# Find the expected payoff for different strategies

I have recorded on a continuous scale (between 0 and 15) the strategy some players used in a video game and their associate payoff (also interval-ratio) in this game, so I have lots of couples of values like (2.34,12), etc.

I would now like to have an idea of what strategy brings the highest payoff in the game, or what would be the expected payoff for each strategy. It is difficult to see a clear relationship between strategy and payoff on a visual inspection. A 2D scatter plot gives this:

but there are lots of points stacked up on this plot. A 3D histogram gives a better idea of the distribution:

So I tried to do a loess regression on this data. Here is the smooth curve computed by loess:

but the R² of this regression is very low, 0.09.

Do you see a regression that would be best suited for this kind of data or should I stick with Loess regression?

• This sounds like a game theory problem. Sep 21, 2014 at 17:48
• I imagine there are more variables involved than strategy that affect the payoff. Sep 22, 2014 at 1:28
• @Glen_b For now I only have the strategy as variable Sep 22, 2014 at 13:44