this ship, Lluca, so all these ships would have been called armoured cruisers at the time, Lluca was actually the German response to what they understood to be building when Britain was building Invincible, the first battle cruiser, and Lluca was probably, I think, well, even the Germans at the time, regardless in retrospect as having been misconceived, it had eight inch guns, not bad armour, but slightly lower speed than the battle cruisers, and many people on both sides thought that Lluca was unfitted to be in a line of battle cruisers. So this is a rather simple battle for us, it's just two lines going pretty much in one direction and slogging it out. You see the potential complexity of the situation is that it's fleet geometry, fleet tactics determining that geometry, that determines the calculus of damage on the two sides, and at the later battle of Jutland, that issue becomes very complex. So the second paper in our series is about Jutland, but I'm not going to try and talk about that today. The Battle of the Dogar Bank really was a battle between two battle lines. It started in the early morning. Some of the big British worries were about a battle starting far over in the east of the North Sea, late in the day, because the worry then would be that British ships would be damaged and not be recovered, whereas German ships would be recovered safely. But this was different, this was on the Dogar Bank, which is a fishing ground towards the British coast, slightly closer to the British coast, and it started early in the day. The battle cruisers engaged just before nine o'clock. Well, at 9.43 the German battle cruiser's sidelets was damaged, she had a flash fire. So I'll talk a little bit more about ammunition handling later on. But you could argue that the irony in that was that it enabled the Germans to understand the dangers that they faced from flash fire. The British did not have a similar flash fire at Dogar Bank. But the flagship lion was hit. There's an artist's impression of lion at Dogar Bank. In fact she was hit many times without anything catastrophic happening. OK, let me come... I should have put in the... The big event at the battle, really, was that lion having been hit, she ended up having to haul out of the line. But before doing so, she put up two signals to the other British battle cruisers, which were intended effectively to say to the rest of the line, you go on, carry on fighting the German line. And the two signals were something like engage the enemy's rear and course northeast. But the trouble is they were understood together as one signal and understood as saying engage the enemy to the northeast, which was Bluker only. And what happened is that instead of carrying on with the battle as it was being fought at that time, the British ships concentrated on poor Bluker, which took a large number of hits and there's a propaganda picture actually of stern British sailors looking on as the beastly harness sunk. That's taken from this, the children's story of the war. The 1915. Only by sheer good luck did any of the German ships escape. Sorry, a class-based society, I'd have to parody. That was the general view. Propaganda view, but it wasn't just the propaganda view. Then Commander Reginald... Oh, I've got to say his name, it's a little bit unfair to it. Eilmer ran furly plunkied hernly earl Drax. You don't need a title if you've got a long enough name for the English aristocracy. Although he only took some of those names later for other reasons. Anyway, Commander Drax on the staff of the British Commander BT at Dogabank said, well, something I neglected to mention was that the second ship in the British line fired on the first ship in the German line because of a misunderstanding really about, well, fleet battle orders. Which meant that the second ship in the German line was unfired on for a while and Drax thought this was the problem. But for Tiger's misdirection of fire we certainly should have sunk the greater part of the enemy's squadron. That, I think, was the common view. We spent some time in the archives. We've come across that view several times. It wasn't universal, as we'll see. But it is a view that's come down to the modern day for some naval historians and even people writing about fleet tactics that the British lost an opportunity to win a decisive victory over the German battle cruisers. So that's the idea we want to test. But just before we get to that this lesson that the battle cruiser was a wonderful ship only Bluco was sunk and Bluco was an earlier version of the concept, really, not a full battle cruiser. This idea that the battle cruiser was vindicated by Doggerbank found its way into the United States. So there are a couple of naval institute proceedings articles from 1915 which say exactly that. There's a plea for the battle cruiser by a constructor and there's the arrival of the battle cruiser. The kind of things they say are that the capacity of the battle cruiser is such that it's employment in future fleet engagements. So remember not just as a destroyer of commerce raiders but employment in fleet engagements is a certainty. We've just seen an engagement between squadrons of battle cruisers and more hyperbolically, the battle cruiser is mistress of the sea. I'm not going to try and do an American accent for that. But certainly that view was common in the Allied navies. OK, so let's try and test it. Now, I'm not going to show you any equations anywhere. And when operations researchers or analysts try to present a mathematical model, you should never trust them. Treat them as if you're an engineer who wants to know how the cogs in the black box, which is the model, work. And you have every right to question everything right back to how the cogs fit together. And that's the spirit in which I'm going to approach what we're going to do next. So there's the black box in the middle. It's not very black model. Some scheme by which the parameters, the numbers that determine the conditions of battle, so shell calibers, damage effects, fire effects, everything in gaming will cause an outcome. So as John said, I'm spending a lot of time in the archives at the moment. And you can pretty much draw a distinction between the parameters, so all of the numbers that feed into the game, and then the rules of the game by which damage is caused or outcomes are reached. And actually there's quite a lot of confusion in the War College archives over the rules of the game in the period I'm looking at from 24 through to 46, which I can explain if anybody's interested later. But I won't do that now. So from our model, we hope to get an outcome. I've written a spray of arrows there because this model might have some randomness in it. War certainly has some randomness in it. So we can get an outcome. We can get many outcomes if we have a random model. And then what we've got to do is to compare the outcomes of the model with the truth. And this is where the word