Hi Skins, hopefully the snow is melting in Buffalo as it is here. Welcome! The BA markings are not regimental markings but Army Korps marks. The BA = AK has to do with the language difference. Germany was divided up into geographic Army Korps districts and each district had infantry, cavalry and artillery regiments assigned to it. Often, on Model 1915 helmets (grey fittings) like yours we only have the BA markings, no JR or IR plus a number eg JR 109. They did this during the war, because our side was able to ID the regiments facing them with captured, well marked equipment. There are many exceptions to this supposed M15 rule however, and many M15's have regimental markings. Helmets with brass fittings made prior to 1914 are often well marked with dates, BA Roman numerals and regimental numbers.
In regards to your helmet.... If we look at the AK for Baden, the number should be BAXIV not BAX or XX. Those AK's are in NW and NE Prussia. Baden is in the south next to the French border. So, if I were a purist, I would not buy your helmet because it does not have Baden Regt markings and the BA is not correct. However, during the war regulations got thrown out the window so if your helmet plate fits fine and there are no signs of re soldering on the loops on the back, or multiple holes in the front of the shell then you should be OK. Your cockades look to be originals, your chin strap is a reproduction....why? Go to the chin strap section.
In conclusion, these helmets are expensive and consequently, we collectors have to protect ourselves from fakers. Your Baden M 15 helmet plate, is worth twice+ as much as a Prussian one. The best advice, that I can offer is that you are in the right place here. Explore the site, learn, ask questions and above all, have us more experienced collectors take a look at what you are thinking of buying. We can save you mego bucks and help you create a very nice collection which will only increase in value.