Hi, Rick - sounds like you've been doing some exciting experiments in elastic collisions!
It's a bit hard to answer your question without knowing more precisely what was different between your test with a tennis ball and basketball and your attempt with a ping pong ball and basketball. But I can hopefully give you a bit of helpful advice so you can answer the question yourself (just like a scientist!).
First, just as you did when testing the first case (tennis ball + basketball), repeat your ping pong ball experiment several times. What's the average result? Was the first time maybe just a weird bounce and not usual?
Now, think about that result in the context of your first experiment with the tennis ball. Are the balls different sizes? Different weights? Different materials? Research how those differences might affect the result. This link provides some insight into why ping pong balls might bounce differently on different surfaces. What sort of surface is the basketball?
Put all of this information together and form a working hypothesis. A hypothesis is an explanation of what's going on, which also has predictive power.
Your hypothesis will look something like this: "I think that the weight of the top ball determines how high it bounces, such that lighter balls bounce higher" or "as the difference between the weight of the two balls grows, the height of the bounce increases."
Now it's time to test your hypothesis with a new case. Try bouncing the ping pong ball on top of the tennis ball, and see if the result matches with what you guessed.
Try with a jacks ball and the basketball, or other tests you can think of. Use the new information to alter your hypothesis if necessary.
...and congratulations! You're doing science!
Kelly Chipps (AKA nuclear.kelly)
Oak Ridge National Laboratory/University of Tennessee Knoxville