Bayesian comes in. So essentially, at its simplest, we go in with some prejudices. Well, that's a bit harsh, calling them prejudices, in Bayesian language we call them priors, prior values of the parameters. We see what outcome the model produces. We compare it with reality and then we go back and adjust our ideas accordingly. And this is... OK, so it's rather in contrast to traditional what is called frequentist statistics. And people who believe in a Bayesian approach have been true believers over the last 30 years. And I think largely they've pretty much won the battle. If you have a background certainly in the sciences rather than in traditional statistics, it's a very natural point of view because consider the sort of thing that might happen. Suppose that you're doing something like a medical trial. You've got a number of different outcomes. Those are the true outcomes. And they're a little bit different from what you were expecting, given the parameters. Well, you can adjust the parameters. And this is a very good tool for doing what Coon called normal science. So nothing very revolutionary going on. You're just trying to get a very precise idea of what the correct parameters are. You can pass it out with an idea based on all of your prior experience and knowledge beforehand. But then you adjusted it a little in the light of the true outcome. Well, back to a single outcome, which you would get, for example, if the model is deterministic. But what about a situation as in history where we only have one set of realised events? We can't run history over and over again and test what the probabilities were of different historical events actually happening. Well, nevertheless, you can use a Bayesian approach in exactly the same way to adjust the parameters a little, of course. I've drawn a true outcome there, a bit off-center. You've got less certainty perhaps than you had if you had a wide distribution of many, many replications of your trial. But nevertheless, you can do something. The name of this procedure is Bayesian computation, or approximate Bayesian computation. That word approximate is actually slightly misleading. It's not really more or less approximate than earlier forms of Bayesian computation. The big revolutionary thing was that it's called, well, Bayesian computation without likelihoods. Let me digress a little bit on the terminology. Probabilists and statisticians use the word probability to describe, okay, what's the chance of a coin that I toss coming up heads. They use the word likelihood slightly differently. Now, in everyday parlance, it means pretty much the same thing. But if probability runs from this way to that, given the parameters, what is the probability of that outcome? Likelihood is used to run the opposite way. So given the outcomes, the likelihood of certain parameters. And of course, the situation in which this particular issue really bites hard is in the law, actually. If you think of court cases, in Britain there are famous court cases concerning multiple cop deaths in the same family. There was actually a ruling in Britain, I think, that effectively said, something that outraged all of us, that said Bayesian thinking is too hard for juries. So the trouble is it's the right way of thinking about the situation. So that effectively amounts to saying that the correct way of arriving at the truth is too hard for juries. So what you do is on the right, there are plenty of articles you can read with no equations in them, which are good reads on this subject. The stuff on the right there in the legal context is evidence. Assorted circumstantial evidence, blood groups, genetic evidence and so on. So the evidence is the right way of writing down the parameters that might include simple categorical things like guilty or innocent. Anyway, right. So this is called approximate Bayesian computation because in the old fashion models, until about 15 years ago, you always had a very precise mathematical way of writing down the distribution, the likely distribution of the parameters. And it was always very hard to do in a case where the model was a bit more complex. The black box had a lot of strange stuff going on the side and it was hard to run backwards. But there was a groundbreaking paper about 12, 13 years ago, Tavaray et al, who called it... OK, so this is the term in modern use is approximate Bayesian computation. Essentially, it means that whenever you've got a lot of decent model and some parameters, you can try and run this procedure. OK, what happens if the true outcome is way off what you were expected? What are we going to do if that happens? Well, you can't just adjust the parameters a bit. You've really got to say one of three things has happened. Something is wrong. Either the model is wrong. That's perfectly possible. So, all of us then have to really delve into the cogs in the black box and work out telling us the right thing or approximately the right thing or if there's some fundamental flaw. Or it could be that the parameters are just very, very wrong. You've missed some parameters. Some things that just change fundamentally what you should have been doing. Or, something unlikely has happened. Isn't that possible? Unlikely things do happen. Now, at this point, of course if you're a historian, well, actually no, let's... If you're a historian, maybe you begin to smell how on earth do we tell whether something unlikely has happened. So, the historians' role is really to understand why things did unfold as they did. Why events unfolded as they did. On the other hand, of course, if you're a historian, you don't believe that everything was inevitable or else history is just one damn thing after another. So, we'll bear that in mind as we go through and I'll make some comments about historical methodology at the end. But for the moment, let's go and have a look at the model and the parameters and what happened at Dogger Bank. So, the model usually called the Lanchester model. Lanchester in Britain wrote his model down just before the First World War and some articles in Engineering magazine. But in classified work for the US Navy, Chase had written it down in 1902. Fisk had written down effectively the same model in 1905. And the way to characterize the difference is that whereas Lanchester and Fisk were using calculus, so if you never did any calculus, that's fine, Fisk used what we would nowadays called spreadsheets. So, he wrote down tables, but just think of it as doing your sums on spreadsheets rather than having the sophistication of calculus at your disposal. Ozipoff in Russia was probably working early during the First World War and then there's another character I haven't known about to whom Wayne Hughes alerted me, Antoine Boudry in France in 1910. And the point about this is that these ideas were coming out absolutely everywhere. It was very much part of the spirit of the age in early operations research was to try to understand this point which