【瀚海数据说】二战军队死亡及其影响分析（中英对照）

第 356 期

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本文是中国科大86级校友孙华的又一力作。继空战飞行员系列三部曲之后，孙华尽显精算师对数据的敏感，开始了一轮二战军队死亡人数的分析。第二次世界大战距今70多年，是人类史上最惨烈的战争，无论是死亡人数还是卷入战争的国家范围，仍然是值得分析和反思的，特别是21世纪的今天，我们更加期盼来之不易的和平，希望能够以史为鉴，看到战争的残酷与代价，因为那不仅仅是数字，而是一颗颗鲜活的心跳嘎然而止的惨烈……那么，在这篇分析中，作者为什么选择军队死亡作为研究指标？他又用了什么数据，采用了什么分析方法，得出了什么结论？让我们一起来看看他的解读。

本文内容为作者原创观点，如果读者有不同看法，欢迎您留言和讨论。

关于各国对二战的贡献常常有很多争论。虽然许多国家参加了二战, 但真正只有少数几个主要的参与者。本文试图通过分析军队死亡来分析各国对二战胜利的贡献。

这个分析得出了一些非常有趣的定量结论，比如：

1. 苏联对二战的胜利作出了最大的贡献。事实上，苏联的贡献是所有其他盟国总和的4倍。

2. 到二战结束时，美国的军事实力是当时最大的。其总军力高于苏联、英国、法国和中国的总和。因此，美国在二战后成为联合国的主导角色也就不足为奇了。

3. 美国是打败日本的主要贡献者。美国干掉的日军比中国多4倍。

4. 很显然，尽管中国在抗日战争期间损失惨重，但中国并不是东方战线的主要战场。这是一个次要战场。国民党的贡献是共产党的3倍多，但共产党的部队在单位基础上的效率是国民党军队的2.5倍。

5. 根据数据显示来理解二战。二战的主战场是在欧洲，次要战场在亚洲。在欧洲，主战场是东部战线。在亚洲，主战场在太平洋，中国战场是次要战场。在中国，主战场是由国民党领导的正面战场，次要战场是由共产党领导的敌后战场。中国共产党相当有效，对二战胜利的贡献是亚洲次要战场中的中国次要战场中的敌后次要战场。

首先，为什么选择军队死亡作为研究的指标？这是因为军队死亡是彻底无法恢复的兵力损失，而其他指标，比如伤亡人数和总损失往往翻倍，因此会高估损失。军队死亡也更容易追踪，因为政府通常需要因为军队死亡赔偿的目的而保存比较准确的记录。

我选择用德国军队作为比较的标尺，因为德国与苏联、美国和英国军队有直接作战。然后，我用美军作为换算工具来衡量日本军队以及与日军作战的国共军队。尽管具体的数字因来源而异，但总体的结论保持不变。

让我们先来看看德国军队的死亡人数。二战中德国军队死亡人数为553.3万（1），详细如下：

这个列表清楚地显示苏联的东线是二战欧洲战场胜利的最重要贡献者。

接下来，我们来研究一下盟军方面的军队死亡情况，详细如下：

如果我们将德军的单位军效（PUE）设置为100，那么我们可以计算：

美军单位军效 = 由美国造成的德国军队死亡/美国在欧洲的军队死亡 = 374/256*100 = 146

英军单位军效 = 300/383*100 = 78

这意味着，总体而言，100万美军的战斗力与146万德军相当，100万英军的战斗力与78万德军相当。这个结论与我对二战的基本看法是一致的。当时美军在空中力量和物资方面远远优于任何其他国家，而德军在装甲方面基本上比英军要更强大。

请注意，单位军效的概念并不一定意味着1名美军士兵的战力与1.46名德军士兵相当，甚至100名美军士兵的战力也不一定相当于146名德军士兵。单位军效的概念是在大规模战场而不是战术层面衡量军事力量的效能。

