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## Math. model, v3

An wise reader pointed out to us a significant shortcoming in the published mat. model v2. To estimate the number of dead and to estimate the number of wounded in the formula

`T = R / (A / Q)`

we use the same `Q` - the total number of applications from relatives.

This number can be used to estimate the total number of AFU fighters, but not to estimate the dead and wounded, because the last two categories are strictly non-intersecting. Instead, for each category `i` you should use `Q_{i}` - the number of applications for people from this or that category. And here's why: a person, with extremely rare exceptions (about them - below), cannot be both captured and dead, that is, any probabilities associated with being in one of these categories will not be independent.

For each category `i` you should use the formula

`T_{i} = R_{i} / (A_{i} / Q_{i}`

At the same time, the v2 model estimate for `T_{i}` is overestimated by `Q / Q_{i}` times (1).

In the v2 model, only the total number of requests is known `Q = Q_{dead} + Q_{captured} + ...` But it is not clear how they are divided into separate categories. What is it? How many applications, in fact, are about the dead, how many are about prisoners, how many are about other categories, if we know nothing about these people except, in fact, applications?

In the v3 model, which we describe below, we tried to make this estimate at the cost of introducing additional assumptions. The new version of the model does not completely replace the previous model, but fixes the v2.

Note: All numbers in this article are at the time of writing. Since new data appears every day, the numbers will change over time. Accurate estimates are published in the form of graphs, the values for which are calculated automatically and at once.

## Part 1: Categories of people

The first issue to be addressed is what categories are possible for those being applied for.

The category set must have the following properties:

1. describe the entire population of VFU fighters (any person should in any case fall into one of these categories);
2. no two categories should intersect (any person must fall strictly into one of these categories);
3. categories should describe any significant part of the people. The fact is that anything can happen in a war: someone dies under shelling, being already in captivity, funerals come for the living, the dead are considered missing, and so on.

We have considered several options:

• the dead: there are such, although they are relatively few (273 people were found on applications);
• prisoners, including the wounded: this is the vast majority of those found (1277);
• others who ended up on the Ukrainian side: wounded soldiers of the VFU, deserters, any other people - nil. During the ten months of our project's work, we have not met a single case when such a person would be found on the application. Please note that we collect information, including from hacker groups such as Nemez1da.ru or Beregini, who publish certain lists, including deserters and the wounded. Moreover, in our database there is a non-zero number of deserters, albeit not a very large one. Therefore, we have to accept that the number of applications for deserters, wounded or other categories is less than 0.1% of all applications because we have not come across a single such case out of more than a thousand people found;
• Missing Persons: upon closer examination, it turned out that any missing person in any case falls into one of the above categories. The only thing that distinguishes him is the lack of information about him. Therefore, this category cannot, in principle, be included in the set under consideration.

We conclude that based on the cases we have encountered, any person who has been reported can either be a prisoner or a dead person (2). We did not observe other outcomes in significant quantities.

## Part 2: estimation of the overestimation of the number of prisoners in the v2 model

Here we will consider two methods that are fundamentally different from those used in the v2 model.

Method one - based on information about exchanged fighters. To date, our database contains more than 1200 entries about the AFU fighters who were exchanged.

We discarded information about exchanges before September 21, 2022 - firstly, it is only a tenth of all known exchanged ones, and secondly, unfortunately, during that period of time we did not structure the information properly, so use it for automatic daily calculation difficult.

Of the remaining 1080 records, we know about 730. Thus, judging by the exchanged ones, our database contains information about approximately 65.1% of the prisoners.

In total, our database contains information about 6555 prisoners, which gives an estimate of the number of prisoners at `6555 / 0.651 = 10069` (3).

Comparing this estimate with the estimate of the v2 model, we get `Q_{in captivity} / Q = 10069 / 33959 = 0.297`, in other words, only `29.7%` of all applications submitted for people in captivity, and the remaining 70.3% - for dead, even if we do not know what happened to a particular person. (4)

Method two - based on applications, according to which relatives found something themselves. At the moment, our database contains 53 applications, according to which 40 people were captured and 7 more were exchanged (the rest, unfortunately, died).

Similarly to the previous method, the number of prisoners is `6555 / 0.75 = 8740` people, and `Q_{captured} / Q = 8740 / 33959 = 0.257`. That is, according to this method, only `25.7%` of those who are sought will be captured. The remaining `74.3%` will be dead.

We believe that the first method is more reliable, since it does not depend on the moral and emotional state of the applicants, which can distort the statistics (will you inform any project if your loved one has died?). However, the closeness of the results of the evaluation of the second method somewhat adds confidence in the estimates.

## Part 3: estimating the overestimation of the death toll in the v2 model

Based on (2) and (4):

`Q_{dead} / Q = 1 - Q_{captured} / Q = 0.703`

Thus, the v2 model estimate in terms of the number of deaths is overestimated by about `29.7%`. Hence the v3 model estimate is `249,035 * 0.703 = 175,071` dead.

## Conclusion

In the v2 model, we made a conceptual error by assuming some states (captured and dead) to be independent. Thanks to the attentive reader in the new version of the model, v3, we offer a correction and an addition. The fix is based on a number of new assumptions.

On the one hand, the new model is still, with an accuracy of a couple of tens of percent, consistent with the statements of various official parties and experts on the number of deaths (the v2 model was 15-20% ahead, the v3 model was 10% behind them).

On the other hand, the estimate of the number of prisoners has become much closer to [information published earlier by the Russian side] (https://t.me/rybar/42236).

For greater clarity, in the near future we will slightly change the publication of charts: All charts will display scores for the v2 model (faded from post day) and v3 model (rich from post day)

In the article itself with graphs, we will leave only a brief description of them and a list of major changes and events, for example, the transition to a new version of the model, the simultaneous addition of a large amount of data, exchanges, statements by officials voicing losses, and the like.

In the meantime, here are the charts:

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