I am just having fun here
I was having fun too. In fact I like Czech humor (but also making fun of Czech humor is fun).
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Pangur Bán:
Last One's post above illustrates my point.
Well his post is somehow exaggerated (I guess he confused 1,5 M with 15 M). But indeed Lithuania had density of population much smaller than Poland.
And all in all the GDL had about as much population as PL or slightly less / slightly more (depends on which estimate we use), despite being much bigger.
Also urbanization was better in Poland. But capital city - Vilnius - was similar in size to Cracow, on the other hand.
And indeed Lithuania was not such a "backwater" as some may think (including maybe TheLastOne). But if you actually read a decent book written by Polish historian in the last 40/50 years (not before), you should know that they don't portray Lithuania as a "total wilderness" - unlike you claim.
You kid yourself with this stuff if you like. We can talk anachronistically about "nations", but Grunwald was a victory for the chief kin-groups of the Lithuanians, of which Poland was but one of their latest (though probably most important) acquired Slavic territories.
Oh man Poland was not "acquired" by Lithuanians. The fact that a Lithuanian born king was on the Polish throne as the result of personal Union between both states doesn't mean that Poland was "acquired" by Lithuania. There are plenty examples of "international marriages" of monarchs in Middle Ages.
Also I wasn't talking about Grunwald - which in the end turned out to be an unexploited victory. Due to unwilingness of Jogaila & Vitold to destroy the Order completely (as this would mean that Poland no longer had any reason to be in a union with Lithuania). This is the theory of historian P. Jasienica.
The fact is that from Grunwald the army marched on Malbok for 10 days - which is hard to explain unless we assume that such a slow march was deliberate (e.g. remnants of the destroyed Teutonic army got from Grunwald to Malbork much faster). The siege of Malbork itself (which lasted for 2 months) was also conducted very sluggishly and with no conviction - not a single determined assault was carried out (apart from one "ad-hoc" which was not even ordered by anyone, but conducted spontaneously by a group of Polish knights - and even despite this almost succeeded, because one ring of walls was captured). There was not even an attempt to hermetically surround the castle! The premature and unexplained abandonment of the siege yet on 19 September even today raises controversy. After Jogaila retreated from Teutonic lands, the Order started counteroffensive and started to regain the lost castles and towns one after another.
And it should be noted that both Polish and Lithuanian army at Grunwald had artillery - they just didn't use their guns in battle (unlike the Teutons). But if they had artillery (and it was strong, according to sources) - this is even one more reason to be surprised why they failed to capture Malbork.
Anyway, it's not a math game ... my point above is that the leaders are Lithuanian.
The commander-in-chief (of both wings) was king Wladyslaw Jogaila indeed. The direct leader of the Lithuanian wing was duke Vitold.
But the direct leader of the Polish wing was Zyndram of Maszkowice - a Polish knight of German descent. Some other sources say it was Mikolaj Traba. However, more likely it was Zyndram because he was "with the troops" (like duke Vitold) - while Traba was "with the King" on the hill behind the lines.
Mikolaj Traba - a vice-chancellor of Poland - was the main author of the strategic plan of war against Teutonic Order created in 1409.
During the battle Mikolaj Traba was side-by-side with king Jogailla on his command post. Who knows who of them was in fact the master-mind? At Warna in 1444, for example, "officially" King Wladyslaw III was in command - but de facto experienced Hungarian general, John Hunyadi, was the master-mind.
Lithuania had both the manpower, military expertise and the territory (that's why it had the latter).
It had just about as much military expertise in combats against the Teutonic Order as Poland. To be precise - both states had much.
Regarding manpower it is estimated that by the end of 14th century the Grand Duchy of Lithuania could mobilize in total a maximum of ca. 18,000 cavalry, not counting peasant infantry (from: "Battle of Kulikovo 1380" by Leszek Podhorodecki, MON, Warsaw 1986, page 107). This is less cavalry than Poland could mobilize at the same time, IIRC, but I don't remember what was the exact number - let me have some time to check my sources.
Of course majority of this army mobilized by the GDL would be of Ruthenian "nationality" - since ethnic Lithuanians were minority in the GDL.
(that's why it had the latter).
I guess you wanted to write - the former, not - the latter?
There are no reliable figures for the battle;
There are no any reliable figures for almost any battle in the Middle Ages (exceptions are rare).
But there are more reliable estimations of mobilizational potentials (see above to check figures for the GDL).
And basing on this - plus taking into consideration other factors - we can estimate strength in individual battles.
BTW - it should be noted that mobilizational capabilities in the Middle Ages depended not only on "crude" number of population of a certain state, but also on concentrations of population. It was harder and took more time to mobilize an army from vast areas with dispersed population.
Poland had a better quality of land, better state-structures and stronger links with Western Europe, and what served it in the end was that its cultural-poilitical system was more appealing for a monarch wanting an easy life.
Polish political system was more appealing for a monarch wanting an easy life? Are you kidding me?
In Poland already in 15th century every monarch had to solicit for support of nobility - while Lithuanian dukes had nearly absolute power.
Basically what happened was the Lithuanian Jogaila and his descendents preferred the security and comforts of the latter more than the risk and demanding political culture of the former.
Lithuania had "demanding political culture"? I wouldn't say so - Lithuanian dukes were nearly like absolute rulers, to my knowledge.
If I were to guess pops, I'd say that Lithuanian Rus in 1400 was more populous than the area under the Polish crown (definitely more in Rus lived in urban environments), but this would be a guess;
Your guess is wrong.
Entire southern Rus was devastated and depopulated by the Mongol invasion and occupation - and did not recover until 1400s.
This is also one of reasons why it was conquered by Lithuania so easily (check the link below):
http://forums.civfanatics.com/showthread.php?t=445172
Also your guess about urban population is wrong - Poland already had numerous urban population by then.
In Poland already ca. 1340 at least 14% of population lived in towns (this is not small level - similar to that in Kingdom of England at that time; in the Teutonic Order it was better but there high urbanization level was a bit "artificial" as it partly resulted from underpopulation of Teutonic countryside).
Even in the Vladimir-Suzdal Russia - which was relatively lightly damaged by the Mongols - the total number of towns by the end of 14th century was 55 (of which 10 were in the Duchy of Moscow - of which Moscow was the biggest). By comparison in the same time number of towns in just 3 main provinces of Poland (Greater Poland, Lesser Poland and Mazovia) - area of which was smaller (see the map) - was +/- 300 by the end of 14th / start of 15th century:
Of course it might be true that in some parts of former Kievian Rus "crude" level / % of urbanization was higher than in Poland. But, if so, then still this would result from underpopulation of countryside and (but this to lesser extent) bigger average size of towns - rather than from density / number of towns.
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Edit:
Also one more thing - the Black Death. It is known that the Black Death relatively lightly affected Poland (at least most of its territory).
On the other hand, most likely majority of Rus territory didn't have as much luck (or didn't have so preventive rulers to at least attempt to close the borders with neighbours - if we assume that this was the reason why Poland was less affected - which it could be).