Interesting question; I guess I must admit to not being a purist on history for a number of reasons. There is of course the problem noted in the old adage that "…history is written by the victors…" so the quest for accurate is frequently quite challenging. Moreover, a factual account is an account of facts by some person who, however well meaning, is imparting his personal impression of what occurred. In battle some impressions can easily be rendered imperfect by the sound, fury, horror, fear, rage, survival needs and general confusion of the scene. Then there is the problem with the observational skills and memory of the observers. All this leads to much variability of results. For example, even in "relatively" simple situations like accidents or acts of crime, you can get wildly varying accounts of the same events, even among trained observers (the FBI School has some great exercises on this). These factors make me wary of the best factual account of any event, especially a battle.
The quest for accurate becomes even more challenging the farther back in time we go. Obviously impressions of modern battles refreshed by video are much more reliable than interviews of survivors said to have been recorded in notes written thousands of years earlier. What in fact was the battle of Marathon really like for example?
So in the best of cases, I think you can come close to reconstructing battles with a reasonable degree of accuracy that varies with many factors. In general, the most accurate representations are probably the beginning and the end of a battle and battles that are more recent than not and with a fair number of accounts by experienced observers in relatively safe positions.
Putting aside the difficulty in being accurate, I am indeed fascinated by not only what happened but what could have happened. Many battles could easily have gone differently with the slightest variation in one or a few small events. I do enjoy pursuing those variations. So I guess I would say I like to explore historically based possibilities using historically accurate resources. Thanks for the fun question.
.