I am working on building a physics model into the xStats home run prediction. In order to do so, I had to learn the equations backwards and forwards. I started with Alan Nathan's calculator as a starting point. I studied it, took notes, memorized it, and created my own version from memory. The result of which you can see below. It is functionally identical to Alan Nathan's calculator with one major difference: it doesn't use wind.
I've also added a few other features that Nathan's calculator does not have. Let me show you its features.
- Select a ballpark. This will Automatically input an elevation. You can search by team or ballpark and it will work either way.
- Initial conditions for a batted ball. You should be most interested in the first three: Exit Velocity, Launch Angle, and Spray Angle. You can edit all of the rest if you'd like. Remember elevation is automatically changed by the ballpark.
- Target Wall Height. The calculator will indicate the point in the trajectory where a ball crosses the height specified. (See 8. Below).
- You can input a known wall distance and wall height and it will be drawn on the chart. (See 9. Below).
- The distance from home plate at the specified target height. There are three results. The red line depicts the upper range for coefficients of drag and lift. The blue result uses the mean values for drag and lift. The green line uses the lower range for drag and lift.
- Vertical and horizontal angles are drawn for reference.
- Various constants and other values used for calculation. Do not edit these.
- Each painted trajectory will have a small vertical line showing where it crosses the target height (See 3. Above).
- The thick black line shows the location for the inputed Real Wall (See 4. Above).
- Calculations. You don't need to worry about these, but you can look at them if you'd like.
I took the upper and lower coefficients from a few studies into baseball coefficients of drag and lift. I was hoping they would approximate the second or third standard deviation, but in my testing I have found that actual MLB batted ball distances have an even wider range than depicted by this calculator.
The difference could be due to wind, I cannot rule that out. I find it hard to talk about wind at all, since it is such a complex issue within a baseball stadium. It swirls around the stadium in difficult to predict, chaotic patterns. Small changes in wind speed or direction can create large changes in the local wind effects at any given point within the park. Wind is difficult, and I'm choosing to ignore it for the moment.
At the end of the day, this calculator is a first step towards the greater goal of integrating a physics model into home run prediction. You can mess around with the spreadsheet as you please. Just open the link below and click File -> Make a Copy.