I have performed a multiple regression with draft order (value between 1 and 80) as the dependent variable and have 3 predictor variables. I am looking for confirmation that I am interpreting the continuous predictor correctly. Height (cm) was shown to predict draft order and had a regression coefficient of -0.45. This is how I interpret that result... Pick 10 (for example) would be 0.45cm taller than pick 11 and likewise pick 11 would be 0.45cm taller than pick 12 with all other variables held constant. Does this sound right?
That is generally correct. But keep in mind that is probably not true near the edges of your data. Depending on your software, you can get the confidence interval of that estimate.
The height relationship is most likely non linear. You could try Tukey's ladder series on height and most likely a transformation on height or a combination of transformations may yield a better fit. Beware over fitting so always use a test set or cross validation.