at its simplest is just that a force causes damage in proportion to its numbers and not in proportion to the enemy's numbers. So, when would that be true? Well in the case of Dreadnought battleships on the whole you expect each gun that's within range to be hitting each gun has a target each ship usually has a single ship as an opposing target and in order to make sure that the force causes damage in proportion to its own numbers but not in proportion to enemy numbers what you really need is a target-rich environment as perceived by both sides but one in which if you miss your target you're not going to hit something else instead because if that were true there would be a density effect and the general view is that in all the history of warfare this is the one circumstance in which that is probably and is typically true. So, that's just weight of opinion. We've got to say something about what these terms mean. Numbers are of the units which stand or fall together so they might be guns, they might be turrets, they might be ships. Fisk thought that the correct unit was turrets and if a turret can be destroyed that's sinking a ship, that's certainly true. If there's a danger that one hit can destroy the whole ship then of course the unit is the ship. Well, is it true? If we're actually looking for some evidence at the time I didn't perhaps appreciate the significance of these documents I was in the British National Archives at few looking through other things but there was a great big tome, a couple hundred pages about gunnery practises in the Grand Fleet during the First World War. This was actually all put together I think just after the war in 18 to 19. And what they were trying to do was effectively to work out whether or not that statement force causes damage in proportion to its numbers. It's true or not. And what they did was look back at all the exercise they've done and try and look at the effects of concentration, of ship concentrations of 2 to 1, 3 to 1, 4 to 1. And usually that is in individual engagements 2 ships against 1, 3 against 1, 4 against 1. And of course the danger was that spotting would be confused so you would mistake the shell smashes of another ship for your own and so full benefit of concentration would not be achieved. But on the whole it was pretty well achieved and they decided that thereafter in exercises, putting all things together a ship concentration of 2 to 1 indeed should stand. 3 to 1 and 4 to 1 there were some danger of confusion and they were given multipliers of 2 and a half and 3 for future exercises. But actually that's ample to justify the use of bold faced assumption there because concentrations of greater than 2 to 1 were rather unusual. They did happen but if 2 to 1 is okay and 3 to 1 and 4 to 1 still give you something better than 2 to 1 then as a baseline assumption this assumption is fine. So what went into our model it's a random, a probabilistic model is simply to say that each turret firing has a certain probability of hitting which of course is a function of the amount of practice the ship has had the range, the target, the armour all of this little stuff. What about the parameters? Well the reason we're able to do something here really is because we have for the parameters not just so okay a lot of the parameters are more or less fixed but many aren't. We have data from the earlier engagement off the Falkland Islands but we also have data from the later and much larger battle of Jutland. And to the extent to which ships and conditions were the same at Jutland as at Dogabank that's a reasonable thing to do. Well what are we talking about? We're talking about shells, ships, guns, armour gunnery practice because British battle crews are shooting was awful. But above all flash fire. So in that body of doctrine before the first world war there was a sort of tension between firing fast and firing accurately and as you know so you see the turret on top of the ship but you have the magazine deep in the ship and various handling chambers and means by which flash fire can be prevented from passing from the turret down through to the magazines. But it's commonly accepted that all of those mechanisms to stop flash fire spreading were not implemented properly. And further that in order to achieve rapidity of fire crews were storing chargers in the various handling chambers where they shouldn't have been storing them. And this was certainly true on the British side and probably true for the Germans as well. Certainly true before Dogger Bank and we've already said that side lits had a flash fire which caused the Germans to become much stricter in their handling procedures before Jutland because they saw the danger of this flash fire. The British didn't get that kind of lesson at Dogger Bank and on the British side probably flash procedures did not change much in the intervening period. The crucial paper for me here the one that best sums the situation up is Nicholas Lambert. That's a reference to the British battlecruiser commander BT's comment to the captain of his flagship at Jutland later on when the British battlecruisers were blowing up. After the first two he said there should be something wrong with our bloody ships today or our bloody system. And of course you can argue that both are true. In terms of the lessons learned from Dogger Bank what we want to know is if there were changes in flash discipline between Dogger Bank and Jutland. And on the one hand we have this statement here a mistake was made in firing too slowly during the earlier stages. Rapidity of fire is essential. Actually the correct lesson would have been that gunnery practice is essential and the British battlecruisers should have been hitting more accurately but we're not interested in that point at this stage but we're interested in whether or not as a result of comments like that flash discipline actually got worse on the British side. But in the same document early Chatfield, captain of Lyon says yes but plunging fire is a great danger to ammunition anywhere between decks. Lids of powder cases should not be removed faster than necessary and he's falling between two stools really. There's an Admiralty memorandum of February 1915 after Dogger Bank which does urge better flash discipline. They don't know what happened to side lids but it's clearly it feels like a lesson from Dogger Bank although it's not explicitly so and Lambert says that actually it was probably not widely acted upon. So it's hard to know it's not clear in which direction the lessons of Dogger Bank run for the British as regards flash discipline and there's nothing at all in the lessons learned. So I guess in our three points model or parameters or something unlikely happened we felt we'd done our due diligence on the flash discipline and we don't have a clear argument that flash discipline got worse between Dogger Bank and Jutland. There's one other nice little thing in the lessons learned I mean that the