Battle of Mohi

Apparently, at the Battle of Mohi (11.04.1241) the Hungarians, although ultimately defeated, gave the Mongols something of a hard time; it was only through the courage and competent leadership of Batu Khan that the horde did not break and flee the field.

So, let's say that at some point, say, during the Mongol attack on the fortified Hungarian camp, a stray arrow pierces Batu through the neck, and that this causes him to, say, fall of his horse and crack his skull open, killing him instantly. Assuming that this was enough to demoralize the horde in the middle of a hard fight and embolden the Hungarians, and assuming that the Hungarians would manage to defeat the attack on their rear flank by Subotai's forces, and assuming that the Mongols would collapse and get slaughtered as a result, and assuming that Ogodei still dies (let's assume that he in fact dies earlier, on account of his alcoholism getting worse and due to stress...) what effect would this have on the Mongol empire and the subsequent course of events?

To restate:

1. POD on 11 April 1241, at the Battle of Mohi.
2. Exact POD is during the Mongol attack on the Hungarian camp after their crossing of the river (the Sajo); the Hungarians, alerted, sallied forth in response.
3. It was hard fighting for the Mongols and not a simple rout; the Mongols were almost sent packing.
4. A stray arrow kills Batu Khan, in rather dramatic fashion (arrow through neck, rather ironically a stray Mongol arrow; subsequent fall from horse onto head, resulting in cracking open of skull and instant death)
5. Mongols, in the middle of hard fighting, demoralized and decapitated; Hungarians emboldened and cut into Mongols.
6. Subotai's force attempts attack, repulsed and suffers heavy casualties. Subotai injured in the fighting.
7. Mongols actually begin to rout; the Hungarians attack again and the Mongol force collapses, fleeing the field. 11 April 1241 will be celebrated in later Hungarian history...

So what happens next? Let's assume Ogodei dies even earlier and the Mongols aren't that motivated to conquer Europe anyway...might they even leave Russia alone, perhaps?
 
Apparently, at the Battle of Mohi (11.04.1241) the Hungarians, although ultimately defeated, gave the Mongols something of a hard time; it was only through the courage and competent leadership of Batu Khan that the horde did not break and flee the field.

So, let's say that at some point, say, during the Mongol attack on the fortified Hungarian camp, a stray arrow pierces Batu through the neck, and that this causes him to, say, fall of his horse and crack his skull open, killing him instantly. Assuming that this was enough to demoralize the horde in the middle of a hard fight and embolden the Hungarians, and assuming that the Hungarians would manage to defeat the attack on their rear flank by Subotai's forces, and assuming that the Mongols would collapse and get slaughtered as a result, and assuming that Ogodei still dies (let's assume that he in fact dies earlier, on account of his alcoholism getting worse and due to stress...) what effect would this have on the Mongol empire and the subsequent course of events?

To restate:

1. POD on 11 April 1241, at the Battle of Mohi.
2. Exact POD is during the Mongol attack on the Hungarian camp after their crossing of the river (the Sajo); the Hungarians, alerted, sallied forth in response.
3. It was hard fighting for the Mongols and not a simple rout; the Mongols were almost sent packing.
4. A stray arrow kills Batu Khan, in rather dramatic fashion (arrow through neck, rather ironically a stray Mongol arrow; subsequent fall from horse onto head, resulting in cracking open of skull and instant death)
5. Mongols, in the middle of hard fighting, demoralized and decapitated; Hungarians emboldened and cut into Mongols.
6. Subotai's force attempts attack, repulsed and suffers heavy casualties. Subotai injured in the fighting.
7. Mongols actually begin to rout; the Hungarians attack again and the Mongol force collapses, fleeing the field. 11 April 1241 will be celebrated in later Hungarian history...

So what happens next? Let's assume Ogodei dies even earlier and the Mongols aren't that motivated to conquer Europe anyway...might they even leave Russia alone, perhaps?
Commanders of mongolian armies commonly stayed at rear, but there were some cases when they were killed in battle.
 
Commanders of mongolian armies commonly stayed at rear, but there were some cases when they were killed in battle.

Yeah, but apparently Mohi almost went to hell for the Mongols; apparently Batu lost one of his lieutenants and his bodyguard unit suffered heavy casualties. So maybe a stray arrow could get him, and...well...who knows? Maybe that would have demoralized the Mongols and caused their attacks to fail, and maybe they would have routed and gotten slaughtered by the Hungarians, and in the chaos Subotai could have been injured.

Hmm...how plausible would Subotai and a small group of Mongols getting trapped in a small village surrounded by Hungarians and getting hacked to death in a frenzied melee be?
 
Yeah, but apparently Mohi almost went to hell for the Mongols; apparently Batu lost one of his lieutenants and his bodyguard unit suffered heavy casualties. So maybe a stray arrow could get him, and...well...who knows? Maybe that would have demoralized the Mongols and caused their attacks to fail, and maybe they would have routed and gotten slaughtered by the Hungarians, and in the chaos Subotai could have been injured.

Hmm...how plausible would Subotai and a small group of Mongols getting trapped in a small village surrounded by Hungarians and getting hacked to death in a frenzied melee be?

I think it would be hard to manage with Subotai, because he was not known as a master tactician for nothing... but then, rumor has it by then he was so fat that he had to be carried on a wagon, which is not very conducive to mobility. So, there is a plausible scenario for him to be trapped...
 
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