"Points" is just another value computed per player for a tournament. That is, if you load a tournament and view a player (on the Players tab), you'll see he has a Points value. It will be zero unless you supply values for one of the fields that affects points, like I mentioned before. Notice you will not see a "Score" value on the Players tab.

Scores are computed only when you run Stats. The formula for Tournament Score is taken from the filter you use to compute your stats. The Tournament Score value is available to the Overall Score formula. One day I hope to add access to other values for the Overall Score formula, but for now, only the Tournament Score is available. This means that, for now, if you want to use a player's Points value to compute their Overall Score, you'll need to set the Score to the player's Points value.

So, are you saying that you want to continue to use the same Tournament Score and Overall Score formulas, however you wish to add to a player's Overall Score for ranking 1st through 3rd in any tournament? Thus, if a player's Overall Score would have been, say, 81.5, but they placed 1st in 2 of the 10 tournaments they played in, then their score would be 81.5 + 2 + 2 = 85.5?

If that's the case, then the answer is unfortunately no. To do this, the Overall Score formula would need to know how many times the player ranked 1st, 2nd, or 3rd. As it stands, only the Tournament Score formula knows this. But if you add the points into this formula, that won't get directly translated to additional points in the Overall Score, since the Overall Score formula averages the scores (and some other math).