Of course you would save a lot of money. Companies may get components for cheaper than you would as a consumer but they would add a big markup and the labour costs for building and testing add on quite a lot.
This is probably (others will have slight variations) the best performance you can get for your budget:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i5-4690K 3.5GHz Quad-Core Processor ($224.29 @ Amazon)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.99 @ NCIX US)
Motherboard: MSI Z97 PC MATE ATX LGA1150 Motherboard ($78.98 @ OutletPC)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($64.98 @ Newegg)
Storage: Samsung 850 EVO-Series 120GB 2.5" Solid State Drive ($68.98 @ OutletPC)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($48.99 @ NCIX US)
Video Card: EVGA GeForce GTX 970 4GB Superclocked ACX 2.0 Video Card ($319.99 @ Newegg)
Case: Azza SIRIUS ATX Mid Tower Case ($24.99 @ Newegg)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($45.99 @ NCIX US)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($19.78 @ Directron)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) ($87.99 @ NCIX US)
Total: $1014.95
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-03-27 05:51 EDT-0400
It is also an overclockable build so you can easily get your CPU up to 4-4.5Ghz with that CPU cooler.
Here is a prebuilt off newegg -
http://www.newegg.com/Product/Product.aspx?Item=N82E16883101018
Intel Core i7 4790 (3.6GHz)
8GB DDR3 2TB HDD
Windows 8.1
NVIDIA GeForce GTX 760 1.5 GB
They are always unbalanced systems... a locked i7 4790 CPU with a last gen graphics card (which you can't even buy anymore as they have been superseded)...
The unlocked i5k in my build is better performing (the i7's hyperthreading) doesn't help you in gaming and also you can't overclock that i7... The 760 is about 2 years old and can play games at 1080 (roughly high/ultra settings) but the 970 in my build is the latest gen enthusiast graphics card. Will play almost anything at max settings and 60fps.
Also you won't get a solid state drive in the prebuilt as you would in the custom build. SSD's boot you into windows in about 8 seconds from a cold boot!
And you get absolute BS on ebay -
http://www.ebay.com/itm/Liquid-Cooled-AMD-FX-4350-4-2Ghz-AM3-Quad-Core-Gaming-PC-Computer-8GB-RAM-HDMI-/170956070975?pt=LH_DefaultDomain_0&hash=item27cdc6a03f
Marketing a terrible low end FX 4300 chip by watercooling it... this would give you less performance than an i3 budget build at $400 (nevermind 1000$!)
Also the GPU in that build is low/mid level... these people are making such a massive profit off the untechy customer.. it makes me mad.