Best performing laptop for $400-$450

Your choices are conflicting; you will need to prioritize. Large screens and long battery life in particular are not found together, especially at a low price.
If you're willing to drop down to a more typical 1368x768 resolution and a smaller screen, you'd get the decent battery life and good graphical performance.

Between screen size + resolution or battery life, I'd rather keep the screen size and resolution as long as the battery can last about 4 hours of use.

Four hours is a LONG time for a budget laptop. There's this one: http://www.newegg.com/Product/Product.aspx?Item=N82E168... but since it uses Intel HD (Highly Deficient) graphics, it may not be good for games.
If you go a little higher, and/or play the rebate game and win, this HP might do it for you: http://www.newegg.com/Product/Product.aspx?Item=N82E168... . The graphics is a little better, and the battery life appears to be quite good. Expect it to be a gross exaggeration though, probably from a rundown test where the machine is sitting idle, not doing anything.

The Acer Aspire V3-731-4695 seems good, I saw an Asus that also had a Intel Pentium B950 running some benchmarks and it did ok on starcraft 2 on low settings. Now that I think about it, battery life is not a big deal, I wouldn't mind carrying an external battery charger around. And I'm not familiar with messing around with laptop bios settings but if possible would lower the voltage make a noticeable difference?

I haven't worked on a lot of laptops, but I don't ever recall seeing any BIOS settings even remotely that detailed. Probably the best things you can do is turn screen brightness down as low as possible. Replacing the HDD with a SSD can lower power use as well, but a big enough one is likely going to add another $200 or more to your budget.

At that price range, if you want to game, you should look at the AMD APUs. I have a little Acer AspireOne that can game quite well at low settings.

I would go with this new: http://www.newegg.com/Product/Product.aspx?Item=N82E168... (1600x900 on a 17.3" screen, Blu-ray - Full specs here http://www.cpusolutions.com/store/pc/Acer-Aspire-AS7250...)

If you don't mind getting a refurb, this would be a lot more powerful (goes from the E-450 to the A6 and gets 2GB more ram):
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

Out of these laptops which one do you think would have the best gaming performance?

http://www.bestbuy.com/site/HP+-+17.3%26%2334%3B+Pavili...
http://www.bestbuy.com/site/HP+-+17.3%26%2334%3B+Pavili...
http://www.bestbuy.com/site/Acer+-+17.3%26%2334%3B+Aspi...
http://www.bestbuy.com/site/HP+-+17.3%26%2334%3B+Pavili...
http://www.bestbuy.com/site/HP+-+17.3%26%2334%3B+Pavili...
http://www.bestbuy.com/site/Toshiba+-+17.3%26%2334%3B+S...
http://www.bestbuy.com/site/Acer+-+Aspire+AS7250-E454G5...

I've looked at the compared benchmarks for all the GPUs and they are all over the place, I couldn't find any benchmarks for StarCraft 2 though and that is the only game I will be playing on the laptop I get.

Best answer selected by jorge89.