complacency of this is appalling I'll do that accent again. German shell for incendiary effect and damage to personnel are far inferior to ours their only good quality lies in armour penetration and damage to material sailors at battle stations armour penetration and damage to material look quite fundamental to me as a civilian I wouldn't know. I mean as for incendiary effects there is use of how much crucial stuff is led around outside the armour well anyway OK so before I just cut to the results let me state again this buzz word approximate Bayesian computation ABC now that it wasn't me who wrote the simulation it was my colleague Jamie Wood who's a systems biologist most of the time that's his day job he writes simulations of swarms of this and flocks of that and bacteria doing this he's basically the go to simulation writer for the biology department in my university and he makes the point that for 12 years now we've had this very standardised methodology we have a tool and everybody knows what tool you're using so if I say I hit it with something if I say I hit it with a hammer you know pretty much what I'm talking about as long as it's not a sledge hammer or a lump hammer in the same way we have a very standardised tool it is in some sense optimal computationally although that's perhaps of less interest to you but above all what it does is to explore all of the parameter space for its capacity to reproduce real results and in a sense there's a nice comment from Drax actually in a 1920 document talking about the value of wargaming which is a very appropriate thing to talk about here and he says well okay what you can do once in a fleet exercise, a fleet problem you can do several times a day on the gaming board these must have been quite quick games and do them 20 times a month well yes but you don't really explore every counter-intuitive possibility for the parameters until you get up to millions and tens of millions of wargames and that's what we're really doing if you do Bayesian computation you're doing a fairly simple wargame but you're doing it 10, 6, 7 at least times and the point of doing that is that if there are a lot of parameters there's a lot of the parameter space to explore and wander around it quite a lot to work out what's going on and you explore it thoroughly and you decide where could possibly explain what you observe okay so here are the results what we have here are two distributions this is what we think the probabilities were what would have happened at Dogabank and this is up to the point of the signals which cause the British battlecruiser to disengage from the rest of the German line and concentrate on Blucher what happened after that point is not typical of what had happened before and you can see that we conclude that actually what happened was fairly typical you've got 7 hits on German ships and we think there should have been about 6 you have 22 hits on British ships and we think that about 24 would have been typical with quite a big distribution the striking thing about that plot is that you should have expected sometimes as many hits on British ships as hits on German ships but this was BT's fault really the British battleships in Scarpa Flow had a lot of space and under Jellico they practised their gunnery hard and later at Jutland their gunnery was pretty good but BT was based in the much narrower Firth of Forth at Recythe and I don't think it's unfair to say that he did seem to be more interested in parties and hunting than he was in organising gunnery practice I think that really is fair now of course it's very hard to organise gunnery practice in the Firth of Forth you've got to go out into the open sea and it would have been difficult in an attempt to improve British battlecruiser gunnery practice what happened was that individual squadrons of battlecruisers were detached to join the Grand Fleet at Scarpa Flow for gunnery practice and in fact that happened just before the Battle of Jutland later on and the shooting of that particular squadron improved enormously anyway so the hits are fairly typical the unit is the turret well the Germans lost two turrets and we can see they got pretty unlucky actually there the median would have been to lose to lose no turrets for the British well they should have expected to lose turrets and indeed they did lose too but the more significant thing is in ships lost so the Germans there have lost no ships that's because at that stage Bluker had not been lost the point is they lost no ships during the three hours of the main battle between the lines of the battlecruisers the British lost no ships but they very definitely got lucky we think so you could say well this is perhaps over quantifying isn't it to say that between 35 the British had a 35 to 40% chance of losing no ships well no it's not so I'm going to get defensive as a mathematician now you see there's a very nice article by Joss Epstein at Santa Fe called Y Model if anybody's interested he kind of makes the point that well one of his points is that if you don't if you claim that you don't have a quantified model well probably you do implicitly because if somebody asked you to take a bet you would be willing to do so you just haven't laid the bones of your model bear in such a way that they can be they can be looked at carefully in this case we think we can quantify and we say that the British had just below a 40% chance of getting away without ships lost during that first phase of the engagement much more likely that was that they would have lost one or with nearly a 20% chance to ships or even more so I said earlier that the general British view was that the Germans had had a lucky escape but that wasn't everybody's view this chap who is a a tenant on a tiger the second ship in the lion said much as lion said we were marvellous so I don't know what his class background was so what his accent should be we were marvelously lucky to escape as we did shooting was damn good strange that two people and the two leading ships could come to such diametrically opposed conclusions of their observations of the battle and we say that essentially the British got lucky at its very simplest well given that the British lost three battle cruisers at Jutland a year and a half later to Flashfire they were very lucky not to lose ships at Dogabank and that's basically the point the question is whether or not we've tested that properly so the idea was to use Bayesian computation to really explore that inference and decide whether it is reasonable and I think we can go to say as far as to say that they would almost certainly have done so had the action not been truncated so as I say they had something like only a one-third chance bit more say 40% chance of not losing ships by the time the action was truncated if the action had continued for same again well square that the chances of their not losing a ship then would have been more like a tenth okay so now let me try and