Using TMR's Fan Cost Index to Model the Chicago Cubs Average Ticket PriceUnlike my other economic themed papers, this article was written over a number of sessions during the span of about 3 months. It is written in a stream of consciousness style, and isn't a finished paper by any stretch of the imagination. However, it uses an intermediate level of statistical analysis in a stepbystep method, which concludes with a working model. Back to the Web Friendly FCI Model By: Byron Clarke

From TMR, explaining the Fan Cost Index (FCI) 
Average ticket price represents a weighted average of season ticket prices for general seating categories, determined by factoring the tickets in each price range as a percentage of the total number of seats in each ballpark. Luxury suites are also excluded from the survey. Seasonticket pricing is used for any team that offers some or all tickets at lower prices for customers who buy season tickets. 
Team 
Avg. Ticket 
% Change 
Ticket Rank 
FCI 
% Change 
Year 
Record† 
Cubs  $10.10  N/A  7  $83.40  N/A  1991  7783 
Cubs  $10.87  +7.6%  6  $96.98  +16.3%  1992  7884 
Cubs  $11.74  +8.0%  3  $103.96  +7.2%  1993  8478 
Cubs  $13.12  +11.8%  4  $108.98  +4.8%  1994  4964° 
Cubs  $13.17  +0.4%  4  $112.68  +3.4%  1995  7371° 
Cubs  $13.12  0.4%  7  $116.48  +3.4%  1996  7686 
Cubs  $14.63  +11.5%  7  $121.02  +3.9%  1997  6894 
Cubs  $14.42  1.4%  15  $120.18  0.7%  1998  9073‡ 
Cubs  $17.46  +21.1%  9  $134.84  +12.2%  1999  6795 
Cubs  $17.55  +0.5%  13  $135.32  +0.4%  2000  6597 
Cubs  $21.17  +20.62%*  7  $166.25  +22.86%*  2001  8874 
Cubs  $24.05  +13.6%  4  $181.69  +9.3%  2002  6795 
Cubs  $24.21  +0.67%  4  $172.84  4.87%  2003  8874‡ 
Cubs  $28.45  +17.53%  2  $194.31  +12.42%  2004 
Team 
Avg. Ticket 
% Change 
FCI 
% Change 
Year 
MLB Average  $9.14  N/A  $79.41  1991  
MLB Average  $9.41  +3.0%  $86.72  +9.2%  1992 
MLB Average  $9.73  +3.4%  $91.38  +5.4%  1993 
MLB Average  $10.60  +8.9%  $96.41  +5.5%  1994° 
MLB Average  $10.73  +1.2%  $97.55  +1.2%  1995° 
MLB Average  $11.32  +5.5%  $103.07  +5.7%  1996 
MLB Average  $12.39  +9.4%  $107.26  +4.1%  1997 
MLB Average  $13.66  +10.2%  $115.06  +7.3%  1998 
MLB Average  $15.00  +9.9%  $121.76  +5.8%  1999 
MLB Average  $16.81  +12.1%  $132.44  +8.8%  2000 
MLB Average  $17.64  *+4.9%  $140.63  *+6.2%  2001 
MLB Average  $18.30  +3.8%  $145.21  +3.0%  2002 
MLB Average  $19.01  +3.43%  $151.19  +3.48%  2003 
MLB Average  $19.82  +3.90%  $155.52  +2.78%  2004 
* — In 2001, TMR did not report % changes in ticket prices or FCI. I calculated the numbers, but I suspect that TMR may have redefined their method of calculating average ticket price (and thus FCI) in 2001.
† — TMR does not note the Team's WonLoss Record, but I feel that this is an important factor to see alongside ticket price changes.
° — In 1994, a labor dispute caused the season to end August 12. The strike and subsequent lockout caused most MLB teams to play about 18 fewer games in 1995.
‡ — In 1998, the Cubs played 163 regular season games. They played a single playoff game against the San Francisco Giants to determine the National League Wild Card. The Cubs won, and played three games against the Atlanta Braves. In 2003, the Cubs won the NL Central Division. They won a five game NL Division Series against the Atlanta Braves. The Cubs then lost in seven games during the NL Championship Series to the Florida Marlins. Playoff games are not included in the Cub's records.
