Lets say during the reign of Trajan, (98-117ad), how many pitched battles would a roman soldier participate in? Would it vary heavily based on location/position?
In short, it would indeed vary based on the location in which a given legionnaire was posted. In general, frontier positions would offer more combat than a position within the Italian continent. This also depends on what you may mean by a "pitched battle", as some legions, such as the Rhine or Danube legions, would have very frequent skirmishes with the surrounding tribes, some of which could be drawn out, but may not involve marching orders or siege warfare. In this instance, since you ask specifically about Trajan, the number could very well be much higher than average considering Trajan favored expansion and often went to conquer. So legions that bordered Dacia or Parthia, regions Trajan was in conflict with and eventually annexed, would have seen many more battles than perhaps an ordinary legionnaire. Trajan serves as a good benchmark for this question in regards to foreign threats, as before and after Trajan, legionnaires would sometimes see more combat against their fellow Romans in an individual's bid for the throne than against foreign enemies. Unfortunately, sources that detail the specifics of individual legionnaires lives and stories (think of American Civil War diaries) are few and far between, but to get a good idea of the frequency of conflict I always recommend reading Julius Caesar's "De Bello Gallico". Though do keep in mind that this work is biased, as Caesar was trying to boost his own image, knowing full well that this would be read in the Forum whenever chapters were sent to Rome. But it is a first hand account of a Roman army being fielded against and engaged in combat with a foreign threat. First time commenter, hopefully I got everything right. Hope this helps! Feel free to DM further questions about Roman history, as it is my field of study and I would be glad to discuss further as much as my time allows. Cheers!