Rensselaer Polytechnic Institute
Lally School of Management & Technology
MGMT 6070 Statistical Methods for Reliability Engineering
Term Project Presentation
Robert Ricker
December 4th, 2008
Summary Description
Problem Statement
The success of a Major League Baseball team relies heavily on the arm of the
pitcher. In general, the pitching staff of a particular team must consistently
provide a certain level of performance, efficiency, and reliability in order for the
team to advance to the post season and eventually into the championship game.
System Overview
The system consists of a 5 man
rotation to cover 1458 innings /
season.
Expanded Roster
40 Man
Pitching Staff
18-20 Man
Active Roster
25 Man
Starting Rotation
5 Man
Project Objective
The objective of this project is
to use pitcher characteristics to
age the population of pitchers
on a team to determine the most
optimal pitching staff.
9 Innings/game x 162 games
= 1458 Innings/Season
Methodologies
Statistical data for inactive pitchers analyzed to determine the
distribution function best representative of the reliability of an
active pitcher in the league.
The distribution function and the associated reliability functions
were then used to determine the significant failure characteristics
of a pitcher.
A Monte Carlo simulation was then performed to simulate the
failure times for a certain number of pitchers.
The reliability of the current league pitching staff will be analyzed
such that each pitcher must be fully operational in order for the
team to be performing efficiently. Each pitcher will have the failure
distribution calculated from the test data.
Results/Discussion
Data suggests a Weibull distribution
for inactive pitchers (i.e. failures)
Probability Plot for IP
ML Estimates-Complete Data
90
99
50
90
10
1
50
10
1
0.1
1000
0.1
10000
2000
IP
90
10
0.1
1
10
100
Percent
P er cent
50
1000
IP
90
80
70
60
50
40
30
20
10
10000
5 100000
Probability Plot for IP
Weibull5000
- 95% CI
IP
Complete Data - ML Estimates
Loglogistic
99.9
99
Table of
S hape
S cale
M ean
S tD ev
M edian
IQ R
F ailure
C ensor
A D*
99.9
99
P er cent
E xponential
99.9
1
A nderson-Darling (adj)
Weibull
10.539
Lognormal
5.573
E xponential
58.867
Loglogistic
4.611
Lognormal
99.9
P er cent
P er cent
Weibull
99.9
90
50
10
1
0.1
2000
5000
IP
3
2
1
0.1
1000
S tatistics
4.04675
3779.08
3427.63
951.550
3451.85
1319.11
187
0
10.425
Overview plot for Top 2.5%
inactive pitchers supports
Weibull failure distribution
10000
IP
• Data set consisted of 8164 inactive and active pitchers
• Data sorted according to innings pitched (from 0 to 7356)
• Top 2.5% inactive pitchers used for analysis
Results/Discussion
Weibull distribution modeled in Maple
Distribution Overview Plot for IP
ML Estimates-Complete Data
P robability Density F unction
Table of
S hape
S cale
M ean
S tDev
M edian
IQ R
F ailure
C ensor
A D*
Weibull
99.9
0.00045
90
50
P DF
P er cent
0.00030
0.00015
Failure Probability Distribution Function
& Reliability Function (Survival)
0.00000
10
1
2000
4000
0.1
6000
1000
IP
S tatistics
4.04675
3779.08
3427.63
951.550
3451.85
1319.11
187
0
10.425
10000
IP
S urv iv al F unction
H azard F unction
100
Rate
P er cent
0.003
50
0.002
0.001
0
0.000
2000
4000
IP
Failure Probability
Density Function
6000
2000
4000
6000
IP
Hazard / Failure
Rate Function
Results/Discussion
Monte Carlo simulation
validated the Minitab
and Maple Results
T-test shows a gradual
increase in ERA as
active pitchers move
into distribution
ERA for Inactive vs. Active Pitchers
4.5
Earned Run Average
4.0
3.5
3.0
2.5
2.0
Inactive
Active
Conclusions
Average failure rate for Inactive Major League Pitchers in the top
2.5% of Innings Pitched is 3427.
Active Pitchers making it to the top 2.5% display a decline in key
statistics such as ERA that suggests the efficiency is reduced.
Teams should therefore draft additional pitchers to their staff to
decrease the burden on the 5 starters and increase the efficiency
throughout a career.
Including all pitching data (both inactive and active) into analysis
will help validate assumptions.
Using a 3-Parameter Weibull Distribution will also add fidelity to
analysis.