Do you really use the formula for speaker placement?


There are lots of good discussions on here about improving the room your speakers are in to get the best listening experience. This includes speaker placement. I've moved my speakers all over creation and found where they sound good to me. But then I saw several "speaker placement calculators" and I thought, great, something else for me to tinker with.  :-)    Besides enforcing the standard guidelines of using an equilateral triangle between the 2 speakers and the sweet spot, and the speakers being equally distant from side walls, the formula specifies the optimum distance from the front and side walls. My room is 15.5 ft x 23 ft. The algorithm says the front of my speakers should be a little over 7 feet from the wall and a little over 4 feet from the side walls. The distance between the speakers then is about 80 inches, which is the measure for the sides of the equilateral triangle. Basically, I was about the same distance from the speakers as they were from the wall. I felt like I might as well be sitting between the speakers. For me, this algorithm did not result in a great listening experience. There are about 5 different algorithms, each arriving at slightly different results. Has anyone found success using one of these algorithms, for example, the Cardas algorithm? Or any other algorithm? Obviously, I'll let my ears be my guide. But I'm always open to the proposition that there's something I don't know that I could benefit from.
pennpencil
There are two main aspects to speaker placement with just two speakers- bass response and imaging. As usual its a trade off.  

Closer to walls improves bass. But closer to walls brings more early reflections which harms imaging. So its a trade off between finding the location with the smoothest bass and good imaging.  

An algorithm is simply a fancy word for a set of steps you go through. With speakers that means first trying them different distances from the front and side walls, and moving the listening position, listening primarily for smooth response. In this step you don't pay a lot of attention to imaging, although you do always keep them equidistant its not critical to be precise about it.  

Once you've found the smoothest frequency response the next step is to get them precisely equidistant, and level, and experiment with toe. Listen for your preferred balance between wide and deep. When you're done with that you'd done with speaker positioning. Time for acoustic embedding, electrical embedding, vibration.....
As you say, there are several calculators/algorithms/methods out there, and if you try two or three of them you'll find they give different recommendations for the same room.  Because the creator/designer prioritized different factors.  They *are* good for getting people to think differently and creatively about speaker placement, and they are often good for getting speakers somewhere in the general region of where an individual likes them best.  Most are free, so there's very little downside.
to add to millercarbon's apt comments

there is also the issue of toe in / out... trading off direct radiation vs side wall reflections... the importance of this depends on the dispersion pattern of the speakers in question
The one algorithm that is absolute garbage is the hokey Master Set where the goal is supposed to be to get your speakers cockeyed just the right amount to sound equally crappy from everywhere in the room. Of course they spend 5 pages detailing exactly how to achieve this exalted state of crap. But crap is crap no matter how many pages or hours you put into it. Avoid.