What an inane post. How can you anticipate the ball breaching the first line of defence when your defender doesn't jump for the ball???
Also the fact that Rooney was actually there in a position to clear surely suggests the defending players were at fault.
I'm sick of this micro-analysis of De Gea every fecking time.
Even Paddy Crerand, staunch defender of United players, was suggesting De Gea should have come for the ball.
I say let the boy play out his mistakes and get better and better.
Which player in the world doesn't make mistakes?
You either didn't read or didn't understand my post, so let me try again.
The main culprit is Carrick who should have headed the ball away. This is clear. But even though Carrick is the one at fault, that doesn't mean that De Gea's actions no longer matter. He can still affect the situation and the probability of Stoke scoring by deciding whether or not to come off his line.
Now, the ball is coming into an area which is so close to the goal, that if a Stoke player gets a header on target, the only way De Gea is saving it is if the ball hits him. It's simply too close to goal for even someone with De Gea's reflexes to do anything about it. So if Nzonzi at the near post (in my previous post I mistakenly said it was Walters at the near post) gets a header on target, the probability of it being a goal is similar, regardless of whether De Gea is on his line or off his line, since De Gea's body can only cover a small fraction of the total goal.
However, the times that neither Carrick nor Nzonzi get a touch and the ball comes flying into the middle of the six yard box there is a big difference in the probability of Stoke scoring depending on whether De Gea is on his line or off it. If De Gea is already off his line and ready, I claim that he can claim that cross a very high percentage of the time, and that is the essence of the argument I presented. I claim that the benefit from De Gea claiming the crosses which bypass the first line of defence outweighs the benefit gained from De Gea being on his line and having a higher probability of saving 1. a potential Nzonzi header and 2. a potential Stoke or OG attempt. This is because the shot-stopping benefit, as determined earlier, is likely small, and the cross-claiming benefit, as determined earlier, is likely large, so that even though the cross clearing both Carrick and Nzonzi is an unexpected event, when you weight the actions based on probabilities of occurence I think the benefit of claiming the cross is large enough to compensate. I formulated this same argument into a couple expected value equations, but I think I've made my argument sufficiently clearly.
I know this is a simplified argument which ignores e.g. the benefit of staying on your line in e.g. situations where Carrick gets a small touch on the ball but only manages to flick the ball up in the air rather than heading it away, but I'm not convinced that that benefit is large enough to make a meaningful difference.
I see my argument as no different to one that says that goalkeepers should anticipate a penalty taker's decision by pre-emptively diving to one side. Sometimes you guess wrong and look like a fool, but on the whole you maximize your chances of saving the penalty by guessing. (Except that in actual fact goalkeepers dive way too often during penalties and would be better served by staying put. My choice of example was just to highlight the basic thought process that I'm trying to convey here.)
Now I'm not saying it's natural or possible for a goalkeeper to do this kind of analysis in the heat of the moment, and really there is only one goalkeeper - Neuer - whom I have seen doing this kind of "EV cross-claiming". I'm also not blaming De Gea for not doing it. But I am saying, that with the benefit of hindsight and time for analysis, I think the optimal action in this situation would have been to come out for the cross before De Gea even knew whether Carrick would head the ball clear.
As for your other points, again, I'm not criticizing or blaming him. I attach no value judgments here; I'm just thinking in general and analytical terms about the situation.