Anthony Lawrence
Southwestern University Case Study B
Problem: Southwestern University is experiencing a quickly expanding football program. As a
result, attendance for home games is increasing and approaching capacity. It is in the best
interest of SWU to forecast attendance to aid them in deciding when the best time to expand the
present stadium, which now holds 54,000.
Data: The following data is from the past six seasons, 2002-2007.
Game
Year – Game – Opponent
2002-1 Baylor
2002-2 Texas
2002-3 LSU
2002-4 Arkansas
2002-5 USC
2003-1 Oklahoma
2003-2 Nebraska
2003-3 UCLA
2003-4 Nevada
2003-5 Ohio State
2004-1 TCU
2004-2 Texas Tech
2004-3 Alaska
2004-4 Arizona
2004-5 Rice
2005-1 Arkansas
2005-2 Missouri
2005-3 Florida
2005-4 Miami
2005-5 Duke
2006-1 Indiana
2006-2 North Texas
2006-3 Texas A&M
2006-4 Southern
2006-5 Oklahoma
2007-1 LSU
2007-2 Texas
2007-3 Prairie View A&M
2007-4 Montana
2007-5 Arizona State
Attendance
34200
39800
38200
26900
35100
36100
40200
39100
25300
36200
35900
46500
43100
27900
39200
41900
46100
43900
30100
40500
42500
48200
44200
33900
47800
46900
50100
45900
36300
49900
Anthony Lawrence
An important thing to note is that the homecoming game of every season is the second home
game (bold), and is always well attended. Also the forth home game always corresponds with a
local festival that always draws from attendance (italics).
Summary of Forecasting Methods: Below is a table of the forecasting methods. The
correlation coefficient, bias, mean absolute deviation (MAD), mean squared error
(MSE), and mean absolute percent error (MAPE) are shown.
Naïve
Moving Average
(3 periods)
Weighted Moving Average
(3 period; .6, .3, .1)
Exponential smoothing
(alpha = 0.5)
Trend Analysis
Seasonal Additive
Decomposition
Correlation
--
Bias
541.38
MAD
6865.52
MSE
69,856,200
MAPE
--
491.36
6,138.27
59,540,560
.17
--
424.81
6,501.58
61,107,180
.18
--
794.28
5,880.56
50,755,960
.16
.54
0.00
4,355.70
31,285,700
.12
.97
0.00
1,251.26
2,386,650
.03
.19
It is obvious that the superior method is seasonal additive decomposition. This makes
sense because of the cyclical nature each season follows, largely due to the homecoming
game and local festival. The other methods cannot take those variations into account,
and this adversely affects their error. Because of this they are not suitable for predicting
at which point the demand of attendance will surpass the stadium’s capacity. They will
show when the average or smoothed demand will reach capacity, but this will occur after
attendance for one or two games will consistently surpass capacity.
Seasonal additive decomposition is definitely the best method, and all indications
support that. The bias for trend analysis is just the same as seasonal, however the
correlation coefficient is not acceptable for this method, well below .70, but the seasonal
correlation is outstanding at .97.
So, now the management has a decision to make whether or not it is worth putting off
expansion of the stadium until the average attendance of a season is above capacity, and
losing potential ticket sales for the games that are above capacity, or to go ahead and
expand before capacity is ever reached in a single game.
Anthony Lawrence
Forecasting: The following table shows the forecasted attendance of the next two
seasons of home games.
Game
2008 – 1
2008 – 2
2008 – 3
2008 – 4
2008 – 5
2009 – 1
2009 – 2
2009 – 3
2009 – 4
2009 – 5
Attendance
46540.23
52555.73
50254.56
38370.06
50202.22
48784.39
54799.89
52498.72
40614.22
52446.38
According to this analysis, the second game of 2009, the homecoming game, will be the
first game that the demand for attendance will exceed capacity. The management can
wait until after the 2008 season to start the completion, so long as it is completed before
the 2009 season starts. One thing they should consider is that a refurbished stadium
would cause a spike in attendance because fans would want to see and experience the
new facilities. With this in mind, these figures could be much lower than what would
actually happen if an expansion were built.
Revenues: Ticket sales will average $20 in 2008 and $21 in 2009 due to a 5% price
increase. Total sales can be found for each season by summing the attendance from each
game and multiplying by the ticket price. The results are displayed in the table below.
Season
2008
2009
Total Attendance
237,922.8
249,143.6
Revenue
$4,758,456
$5,232,016
Again, it should be emphasized that depending on when the expansion is built, these
values could be lower than what actually comes in. It would be smart for them to build
the expansion sooner than later, so that the spike in ticket sales will come sooner. This
could offset some extra costs that could incur from building it sooner.