League-level attendance and outcome uncertainty in U.S. pro sports leagues.
Mills, Brian ; Fort, Rodney
I. INTRODUCTION
Past empirical work investigating what has come to be called Simon
Rottenberg's (1956) "uncertainty of outcome hypothesis"
(henceforth, UOH) for North American professional sports leagues has
overwhelmingly involved analysis of Major League Baseball (MLB)
attendance. (1) What there are on attendance demand studies of other
North American sports leagues have focused on fan substitution, stadium
honeymoon effects, discrimination, and impacts of labor disputes. (2) At
best, as detailed shortly, this literature treats the UOH
inconsistently.
This paper shifts focus to the neglected National Basketball
Association (NBA), National Football League (NFL), and National Hockey
League (NHL) with a full time series assessment of the impact of outcome
uncertainty on league-level annual attendance (while maintaining
comparisons with MLB). The main contributions of the paper are two.
First, unlike any of the work just cited, we assess the impact of all
three main types of outcome uncertainty in these three leagues,
simultaneously--game uncertainty (GU), play-off uncertainty (PU), and
consecutive season uncertainty (CSU). (3) Overall, empirical results on
the influence of the UOH have been mixed. Szymanski (2003) reviews the
findings of a number of studies and concludes that the UOH does not have
any consistent (emphasis added) empirical backing. Borland and MacDonald
(2003) offered a more nuanced take on the issue, surmising that a
winning probability closer to 60%-70% maximized attendance, rather than
50%. (4) However, Fort and Lee (2006) note that the weak and
inconsistent treatment of the UOH as well as complete inattention to
time series issues may be at the root of this inconsistency in outcomes.
Joining Lee and Fort (2008) on MLB, this paper addresses this issue by
incorporating all three main types of outcome uncertainty in a time
series framework for the rest of the North American major leagues.
Second, we investigate a variety of measures of outcome uncertainty
offered in the literature, finding that results are a bit sensitive to
the choice of GU measures. While we choose a particular GU measure for
the sake of comparison among the NBA, NFL, and NHL, we also make clear
what the differences are if other measures are used. The use of GU in
previous time series work on MLB by Lee and Fort (2008) also informs our
choice, In addition, we are able to contrast their choice with ours
concerning the measurement of PU for MLB.
The work here, by its aggregate league-level nature, is
complementary to cross-section/time series analysis. First, most
generally, aggregate league-level time series is only one possible
choice about the unit of observation for analyzing the impact of
competitive balance on attendance. Thus, it will be complementary to
work at less aggregated levels of attendance. Second, the actual break
points identified in our work suggest additional research questions that
may best be addressed using less aggregated data, for example, with
cross-section/time series data on attendance, perhaps even at the
individual team level.
The work here is also of aid to future cross-section/time series
endeavors. Non-stationary data can adversely affect coefficient standard
error estimates and produce spurious correlations (Davies, Downward, and
Jackson 1995; Dobson and Goddard 2001). As also detailed in Davis
(2008), ascertaining that regression analyses are performed on
stationary subsets of data ensures that valid inferences can be made
from regression coefficients. Our work identifies stationary subsets of
the data to help overcome this problem. While a first-differences
treatment of nonstationary time series does not allow the calculation of
direct elasticity estimates for variables within a regression, our work
allows estimation without first differences, and elasticity
interpretations are appropriate.
By way of preview, the attendance data in all three leagues are
nonstationary, but stationary with break points. Also, we find very
limited support for the UOH and, upon reflection on the choice of
measures for GU, suggest that the previous Lee and Fort (2008) finding
that PU matters for MLB is sensitive to the choice of measurement. By
our measures, for the NHL, and for the National League (NL) and American
League (AL) in MLB, the UOH is rejected for all three types of outcome
uncertainty regardless of which measure is used for GU. A particular
measure of GU recommends itself for the NFL with the result that the UOH
matters for PU in that league. Whether GU matters or not for the NBA is
a matter of which GU variable is used. However, while outcome
uncertainty measures do produce some statistically significant results
for Rottenberg's UOH for the NBA and the NFL, the economic impacts
are trivial for league revenues. Finally, there are situational
similarities among some of the break points across the different
leagues, suggesting that further analysis of the impacts of global
conflict, league expansion, league responses to rival leagues (e.g.,
mergers), and fan substitution among pro-sports leagues during strikes
and lockouts will prove insightful.