Year  Winning Percentage  Cubs Payroll  White Sox Tickets  MLB Avg Ticket Price  Attendance  CPI  US GDP Level  Cubs Ticket Price 
1990  0.475  $14,496,000      2,243,791  130.7  7,112.5   
1991  0.481  $26,923,120  $10.26  $9.14  2,314,250  136.2  7,100.5  $10.10 
1992  0.481  $29,060,833  $11.7  $9.41  2,126,720  140.3  7,336.6  $10.87 
1993  0.519  $38,303,166  $11.7  $9.73  2,653,763  144.5  7,532.7  $11.74 
1994  0.434  $35,717,333  $12.91  $10.60  1,845,208  148.2  7,835.5  $13.12 
1995  0.507  $32,460,834  $12.93  $10.73  1,918,265  152.4  8,031.7  $13.17 
1996  0.469  $30,954,000  $14.11  $11.32  2,219,110  156.9  8,328.9  $13.12 
1997  0.420  $39,829,333  $13.33  $12.39  2,190,308  160.5  8,703.5  $14.63 
1998  0.552  $49,383,000  $14.48  $13.66  2,623,194  163  9,066.9  $14.42 
1999  0.414  $55,368,500  $15.04  $15.00  2,813,854  166.6  9,470.3  $17.46 
2000  0.401  $62,129,333  $14.30  $16.81  2,789,511  172.2  9,817.0  $17.55 
2001  0.543  $64,515,833  $18.73  $17.64  2,779,465  177.1  9,866.6  $21.17 
2002  0.414  $75,690,833  $18.73  $18.30  2,693,096  179.9  10,083.0  $24.05 
2003  0.543  $79,868,333  $22.51  $19.01  2,962,630  184  10,398.0  $24.21 
2004    $90,560,000  $23.76  $19.82        $28.45 
CPI data from: Bureau of Labor Statistics CPI Data.
GDP Data from: Commerce Department Bureau of Economic Analysis. Download the spreadsheet of GDP data.
Cubs Payroll information used from USA Today's Baseball Salary Database.
Cubs Attendance information used from Cubs Year by Year Results.
Because the Cubs (and all other major league teams) set their ticket prices at the end of the year for which they take effect, I have adjusted the data in my calculations by setting ticket dates back one year.
For example: my model of Chicago Cubs 2004 ticket prices is based off of the following factors:
The first step in building my model has been to find the correlation between Cubs ticket prices and each individual variable.
Variable  Correlation with Cubs Ticket Price  Coefficient of Determination 
Cubs Win %  11.87%  1.41% 
Cubs Payroll  97.65%  95.36% 
White Sox Ticket Prices  96.92%  93.95% 
MLB Ticket Prices  96.16%  92.48% 
Avg. Attendance  76.64%  58.75% 
CPI  95.04%  90.33% 
GDP  95.00%  90.26% 
Wrigley Attendance  77.24%  59.66% 
Cubs Ticket Price  100%  100% 
Perhaps the most interesting number here is also the most obvious number for Cubs fans. The Cubs ticket prices have very little to do with whether the Cubs win or not.
The interpretation of the above table is this: "coefficient of determination" percent of changes in Cubs ticket prices are accounted for by changes in the independent variable. Thus, we would say that the 95.36% of the change in Cubs ticket price over the period from 19912004 can be accounted for by examining changes in the Cubs Payroll. From a business standpoint, this seems logical as ticket revenues are the Cubs most significant form of revenue, and Cubs payroll is the most significant expense.
Using Microsoft Excel, I have constructed a multiple regression analysis using Cubs ticket prices from 19912004 as the dependent variable, and the above eight variables as the independent variables. I am presenting this work as an initial model now, but will refine it over time.
The model is this:
Cubs ticket price = 7.199 + (11.095 * Cubs win %) + (8.538E08 * Cubs Payroll) + (0.552 * White Sox Tickets) + (.538 * MLB Avg Ticket Price) + (1.221E06 * Avg. Attendance) + (0.004 * CPI) + (0.0004 * GDP) + (0.0001764 * total attendance)
Using this model, which has a (coefficient of determination of 99.2%) I have calculated the Cubs projected ticket price for each of the previous 14 years. I have also listed the actual ticket price, and the deviation from the model.