苏联的情况很有趣。在整个二战期间，苏联红军的单位军效只有4,137/8,656*100 =48。然而，这一数字被红军在战争初期遭受的可怕损失所拉低了。红军能够奇迹般地重建自己，在战争中不仅生存了下来，而且成长壮大为一支完全不同的、更强大的军队。在二战结束时，我估计红军的单位军效已经增长到大约100。德军和苏军在柏林战役中都大约战死10万人的事实就证明了这一点（7）。

现在让我们来看看亚太地区与日军作战的情况。亚洲的情况有点混乱，确切数字很难得到。所以我们必须用间接证据进行有根据的估算。

总体而言,最权威的研究表明，日本有212.1万名军人死亡，其中164.7万是陆军，47.4万是海军（4）。细目如下：

二战期间约有40万日本士兵在中国阵亡。国民党军和共产党军的功绩问题是一个特别难缠和棘手的问题。造成这种混乱的因素很多，比如战时记录的缺失，国民党军和共产党军之间的内斗，甚至国民党军和共产党军之间改庭换面，等等。还不要说战争之雾，也就是战争本来就有的混乱与模糊。

我们只能根据间接证据做出有根据的估算。我估计共产党至少干掉了10万日军。最可靠的间接证据是，共产党军队俘虏了大约7,000名日本战俘（8）。战俘计数可能非常准确，因为必须有被俘的活的敌方士兵才能进行计数。我们可以与冲绳战役作个比较。在冲绳，美军杀死了大约10万名日本士兵，并俘虏了大约7,000名战俘。另一个间接证据是共产党军队的规模从大约5万正规军发展到大约120万正规军和大约200万民兵。共产党除了从敌人（包括日本军队及伪军）身上夺取武器之外，基本上没有其他武器来源。（10）这里也可以看出来共产党军至少要干掉10万以上的日军才能夺取这么多武器来发展出这么大规模的军队。

现在我们可以估计每个国家军队的单位军效：

当我们比较日本和美国之间的军队死亡时,数据是惊人的，两国的比例约为10比1! 日军的是169.3万人, 而美军死亡人数为16.1万人。所以日本单位军效 = 161/1,693*146 = 14。

尽管日本是太平洋战争的罪魁祸首，但与美国和欧洲列强相比，日本的军事实力实际上非常薄弱。这并不奇怪，因为当机械化装甲战在欧洲成为常态时，日本军队基本上没有装甲，而且日本海军在整个战争期间无法增加任何主战航空母舰或新型飞机。最终，这个比率反映了一个事实，也就是日本在二战中只是一个初步工业化的国家。

中国军队的总体单位军效与日军的单位军效比较,为407/1,481*14=3.8。这个数字意味着中国军队的单位军效甚至比日军的还弱4倍左右。这种巨大的差异是一个农业国家与一个工业化国家，即使是一个初步工业化的国家作战的自然结果。

中国国民党军的单位军效是307/1,320*14=3.2。日军的单位军效是国民党军的4.3倍，所以日军在战场上经常能够打败4至5倍的中国军队也就不足为奇了。鉴于国民党师的编制规模较小，那就很容易理解为什么日军一个师团会经常击败10多个国民党军的师了。

中共军队的单位军效同样被计算为100/161*14=8.6。它仍然比日军弱得多，但却是国民党军的2.5倍以上。尽管缺乏武器，共军的组织比国民党军要有效得多。在我看来，这是共军单位军效更高的主要原因。

基于单位军效的概念，我们可以将日本军队死亡转换为同等的德国部队死亡，将日本军队死亡乘以14/100=0.14的系数即可。于是，我们可以计算对盟军胜利的贡献（CAV）。以相当德军死亡总数为指标，可以得到如下的结果：

现在结论就很明显了，苏联的贡献是总贡献的81%，是所有其他盟军总和的4倍。尽管中国损失惨重，但只占全部贡献的1.1%，其中约0.8%属于国民党，0.3%属于共产党。

联合国是二战的产物。人们可能会问，鉴于苏联在二战期间做出的不成比例的巨大贡献，为什么是美国，而不是苏联，似乎在联合国占据了主导地位。为了解释这一点，我引入了总武力值（TMS）的概念，它的定义是单位军效乘以一国军队的规模。总武力值以百万相当德军为单位。结果如下：