This paper proceeds as follows. In Section II, we present data
collection methods, our selection of measures for the three types of
outcome uncertainty, data issues, and our methodology. Section III
presents our results organized around the four main points of
analysis--unit-root tests of stationarity for each league (including
unit root with break points), variable selection for GU, the break
points for each league, and the results for outcome uncertainty on
attendance. A comparison of situational similarities associated with
break points across the leagues as a guide to future general research
areas is in Section IV. Finally, in Section V, we conclude with
remaining suggestions for future research.
II. DATA, MEASUREMENT, AND METHODOLOGY
A. Data
Our data come from Rod's Sports Business Data (2012a, 2012b,
2012c) and the Sports Reference league-specific coverage websites
(Basketball-Reference 2012; Hockey-Reference 2012;
Pro-Football-Reference 2012). (5) As in all of the past works on
aggregate league attendance already cited, we specify attendance as
annual, league-level, per-game attendance (LAPG) because the number of
games and teams has changed substantially throughout the history of each
respective league. LAPG is calculated by dividing annual total league
attendance by the total number of games played for each year within the
series. The length of LAPG series in each league is subject to the
availability of attendance data--NBA: 1955-1956 through 2009-2010; NFL:
1934 through 2009; NHL: 1960-1961 through 2009-2010. We stress that we
do not formally analyze demand, as the models do not account for
sellouts, especially apparent for the NFL In addition, many of the usual
variables of interest in demand analysis are subsumed in trend variables
due to lack of data. Cross-section/time series approaches where more
data are available will prove enlightening.
B. Measurement
We investigated various measures of outcome uncertainty already
available in the literature in order to preserve some comparability for
our eventual estimation results. (6) The variables, their definitions,
and their descriptive statistics are in Table 1. (7) Published measures
of GU capture two possible dimensions of fan preference, the overall
distribution of winning percentage outcomes and just the tails of that
distribution. The Ratio of Standard Deviations (RSD; Fort and Quirk
1995; Noll 1988; Scully 1989) and exposition of the Herfindahl Index of
Competitive Balance (HICB) by Lenten (2009) both measure the breadth of
the entire distribution of winning percentages. The Tail Likelihood
measure (TL, Fort and Quirk 1995) used in Lee and Fort (2008) examines
both tails of the distribution of winning percentages. Since there is no
overwhelming evidence that either of these dimensions is more important
to fans of any particular league, we investigate all of these GU
measures further, in the results section. (8)
For PU and CSU, we were able to compare the published options and
choose based on how measurements adhere to the relevant task. For PU, we
are convinced that the PLU measure from Krautmann, Lee, and Quinn (2011)
is superior due to its robustness with respect to the distribution of
play-off contending teams. (9) PLU contains information about the entire
distribution of team distance from first place while the other published
measure (Lee and Fort 2008) contained only information about the first
and second place finish.
There also are two extant measures for CSU, the correlation in team
performance across seasons (CORR) in Lee and Fort (2008), based on the
measure in Butler (1995), and Lenten's (2009) "mobility gain
function." We believe that CORR is defensible by its "longer
memory" with three prior seasons compared with Lenten's
measure that only uses one prior season. It is more reasonable to think
of CSU across more than one season of reference. (10)
We found that there is the high correlation in all leagues within
the three GU measures listed above, except in the NHL. The correlations
between RSD and HICB are between .856 and .980. However, there are only
a few signs of mild to strong correlation between these GU measures and
PLU (our chosen measure of PU) and CORR (our chosen measure of CSU).
