The brightness measurement on Projector Central is very deceiving.
Having more lumens is rarely a bad thing, but really, isn't a issue. Brightness calculations are based upon projectors having a 'fixed' number of lumens for output.
If you read the reviews of any projector.
The Optoma HD27HDR for example...https://www.projectorcentral.com/Optoma-HD27HDR-Review.htm
You can see that tested lumen output ranges from 2,800 lumens all the way down to 550 lumens.
That's a TON of brightness range, and is typical for most projectors. So, you don't have any world in which you really will have too much light output.
Don't worry about it.
What you DO need to consider:
1. Throw distance is measured LENS to screen, not wall to screen. If your wall to screen distance is 14'9", then your lens to screen distance is about 18" less than that, or right about 13 feet.
2. With a throw distance of 13 feet, there aren't any projectors which fit your limited budget which can produce an image as SMALL as 100" diagonal. That is, you MUST move the projector forward to get the image down to the size you are looking for. OR - You can spend more and get a projector which has more zoom range (or buy refurbished).
The Optoma HD27HDR I listed above, which is a good entry level choice, requires 10'9" to 11'9" to throw a 100" diagonal image. That's not an option. It's where the projector MUST go.
Spending a bit more, on a projector like the Epson 2150...https://www.projectorcentral.com/Epson-Home_Cinema_2150.htm
and you will have a projector with enough zoom range to hit a 100" diagonal from between 13' and 21'. So, a lot more zoom range and a lot more options there.
3. Projector height must be accurate. You can't just plop a projector wherever in a room and have it magically fit any size at any angle you want. It must be at the proper height to ensure the image is square, and it must be centered.
If it is not, you can use digital keystone correction to square the image up. But, this is an ARTIFICIAL correction to the image, and you lose resolution. Like chopping off the corner of the image, you won't be using the full 1920x1080 resolution anymore.
This video shows how keystone correction works, but doesn't really explain why you should never use it.https://www.youtube.com/watch?v=aVNGk7v1BoY
So, there is some information in the FAQs at the top of the different forum sections which may help you understand a bit more that may be worth reading.
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