The board (matte) measures 8 by 11 inches.  This is an original photograph of the W.M. Co. verus the "R" team - most likely in Wisconsin.  Circa 1890s.  After much research, I was able to find out who the W.M. Co. baseball team was -- and it is very interesting indeed.  Here is what I was able to find out:

You are likely thinking of the famous "W.M. Co." in theatrical history that operated a beloved baseball team in that exact timeframe: the Charles E. Blaney Amusement Co. (often abbreviated as Blaney's Amusement Co. or The Blaney Co.).

Charles E. Blaney was a legendary American playwright and theater manager who operated a string of enormously popular theaters across the Midwest and East Coast in the late 1890s and early 1900s. He famously ran multiple Blaney’s Theaters that hosted live stock-company plays and earliest "simulcast" baseball events.

To boost publicity and entertain the public, his theater company sponsored and traveled with its own theatrical company baseball team. They frequently played exhibition games against local teams across Wisconsin, Illinois, and the broader region during their summer theater tours. 

Regarding the "R" on the opposing team, here is the best (but not only) theory:

Racine: By far the most famous and active baseball town starting with "R" in 1890s Wisconsin. Racine fielded powerhouse teams in the Wisconsin State League and independent circuits, often wearing a simple, bold "R" on classic wool uniforms.                

Domestic shipping and handling in the U.S. is $6.50.  Foreign bidders are welcome with the shipping costs to be determined solely by Ebay International Shipping.   I will combine shipping. I have decided to sell my collection of antiques (and other nice items), which I have been collecting for the past 30 years.  Good luck with your bids.