Year 
Projected Ticket Price 
Actual Ticket Price 
Deviation 
1991 
$9.73 
$10.10 
$0.37 
1992 
$11.03 
$10.87 
$0.16 
1993 
$11.64 
$11.74 
$0.10 
1994 
$13.38 
$13.12 
$0.26 
1995 
$13.07 
$13.17 
$0.10 
1996 
$13.48 
$13.12 
$0.36 
1997 
$13.59 
$14.63 
$1.04 
1998 
$14.98 
$14.42 
$0.56 
1999 
$18.22 
$17.46 
$0.76 
2000 
$17.86 
$17.55 
$0.31 
2001 
$20.64 
$21.17 
$0.53 
2002 
$23.47 
$24.05 
$0.58 
2003 
$24.68 
$24.21 
$0.47 
2004 
$28.27 
$28.45 
$0.18 
Obviously, there are some glitches in this model because there are negative components (CPI, GDP, and average attendance). One of the causes, I believe is that when performing a multiple regression analysis the independent variables are assumed to be infact independent. Well, the MLB average ticket price is actually partially dependent on the Cubs, and the White Sox, so I will eliminate it in my next attempt. I also used Cubs attendance in total, and average Cubs attendance per game. I was attempting to account for the strike shortened years, but having both seems to be degrading the quality of my model. As a result, I will eliminate the average attendance per game because it has a lower coefficient of determination. Finally, because the coefficient of determination is only 1.4% for the Cubs winning percent, I will eliminate this variable.
I will run a second multiple regression analysis to determine Cubs ticket prices (dependent variable) using the Cubs Payroll, White Sox average ticket price, Total Home Attendance, CPI, and GDP as the independent variables.
Coefficient 

Intercept 
8.462 
Cubs Payroll 
1.05E07 
White Sox Tickets 
.611 
Attendance 
1.18E06 
CPI 
.0652 
GDP Level 
0.00031 
Year 
Projected Ticket Price 
Actual Ticket Price 
Deviation 
1991 
$9.58 
$10.10 
$0.52 
1992 
$11.13 
$10.87 
$0.26 
1993 
$12.07 
$11.74 
$0.33 
1994 
$13.37 
$13.12 
$0.25 
1995 
$12.24 
$13.17 
$0.93 
1996 
$13.10 
$13.12 
$0.02 
1997 
$14.11 
$14.63 
$0.52 
1998 
$15.90 
$14.42 
$1.48 
1999 
$17.43 
$17.46 
$0.03 
2000 
$18.02 
$17.55 
$0.47 
2001 
$21.20 
$21.17 
$0.03 
2002 
$22.67 
$24.05 
$1.38 
2003 
$25.43 
$24.21 
$1.22 
2004 
$27.80 
$28.45 
$0.65 
After meeting with a professor of mine (thanks to Rex Cutshall), I decided to remove the GDP level because it had a high correlation with the CPI level. This time, my regression results had a coefficient of correlation of 98.12%. However, the pvalues, which are a measure of significance were too large on all of my variables, except the White Sox Average ticket price. Below are the results of the third regression I ran.
Coefficient 

Intercept 
8.00215 
Cubs Payroll (millions) 
.10145 
White Sox Tickets 
.62085 
Attendance (millions) 
1.11171 
CPI 
.04648 
Year 
Projected Ticket Price 
Actual Ticket Price 
Deviation 
1991 
$9.67 
$10.10 
$0.43 
1992 
$11.11 
$10.87 
$0.24 
1993 
$12.03 
$11.74 
$0.29 
1994 
$13.30 
$13.12 
$0.18 
1995 
$12.26 
$13.17 
$0.91 
1996 
$13.11 
$13.12 
$0.01 
1997 
$14.07 
$14.63 
$0.56 
1998 
$15.89 
$14.42 
$1.47 
1999 
$17.44 
$17.46 
$0.02 
2000 
$18.05 
$17.55 
$0.50 
2001 
$21.28 
$21.17 
$0.11 
2002 
$22.63 
$24.05 
$1.42 
2003 
$25.43 
$24.21 
$1.22 
2004 
$27.78 
$28.45 
$0.67 
At this point, I tried monkeying around with the different variables to try and strike a balance between model significance, model accuracy, and common sense. What I ended up doing was a procedure vaguely similar to a stepwise regression. In a stepwise regression, you begin looking for the variable with the highest coefficient of determination, and then you find the two variable multiple linear regression with the highest coefficient of determination, and keep adding variables until you add an insignificant variable.
I just started with the average White Sox ticket price, because it has consistently had a low pvalue in trials #13. I then added the Cubs Payroll and found that both variables were significant (p value below .05). However, when I added in the Cubs attendance, I found that the third variable was statistically insignificant.
So, I will conclude this mess by saying: The best model I care to create of the Cubs Ticket Price relies on the average White Sox ticket price, and the Payroll for the Cubs. These two variables form a model which explains 97.9% of the Average Cubs ticket price, and both variables are significant.
Cubs Ticket Price = $0.53 + ($0.15 x Cubs Payroll in Millions) + ($0.62 x White Sox average Ticket Price) 
Copyright ©2004  2008 Byron Clarke 