I just converted my old MTB to a SS, and had to use a chain tensioner. Because at first the back cog was skipping very easily, the tensioner had to be pushed up (and the chain shortened) in order to augment the chain wrap. Considering the possible variation in the tensioner position, I am wondering whether it can somehow affect the gear ratio. I searched everywhere, but couldn't find an answer to that simple question. My "science" intuition says no, while my "visual" one says yes.. which one is right? Thanks!

No. The ratio of the chainring to the cog stays the same. The tensioner is simply an "idler" gear...

Let's re-iterate.... No.

If you think about it, even with the tensioner in place, the chain is still passing across the same amount of teeth on the rear cog in order to drive the rear wheel. Thus, your gear/inch ratio remains the same. You'll just be running a longer chain, which is probably adding at least 10 grams of rotational weight! Best sort it out and take a hacksaw to the rear dropouts so you can fit some track drops.

Thanks for the quick answers! I think I got it now, and it makes much sense. Just to illustrate my misunderstanding, here's a "pathological" tensioner config I had in mind:

https://goo.gl/hcXsr

I was under the (false) impression that such an extreme config would be equivalent as "widening" the rear cog's radius, thus affecting the gear ratio.

If it did, think of how it would mess with the calculations when a derailleur is involved. Thank goodness it doesn't work that way.

No, it does not, because the gear ratio only depends on the ratio between the teeth on the two wheels that are interacting. You pedal the chainring, it moves X chainlinks per second, and the cog on the back moves at x chainlinks per second driving the wheel. The chain tensioner doesn't do anything.

i think if the chain is big too long like that pic it will not grip an extra teeth if you shorten it one link it will grip one extra teeth. i ride 48/14 with chain tensioner on and i can't tell the difference but when i go too fast and try to pedal the tension feels like its all gone and loose. do you feel the tension of the chain like that after you ride fast enough??