例如，美国在二战末期拥有约1,200万人的军队，因此美国的总武力值计算为12*146/100=17.5。这意味着美国的总军事实力相当于1,750万德国士兵。在二战高峰时期，盟军共有约3,380万士兵，是轴心国1,580万士兵的2倍多。从总武力值来看，这种差别更加显著了。盟军的总武力值相当于3,200万德国军队，而轴心国的总武力值仅相当于900万德国军队，不到盟军的1/3。难怪轴心国会遭遇全面失败。

二战结束时，美国的总武力值为1,750万相当德军，而苏联、英国和中国总武力值的总和仅为1,410万相当德军。因此，美国战后在联合国发挥主导作用是理所当然的。

中国的情况很有意思。中国对盟军胜利的贡献只有略多于1%，其总武力值只有30万相当德军，就这一点总武力值还分裂在国共两党之间。在历史贡献和总武力值这两个指标上，中国都比苏联、美国和英国有数量级的差别，而苏联、美国和英国之间就没有数量级的差别。那么，为什么中国会在联合国安理会常任理事国的议席上占有一席之地呢?

很怪异的答案是因为法国。对于法国，我甚至懒得计算它的单位军效，贡献值和总武力值。俗话说，败军之将不可言勇。法国在二战期间基本是靠边站，因为它在战争初期就投降了。最初，战后联合国安理会本来只有美国、苏联和英国。从历史贡献和总武力值的角度来看，这是很自然的结论。然而，苏联不喜欢这个安排，因为它认为英国将始终追随美国，从而事实上要遮蔽掉苏联的声音。作为解决办法，苏联坚持邀请法国加入安理会常任理事会，因为法国往往与美国和英国意见不一致。作为反制措施，美国邀请中国加入安理会，因为它相信国民党政府会密切紧跟美国的政策。英国不喜欢中国加入安理会，因为中国希望夺回当时英国的殖民地香港。罗斯福明确地指出，中国的历史贡献和总武力值虽然与三大巨头相比微不足道，但仍然比法国好得多。因此，中国就和法国一起入了常。二战后的四大国是指美国、苏联、英国和中国，而没有法国。

日本的情况也相当有趣。从日本的角度来看，日本80%的军队被美国干掉，美国的单位军效比日本高出10倍以上，美国的总武力值是日本的15倍以上。因此，毫无疑问，日本承认它被美国打败了。另一方面，尽管中国也是同盟国，但日本并不认为它被中国打败了。很简单，日军的单位军效是中国军队的3.6倍以上，到二战结束时，日本的总武力值虽然与美国相比很小，但仍然是中国的4倍多。换句话说，日本还可以轻而易举地一对一地击败中国。

日本的观点直到朝鲜战争后才改变了，当时中美两国在朝鲜打成了平局。在朝鲜战争期间，中国军队死亡约183,108人，而美国则遭受约36,574人死亡（5）。假设美军仍然维持146的单位军效，那么中国军队的单位军效为146*37/183=29，是二战期间日军的两倍多，是二战期间中国军队的8倍。中国军队不再是二战中那个懦弱的小孩子了。1951年底，中国常备军约627万人（6），其总武力值为6.27*29/100=180万相当德军，远远超过日本所能达到的110万相当德军。到此为止，日本已经意识到它不能再看不起中国了，因为它不能再在一对一的战争中打败中国了。事实上，到这个时候，中国可以击败日本了。

从总武力值的视角来看朝鲜战争的平局也是很有意思的。朝鲜战争结束时，中美在战场上拥有以下的兵力和总武力值。（9）

在朝鲜，中国拥有相当于39万德军的总武力值，美国拥有相当于48万德军的总武力值。因此，这解释了为什么中国在第五次战役中被决定性地击败了。然而，中美之间的总武力值非常接近，在山地的坑道战中可以消除掉这种差异，而这正是目前朝鲜平局的战线。总体而言，中国队是处于防守状态的，而美国队在战线稳定后处于进攻状态，这也与美军在朝鲜的总武力值高于中国是一致的。

