Wikipedia:Reference desk/Archives/Mathematics/2021 April 7

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April 7

Making educated guesses drawn from inaccurate/incomplete information?

Take the Battle on the Ice for example. One party claims that only 20 or so of their knights were lost in battle, whereas the other party insists that over 400 had been slaughtered. Is there some sort of metric that could be applied to arrive at "the most likely" range of figures, taking into account things like human nature and such? There must be some way to quantify it. Or is the problem just inherently ill defined? Earl of Arundel (talk) 02:26, 7 April 2021 (UTC)

Probably not exactly what you're looking for, but you might be interested in imputation (statistics), which has at least some overlap with your question. --Trovatore (talk) 02:31, 7 April 2021 (UTC)

That's a pretty good start actually. Thanks! Earl of Arundel (talk) 05:15, 7 April 2021 (UTC)

It is well known that chroniclers on either side of a battle tend to grossly underreport the number of casualties on their side and overreport the number for the enemy, so the numbers reported are rather useless for estimation. As far as mathematical methods are concerned, it all starts with the construction of a mathematical model. In my opinion, many of our relevant articles, including Imputation and Estimation theory, do not sufficiently emphasize the pivotal importance of model selection, while Model selection does not clearly describe the possible need for model construction – not all situations can be approached with an off-the-shelf model. In the physical sciences this is a bread-and-butter operation, and we now have the field of econometrics, but in history as an academic discipline this is an underdeveloped area. In this case, very simplistically, the model might be a formula that predicts the number of casualties given the number of combatants on each side. Ideally, it should be based on an understanding on how such battles were fought, and how the generals would make strategic decisions, such as when to accept defeat and retreat. Such a formula would have a number of parameters. These parameters could be estimated by fitting the model to the data of comparable battles for which there are reasonable estimates for the numbers. Not only should this give values for the unknown parameters, it should also give a precision range (spread). Then apply the model to the situation. In this case the combatant numbers are also uncertain, complicating the matter; a historian might perhaps advise one to go with the more conservative estimate.  --Lambiam 08:31, 7 April 2021 (UTC)

Good suggestions! And statistical methods such as linear regression (or even AI) could be used here too. That sounds pretty promising. Earl of Arundel (talk) 18:38, 7 April 2021 (UTC)

To put it another way, math can't create an answer without something to base the answer on. If you're on a jury, and the prosecution says the defendant committed two murders, and the defense says he committed zero murders, in the absence of more information should you take the average and convict him of one murder? It may seem like you're applying math to do so, but sometimes the correct answer is that there isn't enough information. --RDBury (talk) 09:11, 7 April 2021 (UTC)

I see, so the old "garbage in, garbage out" principle! Good point... Earl of Arundel (talk) 18:38, 7 April 2021 (UTC)

• Regarding the specific example you give, I searched and failed to find any semi-decent answer to "how to make a realistic estimate of the number of combatants or dead in historical battles". I had hoped to find one or two review articles on Google Scholar but no luck. I will still drop what little I found for anyone who's interested.

This forum thread gives some answers, but they are all fairly obvious. In academic journals, you can find stuff like this article (paywalled, I only read the abstract); more generally the Journal of Conflict Archaeology probably contains relevant material. Tigraan^{Click here to contact me} 16:16, 7 April 2021 (UTC)

No that helps. Those are the kinds of heuristics that, at the very least, might be useful for the initial construction of such a model. Earl of Arundel (talk) 18:38, 7 April 2021 (UTC)

WHAAOE. We have an article Casualty estimation. However, it does not deal with historical events, and is otherwise scanty on content. The related even shorter article Casualty prediction is also relevant; it mentions agent-based modelling, which could potentially also be used for historical battles.  --Lambiam 18:10, 7 April 2021 (UTC)

Thanks, those might prove to be useful here as well. Earl of Arundel (talk) 18:38, 7 April 2021 (UTC)