C. Data Issues and Adjusted Series
There are a number of issues with raw attendance data. (11) Each
league has had either a strike (players refuse to work) or lockout
(owners refuse to run part or all of a season) at some point. While
previous literature has made use of indicator variables to denote strike
and lockout years (Schmidt and Berri 2002, 2004; Coates and Harrison
2005), this can adversely affect detection of long-term structural
change elsewhere in the data where the series may be partitioned into
short subsamples by the indicator variables. Therefore, in addition to
the raw LAPG, we make use of an adjusted version to handle labor
disputes that actually resulted in lost games for fans. For those years,
the adjustment takes a weighted average LAPG of the seasons just before
games were lost, during the season where games were lost, and just
following the year where games were lost, as in Lee and Fort (2008). In
the case of the 2004-2005 NHL season lost in its entirety, we average
data from one season before and after the work stoppage. This adjustment
ensures that later breakpoint size and location estimation is not
falsely influenced by the short-term shocks that may result from a work
stoppage, as the works just cited find short-term effects of strikes,
rather than long-term. Lastly, we assume the average of reported games
was the same over all games for a few NFL teams that did not report the
attendance at all of their games for 2008 and 2009. (12)
D. Methodology
We follow the approach outlined in Fort and Lee (2006) as actually
implemented by Lee and Fort (2008). The first step is to test each
attendance series against the null of a unit root. Then, if needed,
stationarity with break points is assessed. Third, using what is now
referred to as the "BP method" (Bai and Perron 1998, 2003,
2006), the statistical significance and qualitative characteristics of
the break point is determined. Finally, the impact of our UOH measures
on attendance is estimated, taking into account break points in the
data.
The unit-root hypothesis was tested using the Augmented
Dickey-Fuller (ADF) and Phillips-Perron (PP) tests with both a constant
and with a trend. The numbers of lags were determined by minimization of
the Schwartz--Bayesian criterion for the ADF test, and by the truncation
suggested by Newey and West (1994) for the PP test. Unit-root tests were
further verified using the generalized least squares Dickey-Fuller test
(DFGLS) as described in Elliot, Rothenberg, and Stock (1996).
Leybourne, Mills, and Newbold (1998) highlight the possibility of
spurious rejections of unit-root presence with Dickey--Fuller tests when
breaks are near the beginning of a nonstationary series. We therefore
employ the two-break minimum LM unit-root test irrespective of the
results from the ADF and PP tests (Lee and Strazicich 2001, 2003, 2004;
Perron 1989). Following results from this procedure, we employ a
one-break minimum LM unit-root test (Lee and Strazicich 2001) for series
that are not rejected at the highest level with the two-break test.
Lastly, we further verify the unit root with break results using the
Zivot-Andrews test (Zivot and Andrews 1992). (13)
For each league attendance series in which a unit root is rejected,
or rejected with break points, we apply the approach of Bai and Perron
(1998, 2003, 2006) to ascertain the statistical significance and
qualitative behavior of the breaks allowing changes in both levels and
trends as first described in Perron (1989). Our model for each league
parallels that used on MLB in Lee and Fort (2008) and we do not reprise
it here. Suffice to say that we perform the BP method on each league as
a separate regression, including the impacts of our UOH variables where
only coefficients on the time trend and level are allowed to change
across regimes, while the coefficients pertaining to UOH variables are
not. This is classified as the partial model in Bai and Perron (2003).
We present model results that assume homogeneous error estimates
across regimes for the statistical tests with the suggested trimming
parameter ([epsilon] = 0.15). (14) While we also examined results
assuming heterogeneous error estimates across regimes with a larger
trimming parameter, the only differences produced by the two models
occurred in the NHL and we detail later why we believe the homogeneous
version is more useful. We use current year measures of balance, rather
than lagged versions since it seems reasonable that outcome uncertainty
in the current year would be more desirable to fans than the previous
year. Finally, we report the results of the BP method on the attendance
data adjusted for labor issues (results for unadjusted data are
available upon request).
III. RESULTS OF ANALYSIS
As detailed in all of the above, the results of our analysis should
inform us on four main points--stationarity characteristics of the data
(roughly identifying breaks in the attendance time series), sorting out
the issue of the measurement of GU over the entire distribution of
winning or just in the tails, the determination of the significance of
the break points (we add a brief look at the economic as well as
statistical significance) in the attendance time series for each league.