say something more generally about historical methodology and since we wrote the paper in fact I've had many more discussions with academic historians the academic historians in the audience can tell me whether or not they agree but if I try to get the historical endeavour down to its simplest and say well what we want to do is to understand why did events unfold as they did and as I said earlier there's this slight tension between on the one hand you don't want to engage in speculation on the other hand if history is not to be inevitable one thing after another then if it were then there wouldn't be anything to explain well I guess the lesson from what I've just tried to tell you is that to say well perhaps someone got lucky is no longer council of despair necessarily for a historian so I'm claiming that there's a new tool in the historians toolbox I think we've written the first paper on this approximate Bayesian computation has sort of been rolling out encroaching on various disciplines it's used in archaeology now to try to decide whether or not on the basis of archaeological finds distributions for example of finds events happened as they did so for instance I gave a seminar on this at Oxford and Hugh Strachan suggested that well I live in York most of the battles on English soil seemed to have happened around York there are lots of obsessive collectors of archaeological finds and geographic information systems mapping battlefield finds now maybe we can go back and have a careful look at where exactly the battle of Fulford happened or what exactly was the effects of Cromwell's second charge at Maston more that kind of thing anyway there's a red rag for a bull we made the mistake of framing the paper in terms of counterfactual history which upsets historians a lot so that's why I pushed in red Michael Howard grown up historians don't waste time on counterfactuals because you know if you look at the books on counterfactual history there's a lot of piling supposition on supposition and you think well what have we actually learned by the time we got two suppositions away from reality and in precisely such a book my name's St Neil Ferguson plaintively says how exactly are we to distinguish probable unrealised alternatives from improbable ones if you're playing the counterfactual history game and he doesn't stay for an answer but if you are actually so I showed you that distribution of British ships lost we had the distribution, the distribution was the outcome and the true outcome was one of those things so you know 38% chance of no ships lost 62% chance of at least one ship lost so for us it's the same question saying how exactly are we to distinguish probable real events from improbable ones and if we reframe it like that then I hope the historians can be a bit happier because we would say that when history is quantifiable doesn't happen very often not wildly ramified so not supposition on supposition and all sorts of unquantifiable counterfactuals can be modelled it's not very often that you have a clear model with a good rationale for why things happen and the parameters accurately determined in our case we have really good information on the parameters and the data battle at Jutland which gives us a lot more and well ok perhaps we are back to council of despair almost never then the reason we picked Dogabank was precisely because we could do this game there it's rather rare but perhaps I just haven't thought of the circumstances in which it might apply elsewhere then the answer is approximate Bayesian computation so just to pick one of my favourite sentences by my historian collaborator Chris Price and this shows why it is that he wants to work with mathematicians and systems biologists you see and this is pretty much his view the course of history is complex, contingent and develops within an envelope of probabilities surrounding the historical narrative it has to I think it's a good sentence but maybe that shows why I like historians I quite like purple sentences as we said if you want to understand why things happen we claim that you do have to at least acknowledge the possibility of other things having happened I guess we would say that if you're going to avoid the various causation of fallacies, post hoc fallacy and others then the mindset required by the historian is precisely that of Bayesian probability to understand historical actors implicit prior estimates of chances how these changed its events unfolded and how they compare with real probabilities not just realised events in fact at Christmas I was given three copies of the extended family of Tetlock and Gardener see for forecasting the pop-psych book of last year so they obviously knew what I would enjoy reading so I've been giving the others away essentially what actually let me take a quick show of hands anybody read Tetlock and Gardener no, oh you should it's very good I have no talk for Tetlock runs a project called The Good Judgment Project and the idea, this is a US intelligence idea was to try to see if the normal guy on the street actually not quite the normal guy on the street if members of the public were better at forecasting events than their intelligence analysts so for example you can sign up in 10 minutes for their geostrategic game where you've got to forecast things like will there be an election in Syria by the end of the year will the price of oil drop below $10 a barrel by the end of the year like that and the book goes into great detail about the mindset required to create good forecast actually I think they missed the crucial thing which is time I signed up for it, I really fancy doing it but it would take me about an hour on the web for every individual question quantifying every aspect of it to try to write down something reasonable and I just don't have the time which is a shame but that particular mindset certainly acknowledges that unlikely things do happen just because you make a forecast that turns out to be wrong doesn't mean you were wrong the English boxer Chris Eubank very sort of intellectual middleweight boxer he was briefly world champion 20 odd years ago I remember very much liking an interview and he said he thought I'm a really good bet for this fight and even if I lose I will still a bit a good bet for this fight well so the Bayesian would then say yeah but whatever our prior probabilities were once you've actually lost it you can modify those a bit but of course the same question arises would you modify them a bit how much would you modify them how strong were your priors your prior view about Eubank's abilities before the fight and these kind of mindsets Teplock and Gardiner call them the fox versus the hedgehog the hedgehog who knows one big thing as opposed to the fox who learns lots of little things in the later story of the battle of Jutland so that BT was more of a hedgehog the one big thing he knew was the Nelsonian view of engage the enemy more closely Jellico the commander