Further on regarding your first image, here's a shot from a recent game I covered - not a particularly noteworthy image (other than the subject was hitting .425 at the time), but it's taken under conditions similar to yours: in Av, with a very bright sky behind it.
You can see my ISO is a LOT higher than what you chose; the shutter speeds are close, and the apertures are the same. If you take into account the higher ISO and the +1/3 EC, you get pretty close to 2 stops more exposure than your shot (ISO 400 to 1250 is 1 2/3 stops then add the 1/3 of EC), which is consistent with my original estimate of how under-exposed your image is.
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Exposure Time 1/1250 sec
Aperture f/2.8
ISO Equivalent 1250
Exposure Bias +1/3
I posted the histograms of the two images. Your image is on the left, my sample is on the right. I based my original estimate of 2 stops under exposure on your histogram. On the histogram of my image, you can see a lot more information on the right side which tells me it's better exposed, without even looking at the photo.
So, this makes me wonder again which metering mode you were using?
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