Finally, and the punch line, is the impact of the UOH on attendance
through GU, PU, and CSU.
A. Stationarity
Unit-root test results are in Table 2. For all three leagues, we
fail to reject the presence of a unit root in the data using the
Augmented Dickey-Fuller and Phillips-Perron tests. We follow with
Lagrange Multiplier tests for stationarity with break points from Lee
and Strazicich (2001, 2004). The two-break test rejects the presence of
a unit root at the 95% critical level for all three leagues.
If the attendance series are stationary with only a single break,
the power of the two-break test may be reduced. Therefore, we also apply
the one-break test for all leagues, as none of the attendance series
were rejected at the highest critical level (99%). The one-break test
rejects the presence of a unit root with breaks at the 99% critical
level for the NBA but not for the NFL. We proceed under the assumption
that all attendance series are stationary with one or two breaks.
B. Sorting Out GU
In order to investigate how GU might enter into the determination
of attendance, we investigated break points using each of RSD, HICB, and
TL in combination with PLU and CORR (results available upon request). We
compared the UOH results for each combination and the outcome was
completely consistent for the NHL, AL, and NL--the UOH for all three
types of outcome uncertainty was rejected regardless of which GU measure
was used. However, for the NBA and NFL, the UOH results depended on
whether TL or HICB was used to measure GU (but not RSD, so it was
dropped from further consideration).
"We chose TL for the NFL since the adjusted [R.sup.2] value
was about the same as for HICB but HICB identified one more break than
did TL. (15) To us, this suggests that the TL measure captured something
that HICB simply left unexplained in the added break point. Further,
since UOH results were the same in the NHL, AL, and NL for any of the GU
measures, we also use TL for hockey and baseball. However, none of these
criteria distinguished TL from HICB for the NBA; both gave the same
break points (by overlapping confidence intervals) and about the same
adjusted [R.sup.2]. For the sake of comparison, we report results
consistently across all leagues using TL but point out the differences
that occur when HICB is used instead for the NBA.
C. The BP Method and Break Points in Attendance
The BP test results are in Table 3. Since we employ a different
measure for PU than Fort and Lee (2008), we also include the results of
our model for the AL and NL. The break points we find for the AL and NL
are quite different beyond the earliest in 1918 and 1945 in both leagues
and then 1962 in the AL. We note that very little information can be
gleaned from the upcoming discussion of coefficient estimates for level
shifts in the model. For this reason, we plot the fitted value of
adjusted attendance for all leagues in Figures 1 and 2. We offer the
example of the results for the NBA and leave the results for the other
leagues to the reader (more substantive coverage is in the following
section on situational similarities). Figure 1 shows that the 1987-1988
break point for the NBA dramatically shifted attendance upward. An
upward trend followed at about the same rate as the upward trend that
characterized NBA attendance prior to the first break. The 1997-1998
break point shows only the slightest decline in attendance followed by a
barely perceptible upward trend.
D. Attendance and Outcome Uncertainty: Statistical and Economic
Significance
Table 4 shows the attendance estimation results. Table 5 summarizes
the implications of our estimation for the UOH for all leagues. We also
include the results for MLB from Lee and Fort (2008) on MLB. We note
immediately that we do not find the same support for the UOH regarding
PU that they found earlier. Partly, their analysis was on a shorter
sample but the primary difference is that the measure of PU we use, PLU,
incorporates the entire distribution of play-off contending teams rather
than just those in first and second place.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
The first striking result to us in Table 5 is that there is
extremely limited evidence supporting Rottenberg's UOH. GU for the
NBA impacts attendance in accord with the UOH. As TL rises, and GU
improves, attendance increases. If the NBA owners care about balance
because fans do, then they are better off facilitating closely contested
individual games. But we hasten to add that if one uses HICB rather than
TL for the NBA, it would be CSU rather than GU that would have a
statistically significant impact and fail to reject the UOH (break
points remain the same plus or minus their confidence intervals). This
suggests to us that further empirical work on the actual preferences of
NBA fans toward GU is in order--in other types of fan preference models,
are they more in tune with the tails or the overall distribution of
winning percentages? The only other piece of evidence supporting
Rottenberg's UOH is for PU in the NFL. If NFL owners care about
balance because fans do, they should facilitate tight division
championship races.
