What is the difference between lm(offense$R ~ offense$OBP) and lm(R ~ OBP)?

In the first case, you get this if you print the model:

Call:
lm(formula = offense$R ~ offense$OBP)

Coefficients:
(Intercept)  offense$OBP  
    -0.1102       0.5276 

But in the second, you get this:

Call:
lm(formula = R ~ OBP)

Coefficients:
(Intercept)          OBP  
    -0.1102       0.5276  

Look at the name of the coefficients. When you create your newdata with newdata=data.frame(OBP=0.5), that not really make sense for the first model, so newdata is ignored and you only get the predicted values with the training data. When you use offense$R ~ offense$OBP, the formula has just two vectors at each side, with no names associated to a data.frame.

The best way to do it is:

obp = lm(R ~ OBP, data=offense)
predict(obp, newdata=data.frame(OBP=0.5), interval="predict")

And you'll get the proper result, the prediction for OBP=0.5.