# Is there a way to make this curve fit my data better?

I'm working off Safe Leads and Lead Changes in Competitive Team Sports and trying to apply the same techniques to baseball scores, using number of outs remaining instead of the number of seconds. I'm pretty far out of my depth reading the paper so I'm just cherry-picking the algorithms that look right and trying to use them with baseball data. I get a pretty reasonable curve (similar to Figure 16 in the paper), but as the game gets more safe, the erf(v) curve overestimates the probability the lead is safe by a few percentage points (I wouldn't mind if it underestimated a little). Here's a picture: the red triangles are the observed values, and the black line is the erf(z) curve; the hand-drawn blue line is roughly what I wish the erf(z) curve looked like.

Is there a way to make my curve fit the data better, either by applying some additional transformation to the result of erf(z) or using something other than erf in the first place? Preferably also something easy to implement in Java (for my Android app).

If you want to examine the data yourself:

That said, by eye one can see that $1-\exp(-\theta\:\! x)$ will be a better fit than what you have (looking more closely at the picture, it looks like $\theta\approx 1.8$, or possibly a bit lower, would fit adequately).