Now, as we have repeatedly stated, Rottenberg never directly
addressed the question of CSU; that is, dynasties. The results in Table
5 show overwhelmingly that any version of the UOH extended to dynasties
is simply rejected (unless NBA fans adhere to HICB rather than PL for
GU, in which case the evidence supports the UOH for CSU in the NBA). In
addition, judging by the significantly negative response of attendance
to an improvement in CSU, NHL fans appear to like dynasties. However, we
caution that the result for the NHL may be due to the inability of the
BP method to handle two closely adjacent break points. In 1967-1968, the
NHL doubled in size from 6 to 12 teams. This expansion had an effect on
the competitive balance of the league, especially for CSU measured by
CORR. The CORR measure during the first 3 years of expansion includes
six NHL teams in its calculation, as the expansion teams do not have 3
years' worth of win data to include in the measure. This
calculation issue made the CSU variable drop considerably for these 3
years only, returning to previous levels once all teams have available
data to include in the calculation. Given that the first NHL break is
not as large as the entire attendance dip during this short period, the
approach may be attributing much of the decrease in attendance to the
improvement in CSU.
This lack of any support at all for the UOH in the NHL and the two
MLB leagues makes them much like the European leagues as assessed by
Szymanski (2003). However, at least at the annual league level, there
appears to be variation in the importance of outcome uncertainty and the
type of outcome uncertainty that matters for attendance in the NBA and
the NFL. This suggests that there are truly interesting and insightful
differences to be discovered among fans of the major North American
sports leagues in future work on data at a less aggregate level However,
we repeat the caution that researchers using those data mind the break
points determined in the last section.
Statistical significance does not guarantee economic significance.
Therefore, we take the Lee and Fort (2008) approach that incrementally
changes balance measures to produce attendance increases to estimate the
effects this would have on stadium revenues. The data are from Team
Marketing Report for 2009 found at Rod's Sports Business Data
(2012a, 2012b, 2012c). For example, for GU, statistically significant
for the NBA, we improve GU by the average change in the TL measure from
year to year. We do similarly for an improvement in PU for the NFL and a
worsening in CSU for the NHL. We then determine the change in attendance
that results and apply the correctly normalized dollar values from the
Team Marketing Report, Fan Cost Index data for 2009. The results are in
Table 5.
If the NBA were able to take actions in our chosen incremental
fashion, the league would enjoy a 0.60% increase in revenues for
improved GU. While statistically significant, this result indicates that
the economic significance of outcome uncertainty to the NBA is minimal,
about $7,300 per game or about $300,000 for 41 home games for a team.
(16) This would seem to require extreme micro-level management for a
less than 1% increase in total league revenues.
Using a similar approach to PU in the NFL, the revenues gained are
again minimal for the league, an increase of only 0.93%. This amounts to
about $65,000 in game revenues, or about $520,000 for eight home games
in the regular season for each team. This total for the entire league
equates to the salary of one 3-year veteran player contracted at the
league minimum.
Exactly the same approach and logic also reveals that the
statistical significance of CSU for the NHL ends up truly trivial,
economically. If the NHL were able to take action that reduced CSU in
the incremental fashion we devise, the result would be about a 0.97%
increase in league revenues translating into approximately $520,000 per
team for 41 home games.