of the battleships of the Grand Fleet was much more of a fox and from everything that he does you can see him weighing probabilities trying to maximise the chances and essentially the the game at Jutland I'm not going to give a Jutland talk now but the game at Jutland is for Jellico to try to create as much certainty as he can from the situation as it unfolds of a strategic victory even at the expense of a tactical victory foregone but anyway as I say that's another story I guess that's my punchline sometimes Bayesian methods can help they're an interesting tool in the historians toolbox and anybody can think of a really good situation which is tractable in exactly the way I said on the last slide then do tell me we can set Jamie to work thank you for your attention so I'm happy to answer questions questions about dogabank Jutland because I'm a mathematician actually I also run a bachelor's project on forecast verification and probability scoring which is another reason for that but also another one on statistical evidence and the law even though I'm really more of a physicist so any of those aspects of it I can perhaps say something interesting about but anyway so first question what was Churchill's role at this time what was he running around doing a lot of things I can't remember but what I do recall so something I recall in particular is correspondence between Jellico and Churchill Churchill has a very naive view that's big guns Jellico always says no look you've got a certain tonnage you can put in guns, propulsion or armour and you mustn't because Invincible looks like Dreadnought you can still see the guns but what you can't see is the 4 inch armour don't Mr Churchill think that a battle loser is a battle ship so that's my only comment actually about the interaction between what we've been talking about and Churchill I think Churchill would ideally like to be a bit more subtle in his thinking but his worst self gets the better of him and he just likes big guns I think that did he have something official to do in this was he first lord at that stage or was he and then he went back into the trenches didn't he and then he you were still first lord when did he was after the Dardanelles so that places that late 15 or something I don't think Churchill has any direct involvement Churchill liked Beatty a lot there's a story about Churchill being a young war correspondent in the Sudan and an encounter with Beatty jumping a shore off a gunboat and ever since then Churchill was an admirer of Beatty Churchill very much likes Beatty's style which accords with his own of course sorry but I can't really say more in fact I'm sure there are many people in the room who can fill in details of Churchill as first lord and background to this you showed a picture of the Parsons Turban and I presume it works in a case of yeah oh yes yes that was the actual the guts of the turbine that was actually from Botanic was not from a warship sorry what kind of horsepower would you get I presume they had the fire tool boilers yeah I don't know I'm not competent to answer that I do recall one anecdote by somebody I think on the quarter deck of Dreadnaught when Dreadnaught got underway saying how amazing it was they've been on many ships and normally with a reciprocating engine you get a hell of a vibrating and juttering and banging and you know the thing is moving and that Dreadnaught just seemed to just glide off without any noise at all sorry that's a little anecdote I can't tell you what the horsepower is of the Parsons Turban at that time and how it relates to the reciprocating engines of the time which the Germans carried on using for a couple of classes of ships but somebody at the back maybe can no? oh no I'm going to ask him about that it's a lot of work your approach with the what extent are you exploring options following major decisions in the cycle of what happened? not a lot, not yet but we think this is very important so having talked about it as historical methodology of course what you want to understand if you're to understand the historical actors is why they thought what they did whether they were right in thinking what they did and how clearly the natural thing after an event is for people to assume it was likely unless there's a particular reason to assume it was unlikely then people modify their behaviour on the basis of these things which perhaps we can show were unlikely so I had the example of the two Naval Institute proceedings articles there I don't think there's anything very striking for me about the way about either the way that a belief that Dogabank was likely affected things except in the Royal Navy complacency I think they were complacent the view that it was a victory they should have won which fitted in with the propaganda approach was absolutely fine and so they didn't well okay it's nuanced they certainly didn't act a lot to remedy the deficiencies of the shit there was that Admiralty Memorandum that was managing better flash discipline which didn't if I recall correctly say specifically that it was in the light of experience at Dogabank but was clearly going in the right direction but perhaps it was doing so a bit half heartedly I don't know the Germans learned the lesson biggest of the disaster to sidelits and who knows well actually who knows maybe we should what would have happened to the German battlecruisers at Jutland if they had not improved their flash discipline we know German cordite was much more stable so a German and American cordite was more stable than the cordite the British used on the other hand they had that fire on sidelits could have happened again and then going back to the before the battle this becomes a matter of historiography really is there anything in the historical literature that would change our views so historians views of the actors now that we know let me go that far now that we know that the British got lucky at Dogabank and I don't know of any glaring examples but these are interesting questions I think and certainly for any other example where one were able to do this kind of analysis I think from the historians point of view the interesting things then become the questions about well historical actors judgments in the light of our knowledge about the probability of what happened and also historians later judgments but I'm not really at the moment one of these sort of tertiary historians who sorry Kyle yes I was saying there seems to be two aspects of this if you're modelling before an event or modelling after an event to make decisions if you're modelling before an event you have factors which can hardly be considered in the parameters for example you mentioned the word luck several times and the other factor you can't consider is human error well hang on luck we can consider luck is all you don't know what it's going to be the whole message of what I've been saying is that for the last 15 years so in a sense across mathematics and