诚然，只从军队死亡的角度看待历史,也有其缺点和局限性。例如，支持这一分析的基本前提是单位军效在整个战争中保持不变，而现实是，获胜方的效能普遍提高，而失败方的效能在下降。此外，同样数量军人的死亡对不同国家的战争能力可能有不同的意义。要是美国经历了苏联的同样的军队死亡，美国早就会退出二战了。然而，基于军队死亡的分析是研究不同国家军事实力的一个重要指标，如果不是最重要的指标的话。我还没有看到别的更客观和相关的指标。用其他信息补充军队死亡分析，可以使人们更好地了解军事历史。

我发现挖掘历史军队死亡数据确实很有启发性。用单位军效、贡献值和总武力值的概念，可以将各国的力量明确对比。这些数字阐明了一些模糊的问题，并清楚地说明了谁在二战中对胜利做出了最大的贡献以及谁的军队是最强的。数学爱好者对历史的看法可能相当地独特和有洞察力。

An Analysis of WWII Military Deaths and Their Implications

There are usually a good amount of arguments about WWII contributions from various countries. While many countries participated in WWII, there are really just a handful of major players. This article seeks to examine the contribution to the victories in WWII through an analysis of military deaths.

This analysis leads to some very interesting quantitative conclusions, such as：

1. The Soviet Union had by far the greatest contribution to the victories in WWII. In fact, the Soviet contribution was about 4 times as much as all other allied countries combined.

2. The US had by far the greatest military strength by the end of WWII. Its military strength is higher than the sum of the Soviet Union, UK, France, and China, combined. So it is no surprise that the US was the dominant player in the UN after WWII.

3. The US was the dominant contributor to defeating Japan. The US destroyed about 4 times more Japanese forces than China did.

4. It is clear that China, despite its heavy losses during the Japanese occupation, was not the primary battleground on the eastern front. It was a diversionary front, where the Nationalists’ contribution was more than 3 times that of the Communists, but the Communist forces were about 2.5 times more effective on a per-unit basis than the Nationalist forces.

5. Now we can have a clear picture of WWII. WWII’s primary theatre was in Europe and the side theatre was in Asia. In Europe, the primary theatre was on the Eastern front. In Asia, the primary theatre was in the Pacific with the side theatre in China. In China, the primary theatre was led by the Nationalists and the side theatre was led by the Communists. So the Chinese Communists’ contribution to the victory was the side theatre in the side theatre of China in the side theatre of Asia, although it was rather effective.

First of all, why choose military deaths as the indicator for the study? This is because military deaths are the ultimate irrecoverable force reduction, whereas other indicators such as casualties and total losses often double count and therefore overstate losses. Military deaths are also easier to track because governments usually need to keep fairly accurate records for military death compensation purposes.

I chose to use German forces as the yardstick for comparison purposes because Germany had direct conflicts with the Soviet, US, and British forces. I then used the US forces as a conversion tool to measure Japanese forces and various factions fighting the Japanese. Although the specific numbers vary depending on the sources, the overall picture remains the same.

Let’s first see German military deaths.

Total German military deaths in WWII is 5,533 thousand (1), with the following distribution.

It is already very clear that the Soviet Union’s eastern front was by far the most significant contributor to the victory in Europe.

Next, let’s examine military deaths in the allied forces.

If we set the per unit effectiveness (PUE) of German forces at 100, then we can calculate, US forces PUE = German Military Deaths Caused by the US / US Military Deaths in Europe = 374/256*100 = 146, and UK forces PUE = 300/383*100 = 78.

This means, in general, that 100 thousand US forces had the same fighting power as 146 thousand German forces, and 100 thousand UK forces had the same fighting power as 78 thousand German forces. This conclusion is consistent with my general observation in WWII, where the US forces were far superior in air power and material than any other players, and the German forces were generally stronger than the British forces in armor.