IV. SITUATIONAL SIMILARITIES AND FURTHER RESEARCH
A few situational similarities across leagues suggest interesting
general topics for further research. The first concerns truly macro
events. The earliest break points are only found for baseball and have
been attributed elsewhere to the two word wars (Fort and Lee,
forthcoming). The NFL (founded 1920) came after World War I and was
fully functioning at World War II. One interesting area for future
research might be why World War II impacted baseball but not hockey or
football (at least as far as attendance shifts go). (17)
The next situational similarity is league expansion. The break
points in the 1960s coincided with expansion in both the AL in baseball
and the NHL; the shifts were both downward. The only break point in the
1980s coincided with expansion in the NBA and the shift was in the
opposite direction. It is easy to see why there was this difference
between baseball and hockey, on the one hand, and basketball on the
other. AL expansion followed the move of the Washington Senators to
Minnesota (Twins); expansion teams were placed in Washington, DC
(Senators II) and Los Angeles (Angels). Neither the moves nor the
expansion involved especially talented teams and none drew very well.
The NHL added Philadelphia, Los Angeles, St. Louis, Minnesota,
Pittsburgh, and Oakland to become a 12-team league in 1967-1968. The
downward shift could easily be a combination of the complete segregation
of all expansion teams into the West Division with all original eight
teams into the East Division, and poor attendance in these new markets
(especially true of Oakland). (18) In the NBA, it is reasonable that
attendance would shift upward instead. The Charlotte Hornets and Miami
Heat joined for the 1988-1989 season and the Orlando Magic and Minnesota
Timberwolves joined the very next season, 1989-1990. The Florida markets
were large and attendance was high. (19) Additionally, Detroit,
Milwaukee, and Sacramento moved to new arenas, nearly doubling the
seating capacity for these teams. Of course, this begs the research
question on just why leagues took such different expansion approaches
and why other expansions do not coincide with any break points at all
(e.g., the NL for the 1993 season).
A third situational similarity coinciding with the break points in
the 1970s is league merger. The NFL merger (1970) occurred just prior to
an attempted rival league, the WFL (1974-1975). The NHL, on the other
hand, faced a truly viable rival league, the WHA (1972-1973 to
1978-1979). The Edmonton Oilers, New England Whalers, Quebec Nordiques,
and Winnipeg Jets merged into the NHL and that was that for the WHA. The
similarity here suggests fruitful research on the choices made by owners
through their leagues in the face of potential and actual rival leagues.
The final situational similarity is strikes and lockouts that
actually denied fans portions of regular season games and in some cases
playoffs and championships. The break points in the 1990s coincide with
the 1994-1995 MLB strike (lost portion of the 1994 regular season,
play-offs and "World Series, and a portion of the 1995 season) for
the AL, (20) the 1994-1995 lockout in the NHL (reduced the regular
season from 82 to 48 games), (21) and the 1998-1999 NBA lockout (reduced
the regular season from 82 to 50 games). For baseball, attendance shifts
down and the trends are flatter than before the shift. This seems
entirely consistent with fans that are put off by the strike and dampen
their attendance after it ends. Despite adjusting our LAPG for just such
an occurrence, there are perhaps more lasting impressions from a strike
in MLB than could be found in previous work on the subject (Schmidt and
Berri 2002, 2004; Coates and Harrison 2005). For the rest, the timing of
the break points suggests a complex substitution process that may have
been missed in previous work and goes as follows.
First, there is a rather large upward movement in attendance that
coincides with the NHL break possibly indicating fans from MLB
(specifically the AL based on the break dates) began attending NHL games
due to the absence of baseball. Second, the lower end of the confidence
interval on the NBA break point (1996-1997) suggests that NBA attendance
demand may have reached its peak or that reported attendance was at or
near capacity just following the labor issues that plagued both the NHL
and MLB in 1994 and 1995. Perhaps the upward movement in NBA attendance
followed fan substitution from these two sports to the NBA and abruptly
ended as these leagues returned to play. Finally, while there was no
strike or lockout in the NFL at its break point (well after the
1993-1994 strike), (22) the league may well have enjoyed an attendance
bump coincident with the decline that occurred in the NBA. Previous work
has found little evidence of hockey-to-basketball substitution (Winfree
and Fort 2008) but perhaps the substitution patterns are more complex
than captured there.