statistics the big growth subject of the last 20 years and for the future in which fields medals are now being awarded is getting a precise mathematical handle on probability on what are called stochastics but not luck luck is what, realised events or unknown unknowns so what is luck unknown unknowns, black swans that kind of it absolutely right unknown unknowns let's see and tell it call them black swans right to borrow from Closivitz you like to talk about chance my question is given the influence of people like Frank T. Jane on the method of wargaming how it was applied here by people like McCartney Lill before the First World War how does the wargaming methodology play out in terms of creating the estimate of the situation before the battles of Doverbank and Jutland and then given that question how did the assumptions that are articulated in their estimate play out in the reacting to things that they hadn't foreseen before engaging in the battle I think that the big thing of the 10 years before Doverbank was lengthening ranges and the more the range increases the more fleet geometry matters and the commander's job becomes to create the right geometry so Doverbank was forked at ranges far greater than those typically on the tactical board and the Royal Navy before the war let me see I think it's like the Custins or Bacon who says that people have tried all sorts of things against me on the gaming board and nobody was ever able to beat a line but that was at shorter ranges I don't know of most of the papers in the Royal Navy no longer as far as I know on gaming even in the 1920s don't seem to be extant it's clear that there was tactical gaming on a tactical level board but I only have other people's comments in their memoirs typically about it and the one I just gave you is one interesting one I can't say much about the gaming of the rapid increase in range and thereby the changes in geometry that happened in the five years before Doverbank and I don't think anybody else can if I think of the papers by Sumida, Alan Garcia, Robert lots of them there's not much on that because I think the papers just aren't there that the archives material isn't there you mentioned in your research here that between the 20s and 40s you have seen a lot of confusion about how to come up with this effective model how to write it into the rules of a working and just wondering if you have any ideas at this point of what was causing so much of that confusion and what was the difficulty there's one particular point which so this is a a sort of a simple but a mathematical point that I'd need to explain on a board about ok so the result of damage being caused in proportion to numbers is what's called Manchester's Square Law if anybody's heard of that basically you have to get the idea that there are two things going on there's what happens instantaneously and there's what happens over the course of a battle if you're doing a tactical game in one move so instantaneously if you cause damage in proportion to numbers instantaneously then the result as you integrate is the calculus word but sum that up over the course of the battle is that the side wins which has the greater ok so a side's capacity to win depends on is in proportion to the square of its numbers but that's a summing effect over the course of the battle now just looking through the walk colleges gaming rules there's a point that I find rather interesting when Reeves was head of tactics in 1924 to 25 in the big tactical games of those two years when they say in the manoeuvre rules that if you got fighting between two forces of patrol or fighter aircraft that the umpires will decide so there's no formal rule the umpires will decide what the outcome is but the fighting strength of the two forces is in proportion to the square of its numbers and that's a terrible terrible error because remember the square is what happens over the whole course of the battle at an instant effectively the damage should be just in proportion to numbers not their square and then you can trace that through the war gaming right through to 1946 by 1941 they've started implementing the Lanchester's rule correctly that each side in each move causes damage in proportion to its numbers there's a two year gap in 1944 and 45 for some reason and then in 1946 they've got a slightly nuanced and different rule which is no longer quite the Lanchester rule but in another body of work which I've done with my colleagues I think we've shown from the historical data certainly from the data of the Pacific Air War that the Lanchester rule that each side causes damage in proportion to its numbers is wrong anyway so the danger is that in all the war gaming there is a greater emphasis or value placed on numbers of planes together in the air at one time and of course you could argue that there were actually unintended consequences that had a revolutionary positive effect I'm just forming these ideas in the US Navy because of the ability of the pushing of carrier aviation in the United States in the interwar period of course you also have Moffat in charge of the Bureau of Aeronautics and all sorts of other factors but certainly the impressive significance of aircraft and the importance of making sure that bomber and torpedo and observation aircraft were accompanied by fighters in the air to ensure control over the air was probably exaggerated by the games on the other hand it's probably a very good thing that it was now there's a as you can tell I'm beginning to your eyes are glazing over a little bit I'm beginning to download lots of my thoughts on this there's quite a lot to be said and I'm sure that in well okay there are plenty of people who could look at rules for current war games so I've just said some time as you know at the postgraduate school and I know some of them come over here to do annual gigs on combat modelling so use the intelligence of those guys you can look over the actual game rules and the instantaneous game rules and make sure that they're reasonable and that would be a very well worthwhile thing to do I think and maybe everything is just much better now if we take a wiggish view of history then I assume that the rules nowadays are just all perfect black box doesn't need to be examined whereas back in those days those are just old fashioned people they knew nothing somebody else give you a full disclosure I'm from the wargaming department here okay and when you say the model is wrong and there is a simulation that is not necessarily accurate I mean all models are wrong some are useful there are several levels of wargaming some of which like campaign analysis has a series of inputs the black box and a series of outputs there are other types of gaming analytic gaming is a little bit higher level that's the question I asked about decision making doesn't really matter it matters to a certain extent obviously but it is not necessary for the models of engagement to probability kill probability