Note that the concept of PUE does not necessarily mean that 1 US soldier is as powerful as 1.46 German soldiers, not even that 100 US soldiers were as powerful as 146 German soldiers. PUE is meant to measure the effectiveness of military forces on a grand scale and not on a tactical level.

The Soviet case is more interesting. Across WWII, the Red Army’s PUE was only 4,137/8,656*100 = 48. However, this number was dragged down by the horrendous losses the Red Army suffered in the earlier stages of the war. The Red Army was miraculously able to rebuild itself to a completely different and much stronger army while fighting for its survival. At the end of WWII, I estimate the PUE of the Red Army has increased to about 100, as evidenced by the fact that German and Soviet forces suffered about equal deaths of 100,000 during the battle for Berlin (7).

Now let’s look at the situation in the Asia Pacific fighting the Japanese. Here the conditions are a little messier and concrete numbers are hard to come by. An educated guess had to be made with circumstantial evidence.

Overall, the most authoritative study shows that Japan suffered 2,121 thousand military deaths with 1,647 from the army and 474 from the navy (4). The breakdown is the following.

It is generally believed that about 400 thousand Japanese soldiers died in China during WWII. The question of credits to the nationalists and the communists is an exceptionally hairy and thorny one. Many factors contribute to the confusion, such as lack of wartime records, infighting between the nationalists and communists, and even forces changing sides between the nationalists and communists. And let’s not forget the general fog of war.

One can only make an educated estimate based on circumstantial evidence. My estimate is that the communists killed at least 100 thousand Japanese forces. The most reliable circumstantial evidence is that the communist forces captured about 7,000 Japanese POWs (8). The POW count could be very accurate because one must produce a captured living enemy soldier to make the count. One can compare this to the Battle of Okinawa, where US forces killed about 100,000 Japanese soldiers and captured about 7,000 POWs as well. Another piece of circumstantial evidence is the size of the communist forces, which grew from about 50,000 regulars to about 1.2 million regular and about 2 million militia. The communists had little other sources for weapons other than capturing them from its enemies, both the Japanese forces and its collaborator forces. (10)

Now we can estimate the PUE of each force.

The data is astonishing when we compare military deaths between Japan and the US, where the ratio is about 10 to 1! Japan’s 1,693 thousand vs. US’s 161 thousand in military deaths. Japan PUE = 161/1693*146 = 14.

Despite being the perpetrator of the Pacific War, the Japanese military was actually very weak when compared with US and European powers. This is not surprising given that the Japanese army essentially had no armor when mechanized armored warfare was the norm in Europe, and that the Japanese navy was not able to add any main battle aircraft carrier or new models of airplanes during the entire war. Ultimately, this ratio reflects the fact that Japan was only a lightly industrialized nation in WWII.

Chinese forces’ overall PUE is compared with that of Japanese forces at 407/1481*14 = 3.8. This figure means that the Chinese forces were even about 4 times as weak as the Japanese forces. This dramatic difference is the natural result of an agricultural nation fighting an industrialized nation, even a lightly industrialized nation.

Chinese nationalist forces’ PUE is 307/1320*14 = 3.2. Compared with Japan’s PUE of 14, which is 4.3 times that of the nationalist forces, it is not surprising that Japanese forces were often able to defeat Chinese forces 4 or 5 times its size on the battlefield. Given the smaller size of Chinese divisions, one can easily understand why one Japanese division could routinely defeat over 10 Chinese nationalist divisions.

Chinese communist forces’ PUE is similarly calculated as 100/161*14 = 8.6, which is still much weaker than that of the Japanese forces but is over 2.5 times that of the Chinese nationalist forces. Despite its shortage in weaponry, the communist forces had a much more effective organization than the nationalist forces, which is the primary reason for its higher PUE, in my opinion.

Given the concept of PUE, we can convert Japanese force deaths to equivalent German force deaths by applying a factor of 14/100= 0.14 to Japanese force deaths. Now we can calculate the contribution to allied victory (CAV) on a total equivalent German death basis, as in the following.

