Statistics and Fangraphs

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The popular site fangraphs updates winning percentages live for MLB games. It creates a graph of how its changed throughout the game, changing after every play. I was wondering, if you average all points on all the graphs, what would that graph look like. So my question basically is, without considering that the home team is always put on one side, would it just be a straight line at 50% because of law of large numbers, or is there potentially a factor that would affect this.

This is an example of what a low scoring game's graph looks like. This is an example of what a low scoring game's graph looks like.

A great example of what a wild game's graph looks like. A great example of what a wild game's graph looks like.