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Hitting One Out of the Park

Explore how calculus can predict the number of home runs a baseball player might hit in a season based on batting average. Learn about the process, data collection, grouping strategies, and graphing techniques involved in this predictive model. Discover the practical applications of such analysis in player scouting, talent evaluation, and contract negotiations.

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Hitting One Out of the Park

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  1. Hitting One Out of the Park Presentation by: Richie Veihl Derek Monroe

  2. Can-of-Corn With all the controversy over the use of steroids in professional baseball, we thought it was about time that somebody returned America’s pastime to it’s roots (get it?) √ + That’s right, calculus. After all what is baseball but a big physics and calculus equation?

  3. The Pickle • Offense fills the seats, brings in revenue and attracts new fans to the game. Def.Home Run- A hit that allows the hitter to round all 3 bases and return to home plate to score a run. What if one could predict how many home runs a player could hit in a single season? For any given team this would be pretty useful in scouting prospective players, coaching current players, and in the management office when it comes time to “re-evaluate the efficiency” of current players. This is not even to mention the advantage it would give those with large amounts of money invested in gambling on the game of baseball each season.

  4. Initial Scouting Report So using calculus, how could we predict the number of home runs that a player will have in a season? Calculus to us is all about relations… Say, the relation of x (age) and y (percent of body covered in wrinkles) for instance. So we knew we would need something to relate the number of home runs to. Not that kind! More like THAT

  5. Scouting Report, p. II This was our list of realistic possibilities for basing a prediction of home runs on: Realistic Possibilities • -On Base % vs. Home Runs • -Position Played vs. Home Runs • -Number of Years in League vs. Home Runs • -Batting Average vs. Home Runs After much deliberation we decided on relating the batting average of a single player to his home runs in a single season. Def.Batting Average- Hits by a given player divided by that player’s “At Bats” over a selected time period. Now we need to do research and determine the best way to relate our two variables.

  6. Batting Practice GOAL: To relate home runs and batting average in a manner so that it is possible to predict the number of home runs a player would hit in a given season. Our first step was to go to MLB.com and collect data, what better place to start than the league’s site, right? After seeing the very large number of players we had to work with, we decided to cut the list to players that had 450 at bats (AB) or more. (an average of 2.77 AB a game.)

  7. Opening Pitch We decided to take all 147 points and plot them. STRIKE ONE! Not too good. This did not give us results we wanted or expected. There is no way to predict anything from this graph.

  8. Second at bat Next we decided to put players into groups by every .005 points of batting avg. (i.e. .230-.235 or .340-.345) Within these groups we averaged their respective home runs and plotted the results. FOUL BALL! Once again, not very workable data. It was obvious that we needed to do something different.

  9. Seventh Inning Stretch We really had to put our heads together and think of a way to group the players so that a correlation would be shown. Then it dawned on us… Why not group the players by home runs, then take the average of their respective batting averages? Could it work? Would flipping our entire game plan by 180o actually provide solid data?

  10. Suicide Squeeze So now we group the players by every five home runs. (i.e. 0-5, 5-10, 25-30) A WALK OFF HOME RUN! Notice the batting average is still on the x-axis and home runs are still on the y-axis.

  11. Extra Innings We now have a great graph and a useful equation: Y=.001x2+.0978x+5.0082 X=(1000(Avg.-.215) So say we have a player who has an average of .230. X=(1000(.230-.215)=15 Y=.001(15)2+.0978(15)+5.0082 Y=6.700 HR

  12. The Locker Room So suppose we didn’t have a graph, how could we use only the equation and get a graph? Answer: Euler’s Method! We will take the derivative of many points very close together so that it will give us an accurate picture of the graph of this equation.

  13. Press Conference Using Euler’s Method we get Slope: YI=.002x+.0978

  14. Which gives us a graph that looks like this: Which looks very similar to this:

  15. Post Game Wrap-Up - Used Calculus to derive an equation for predicting home runs in a season using a player’s batting average. - Used Euler’s method to get a graph from the equation. Possible uses for this include: (but are not limited to) -Endorsement deals -Scouting prospective talent -Contract clauses and disputes

  16. And the Game Ball Goes TO: Produced by veihl/monroe productions Directors Richie Veihl Derek Monroe Research Dr. Richie Veihl & Dr. Derek Monroe Style and Design Richie K. Veihl & Derek C. Monroe Special Thanks TO: MLB.COM Professors Buckmire and Gallegos Google Images Analysts: Steven Michael Salisbury II Eliza Schillhammer Ali Newcomer

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