Now it is clear that the Soviet Union’s contribution was 81% of the total credit, which is 4 times that of the combination of all other allied forces. China, despite its heavy losses, only contributed about 1.1% of all credits, of which about 0.8% belonged to the nationalists, and 0.3% belonged to the communists.

The United Nations was a product of WWII. One may wonder, why the US, and not the Soviet Union, appeared to be dominant in the UN, given the disproportionate contribution the Soviet Union made during WWII. To explain this, I introduce the concept of total military strength (TMS), which is defined as the PUE multiplied by the size of a country’s military. The TMS is measured in million German equivalents. The results are as the following.

For example, the US had a military of about 12 million personnel towards the end of WWII, so the TMS for the US is calculated as 12*146/100 = 17.5, which means that the US had a total military strength equivalent to that of 17.5 million German soldiers. At their peaks, the allied powers had a total of about 33.8 million soldiers, more than 2 times that of the axis powers at 15.8 million. On a TMS basis, the differential is even more dramatic, with the allied powers had a total TMS equivalent to 32 million German forces, and the axis had only a total TMS equivalent to 9 million German forces, less than 1/3 that of the allied powers. It is no wonder the axis powers suffered a total defeat.

At the end of WWII, the US had a TMS of 17.5 million German equivalents, whereas the sum of the TMS of the Soviet Union, UK, and China was only 14.1 million German equivalents. As such, the US deserved a dominant role in the UN.

The case of China is very interesting. Its contribution to the allied victory was only a little over 1%, and its TMS was only 0.3 million German equivalents, and even that was split between the nationalists and communists. China is a magnitude lower than the Soviet Union, the US, and the UK on both measures, whereas there is no magnitude difference between the Soviet Union, the US, and the UK. Why, then, did China deserve a seat at the table of the permanent members of the UN Security Council?

The answer, curiously, is France, for which I did not even bother calculating the PUE, CAV, or TMS. As a Chinese proverb says, a defeated general can speak of no bravery. France essentially was on the sideline during WWII since its surrender early in the war. Initially, the UN Security Council was going to have only the US, Soviet Union, and the UK, which is the natural conclusion from either PUE or TMS perspective. However, the Soviet Union did not like this proposal because it felt that the UK will always follow the US and therefore effectively muting the Soviet Union’s voice. As a solution, the Soviets insisted on inviting France into the Security Council, because the French often don’t see eye to eye with the US and the UK. As a countermeasure, the US invited China to the Security Council because it believed the Chinese nationalist government would follow US policies closely. The UK did not like China to be in the Security Council because China wanted to take back Hong Kong, a British colony at the time. Roosevelt effectively pointed out that the CAV and TMS of China, although tiny compared with the three big players, were still much better than that of the French. So China was in. The four major powers after WWII referred to the US, the Soviet Union, the UK, and China, but not France.

The case of Japan is also quite interesting. From the Japanese perspective, 80% of its forces were destroyed by the US, the US is over 10 times more lethal than Japan as measured by PUE, and the US had over 15 times TMS that of Japan. So there is no question Japan felt it was rightfully defeated at the hands of the US. On the other hand, Japan did not believe it was defeated by China despite China was in the winning league of the allied powers. It is simple, the Japanese forces were over 3.6 times as lethal as the Chinese forces in terms of PUE, and, by the end of WWII, Japan’s TMS, while tiny compared with that of the US, was still over 4 times that of China. In other words, Japan could have easily defeated China on a one-on-one basis.

Japan’s view changed only after the Korean war, where the US and China fought to a stalemate. During the Korean War, Chinese forces suffered about 183,108 deaths, while the US suffered about 36,574 deaths (5). Assuming the US forces still maintained a PUE of 146, then the PUE of the Chinese forces would be at 146*37/183 = 29, which is more than twice that of the Japanese forces during WWII, and 8 times that of the Chinese forces during WWII. The Chinese forces were no longer the wimpy kid it was in WWII. The standing army of China at the end of 1951 was about 6.27 million men (6), which gave a TMS of 6.27*29/100 = 1.8 million German equivalent, far greater than Japan could ever achieve. By now, Japan realized it could no longer look down upon China because it could no longer defeat China on a one-on-one match. In fact, by this time, China could have defeated Japan with its peak TMS of 1.1 in a pitched battle.

