After looking at the history of early ball playing in pioneer Illinois, I was thinking that early forms of base ball arrived in that area first and then spread to Missouri. Generally speaking, Illinois was settled prior to Missouri and a culture of ball playing came with the earliest pioneers. I figured, through economic and cultural exchange, the early ball games were exported from Illinois to Missouri and Iowa. Now, after looking closer at the pioneer history of Missouri, I no longer believe that to be true.
On of the reasons I don't believe that my earlier thinking holds up is that Illinois really wasn't settled prior to Missouri. While settlement in Missouri wasn't at the same volume as in Illinois at the beginning of the 19th century, the earliest settlements of European/Americans were taking place at about the same time in each state. Both areas saw an influx of settlers in the first two decades of the century and ball playing appears to have been part of the culture that they brought with them. Early ball games didn't spread from Illinois to Missouri but, rather, were brought to each area by the pioneers who came to settle the area.
The evidence suggests, rather strongly, that when the first European/Americans came to the middle frontier, they brought their ball games with them. I'm speaking generally here of the greater Illinois country, an area which Stephen Aron refers to as the American Confluence region and which Cathy Johnson calls the Middle Waters frontier. The area that I'm looking at includes western Indiana, western Kentucky, central and southern Illinois and eastern Missouri, with western Tennessee and northern Arkansas possibly thrown into the mix.
There's a complicated settlement pattern to this area, with French, British, Spanish and American settlements being established at different times and with different levels of success (hence my use of the ambiguous "European/American" tag). You had French settlements in the area at Cahokia in 1699 and French involvement in the area really complicates things, as far as the early history of ball playing is concerned. The Gratiot reference, however, does imply that the French settlers did have a culture of ball playing that they brought with them to the New World and our understanding of French ball playing in general supports this to some extent. While I don't have much in the way of references to support this, I believe that ball playing existed in St. Louis from its founding in 1763. It probably wasn't baseball, in any sense of the word, but the general pattern, supported by Gratiot, would suggest that there were ball games being played. While the adults may have been more interested in cards, gambling and horse racing, the children, as was usually the case, were entertaining themselves with ball playing.
But when I speak of ball games coming with European/American settlers, the people I'm really talking about are the nascent Americans who began to settle the middle frontier in earnest at the beginning of the 19th century. Regardless of whether they were Yankees, who settled the northern part of the region, or Southerners, who settled the southern regions, these people brought ball games with them and these games, including town ball, cat, trap ball, cricket, and bull pen, were being played in the region as early as the first decade of the 19th century. They brought these games with them from the old country, played them in the eastern part of America and brought them with them to the middle frontier.
Ball playing was part of the culture that these people took with them wherever they went. I see no other conclusion to draw from the evidence. The answer to the question of how ball playing spread across the United States is a simple one: When the Europeans arrived on the continent, they brought ball games with them; as they spread out across the continent, they took their games with them.
The one disappointment I have with this research is the lack of sources that I've found regarding what was going on in St. Louis, specifically. I have the Gratiot reference, another reference from 1860 implying that base ball was a game that had been played in the city for a long time and the Tobias reference to St. Louis as a hot bed of town ball. However, I have enough references to ball playing in the general region surrounding St. Louis that I can make an educated guess as to what was happening in the city. My belief, at this moment, is that the French brought some ball games to the area with them and there were ball games being played in St. Louis by the mid-18th century. In the late 18th and early 19th century, there was a heavy influx of Anglo-Americans into the region and these people brought their proto-baseball games with them. The Tice reference places ball playing within 60 miles of St. Louis in the first decades of the 19th century and I believe that some variant of base ball was being played in the St. Louis area within the first decade of the century. I think it's only a matter of time until I find the references that back that up.