detection to be super precise yep I accept that because the games that are of the most interest and there is some work done here to Alan Lofi's book on the interwar games here is fascinating I've got that out from my desk at the moment that the the real value of the games at the level of the analytic game is when the outcome is determined what decision do you make and why how do you view your force ratios how do you view your relative combat power you know we tend to especially in the computer age because processing is so much easier now than it was we tend to get focused on is this a 0.7 or 0.67 probability of hit probability of kill doesn't really matter it's an effective missile it does its job if you are in its envelope what decisions do you make so I just talked about that out there absolutely and I guess a couple of thoughts first of all 0.67 versus 0.7 you don't care about you do want to know what the cogs in the black box are doing they might be important I agree absolutely that these details matter much less at the higher and more analytic level just as long as nobody is making any false assumptions in or inappropriate assumptions in force planning nobody ever does that before gaming yes I shouldn't overstate the significance of that imbalance but at least it worked in the right direction if it had worked in a different direction it might have caused a different course of construction in the United States Navy between the wars maybe I don't know maybe it wouldn't have done maybe Moffat and Reeves would always have made their points and it would have been okay that one is a wildly ramified bit of history which we can't model using Bayesian computation I think it sounds as though in your fire control equipment was not up to the Germans no I think the German fire control equipment on might be a bit out of my depth here on the sidelets there was absolutely out of control and of course there was a case on Lyon at Jutland where the major in charge of the turret basically flooded the turret thus killing himself and the remainder of his crew but saving the ship yeah I don't know I don't know enough about German fire control sorry by fire control you mean fire well the ability to fire as a target oh sorry okay you mean okay so for director firing the Germans had better better optics basically the British there's been a long controversy over what we can call analog computers should be used the Argo clock which was a particular form of rangefinder fitted to the dryer table and this sort of stuff actually the British had pretty effective director firing certainly on the battleships and certainly on the battleships that were fitted with the Argo clock the Germans tended more to fire independently but they fired better and they had good optics I think that's probably the most significant thing as far as I know but somebody else may know better than me so I thought you meant damage control did any of these theories change when like in the late 30's early 40's when the German pocket battleships broke up pick up spray etc which theories what well this linecast that very the Lanchester theory because those battleships really those pocket battleships really tore it up for I'm not sure I see the connection really between when the Germans built what they could and you could make an argument that the pocket battleships were not well conceived on the German side on the German side I think I mean as commerce raiders of course they were good but so would anything have been in terms of the forces they were likely to meet they were constructed within the constraints on German construction in the 30's and that perhaps was more significant you know that that was the real constraint rather than what they would have wished to build I don't think there's much to do with the Lanchester models anyway I guess we should probably I'm happy to talk to anybody else who what's going to say that you couldn't hardly apply that theory to the battle of Britain for example where the couldn't apply it to the battle of Britain the theory of numbers and multiplication thereof to predict an outcome I mean because the relative numbers were quite out of balance the Germans have far larger well hang on you're interested in sortie numbers and sortie numbers as a time series day by day and in fact we've got four papers on that now so if you're interested please feel free to have a look at the literature on the battle of Britain sorry what am I saying well you talked about the Germans having a larger force and that there was more imbalance in numbers imbalance in numbers is precisely what enables you to test Lanchester assumptions and also when you're testing it you're interested in forces engaged so really you're interested in comparing loss rates with sorties flown and because you can do that day by day and to a large extent one day is much like another and in fine weather one place is much like another although one height is not like another you have some homogeneity in the time series data which enables you to some stationarity in the time series data which enables you to conduct analysis much more effectively than you ever can of land and all arms war where people have made various attempts to test Lanchester and related models and they usually come to nothing essentially foundering on the variability of the conditions underlying the data I think but as I say if you're interested in the battle of Britain we've got both quantified and narrative history papers When England started going into World War II did they have the same World War I firepower and equipment because the battle-tip was built in 1918 and she lasted one salvo from the Prince Aigan Yeah, I mean as Rangers opened out there was a crucial story of the battle of Britain and the British but there was a crucial story about how much you armoured a deck and there are if you think as the range closes in you're vulnerable in different ways the different sorts of fire as things close in Hudd was passing through a so Bismarck's shooting was excellent but so you know a second salvo I think while she scored a hit but Hudd was passing through a zone at which she knew she was vulnerable because she was basically an old super battle cruiser I think it's still fair to say to say not enough armour now there is a test to be done a sort of question was Hudd desperately unlucky or not but that's quite a tricky question to answer but in principle well the trouble is that there was only one Hudd so you don't have good data on the parameters really you can estimate you can count the priors but they'll have nothing like the strength you get for the first of all battle cruisers from Dogabank and Jutland we have luck again unknown unknowns well no I think the unknown unknowns are pretty you know what Hudd's potential vulnerabilities are and so do her captain so does anybody who's sorry they try to rebuild her deck yes anyway I think we probably spent enough time so thank you very much