Hitting One Out Hitting One Out of the of the ParkPark

Presentation by:Richie Veihl

Derek Monroe

Can-of-CornCan-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?

The PickleThe 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.

Initial Scouting ReportInitial Scouting ReportSo 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.

More like THATMore like THAT

Not that kind!Not that kind!

Scouting Report, p. IIScouting 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 RunsAfter 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.

Batting PracticeBatting 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.)

Opening PitchOpening 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.

Batting Average vs. Home Runs

0

10

20

30

40

50

60

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36

Batting Average

Hom

e R

uns

Second at batSecond at batNext 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.

Batting Average vs. Home Runs

0

5

10

15

20

25

30

35

40

0.22

0.25

0.26

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.29 0.3

0.31

0.32

Batting Average

Hom

e R

uns

Seventh Inning StretchSeventh 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?

Suicide SqueezeSuicide 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.

The Relationship Between Home Runs And Batting Average

y = 0.001x2 + 0.0978x + 5.0082

0

10

20

30

40

50

60

1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145

Batting average

Hom

e R

uns

hr

avg

Poly. (hr)

Extra InningsExtra 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

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.

The Locker RoomThe Locker Room

Press ConferencePress ConferenceUsing Euler’s Method

we get

Slope:

YI=.002x+.0978

x y slope step chnge y

0 5.0082 0.0978 5 0.489

5 5.4972 0.1078 5 0.539

10 6.0362 0.1178 5 0.589

15 6.6252 0.1278 5 0.639

20 7.2642 0.1378 5 0.689

25 7.9532 0.1478 5 0.739

30 8.6922 0.1578 5 0.789

35 9.4812 0.1678 5 0.839

40 10.3202 0.1778 5 0.889

45 11.2092 0.1878 5 0.939

50 12.1482 0.1978 5 0.989

55 13.1372 0.2078 5 1.039

60 14.1762 0.2178 5 1.089

65 15.2652 0.2278 5 1.139

70 16.4042 0.2378 5 1.189

75 17.5932 0.2478 5 1.239

80 18.8322 0.2578 5 1.289

85 20.1212 0.2678 5 1.339

90 21.4602 0.2778 5 1.389

95 22.8492 0.2878 5 1.439

100 24.2882 0.2978 5 1.489

105 25.7772 0.3078 5 1.539

110 27.3162 0.3178 5 1.589

115 28.9052 0.3278 5 1.639

120 30.5442 0.3378 5 1.689

125 32.2332 0.3478 5 1.739

130 33.9722 0.3578 5 1.789

135 35.7612 0.3678 5 1.839

140 37.6002 0.3778 5 1.889

145 39.4892 0.3878 5 1.939

Which gives us a graph that looks like this:

Which looks very similar to this:

The Relationship Between Home Runs And Batting Average

y = 0.001x2 + 0.0978x + 5.0082

0

10

20

30

40

50

60

1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145

Batting average

Hom

e R

uns

hr

avg

Poly. (hr)

Batting Average vs. Home Runs Using Euler's Method

05

1015202530354045

0 20 40 60 80 100 120 140 160

Batting Average

Hom

e R

uns

Post Game Wrap-UpPost 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

And the Game Ball Goes TO:

Produced byveihl/monroe productions

DirectorsRichie Veihl

Derek Monroe

ResearchDr. Richie Veihl

&Dr. Derek Monroe

Style and DesignRichie K. Veihl

&Derek C. Monroe

Special Thanks TO:MLB.COM

Professors Buckmire and GallegosGoogle Images

Analysts:Steven Michael Salisbury II

Eliza SchillhammerAli Newcomer