It is also interesting to see the stalemate in Korea through the lens of TMS. By the end of the Korean War, the two primary players had the following manpower and TMS on the battlefield. (9)

China had a TMS of 0.39 million equivalent German, and the US had 0.48 million equivalent German forces. So this explains why the Chinese were decisively defeated at the 5th campaign. However, the TMS between China and the US was close enough that the difference could be balanced in trench warfare in mountainous regions, which is exactly what the current demarcation line is at. Overall, the Chinese side was on the defensive and the US side was on the offensive after the front was stabilized, which is consistent with the US forces’ higher TMS in Korea than China’s.

Granted, looking at history only through the lens of military deaths has its drawbacks and limitations. For example, the basic premise underpinning this analysis is that the PUE remains constant throughout a war, and the reality is that the winning side generally experienced improving effectiveness and the losing side experienced declining effectiveness. In addition, military deaths may have different meanings to different countries’ ability to wage war. The same military deaths experienced by the Soviet Union would have long put the US out of WWII. Nevertheless, military deaths based analysis is an important, if not the most important, metric in studying different countries’ military powers. I have yet to see another metric that is more objective and relevant. Supplementing military deaths based analysis with other information could lead to a better understanding of military history.

I found digging through historical military death data was really illuminating. Using the concepts of PUE, CAV and TMS put the forces of various countries on the same comparison scale. The numbers shed light on some fuzzy questions and make it crystal clear who made the greatest contribution to victories in WWII and whose army was the strongest. A math geek’s view on history could be quite unique and insightful.

 【参考资料】

1. https://en.wikipedia.org/wiki/German_casualties_in_World_War_II

2. https://en.wikipedia.org/wiki/Eastern_Front_(World_War_II)

3. https://en.wikipedia.org/wiki/German_casualties_in_World_War_II#United_States_Army_Figures_for_German_and_Italian_Losses

4. http://ajrp.awm.gov.au/ajrp/AJRP2.nsf/530e35f7e2ae7707ca2571e3001a112d/e7daa03b9084ad56ca257209000a85f7?OpenDocument

5. https://en.wikipedia.org/wiki/Korean_War#Casualties

6. http://politics.people.com.cn/n/2015/0903/c1001-27543904.html

7. https://en.wikipedia.org/wiki/Battle_of_Berlin

8. 《中国人民解放军战役战斗总览》865页：1937年9月-1938年6月: 俘虏124人;1938年6月-1941年5月: 俘虏1771人;1941年6月-1942年5月:俘虏 442人;1942年6月-1943年5月: 俘虏428人;1943年6月-1944年5月: 俘虏519人;1944年5月-1945年5月: 俘虏773人。1945年6月-1945年10月11日: 俘虏2156人。总计6213 人。另有746名日军主动投诚。合计6959人。

9. https://en.m.wikipedia.org/wiki/Korean_War

10. https://www.historynet.com/what-did-mao-and-his-communist-army-contribute-to-defeating-japan.htm “the communists also captured 320,000 rifles, 9,000 machine guns and 900 artillery pieces from the Japanese.”

【作者简介】

孙华，1986年毕业于河北师大附中，进入中国科技大学无线电电子学系，1991年毕业后赴美留学，1993年获得康州大学数学硕士后进入保险精算行业，目前是芝加哥一家精算咨询公司的合伙人。

孙华喜欢一些比较特别和小众的东西，比如他是个波士顿马拉松达标的长跑爱好者，也拉拉撒撒写一些自己喜欢的文，没有啥固定的题目，在知乎上以“庄户人家奔跑的小彼得”开设了专栏。

庄户人家说：“好啦，你喜欢吃鸡蛋也没必要认识下蛋的母鸡，就不多讲我自己了。谢谢惠读！”

编辑：林燕 0318&0306S  陈颍 8714

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