V. CONCLUSIONS AND REMAINING IMPLICATIONS FOR FUTURE RESEARCH
We use the BP method to assess the time series behavior of annual
league attendance per game for the North American major leagues. The
series are all nonstationary but stationary with break points. This
result should be of interest to statistical analysts using level data.
If they wish to avoid spurious correlation outcomes, they should
exercise caution and use the stationary subsets of the attendance data
we identify.
We also estimate the effects of game uncertainty and play-off
uncertainty, addressed directly by Rottenberg's UOH, on aggregate
league attendance. Supporting evidence includes only game uncertainty
for the NBA and play-off uncertainty for the NFL. Our findings of no
support for the UOH in MLB is at odds with the previous findings, using
a different PU measure, by Lee and Fort (2008). In addition, we estimate
the effect of consecutive season uncertainty, which Rottenberg did not
address, on gate attendance in each of these leagues. Increased
consecutive season uncertainty decreased attendance in the NHL. The
result might be due to a shortcoming in our technique, as closely
adjacent break points would require reducing the trimming parameter
below that suggested by Bai and Perron (2006), We hasten to point out
that some results depend on which measure of GU is used and that future
work should pay explicit attention to the investigation of such
measures. Almost certainly these results will prove interesting in all
further cross-section/time series assessments of the role of fan
preferences in attendance demand. It would also be interesting to see
how these results relate to television demand, and the natural extension
of GU research calls for further examination of attendance at the game
level.
It is important to note that we do not consider sellouts for
league-aggregate attendance, and this could affect our findings with
respect to the effects of balance measures especially for the NFL where
sellouts are the most common. More work is needed to evaluate the
effects of uncertainty on NFL attendance because of this issue.
Unfortunately, our breakpoint method only allows for ordinary least
squares regression at this point in time. Further inspection at the
franchise level for some teams--especially in the NFL--would certainly
require further consideration of sellouts in a limited dependent
variables framework.
Finally, despite the statistical significance of some of our
estimated outcome uncertainty coefficients, the economic significance of
outcome uncertainty tends to be minimal. Marginal alterations in outcome
uncertainty can improve league revenues only trivially in the NBA, NFL,
and NHL. It may be that the leagues in this analysis have managed
balance well enough that it does not negatively affect fan interest in
the league.
Given that balance seldom matters at this aggregate level, and when
it does it does not matter much, leads to our final research
suggestions. There is now ample evidence that outcome uncertainty really
just does not matter (much) for North American pro sports in the way
Rottenberg suggested. However, Rottenberg's is the typical logic
espoused by team owners, acting through their league, as justification
for policy impositions like the draft, revenue sharing, and salary caps.
If not for the sake of balance, then why are the policies actually
supported? Economists are well equipped to examine the distributional
consequences of these policies between players and owners, and some
owners and others.
ABBREVIATIONS
ADF: Augmented Dickey-Fuller
AL: American League
CSU: Consecutive Season Uncertainty
DFGLS: Generalized Least Squares Dickey-Fuller Test
GU: Game Uncertainty
HICB: Herfindahl Index of Competitive Balance
LAPG: Annual, League-Level, per Game Attendance
MLB: Major League Baseball
NBA: National Basketball Association
NFL: National Football League
NHL: National Hockey League
NL: National League
PP: Phillips-Perron
PU: Play-off Uncertainty
RSD: Ratio of Standard Deviations
TL: Tail Likelihood
UOH: Uncertainty of Outcome Hypothesis
doi: 10.1111/ecin.12037
Online Early publication October 18, 2013
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BRIAN MILLS and RODNEY FORT *
* We would like to thank Professors Junsoo Lee and Mark Strazicich
and Pierre Perron and Jushan Bai for making their unit-root and
breakpoint estimation codes publicly available, respectively. Finally,
we would like to thank the anonymous reviewers that improved this work
immensely.
Mills: Assistant Professor, Department of Tourism, Recreation and
Sport Management, University of Florida, Gainesville, FL 32611-8200.
Phone 352-294-1664, E-mail bmmillsy@hhp.ufl.edu
Fort: Professor, Department of Sports Management, University of
Michigan, Ann Arbor, MI 48109-2808. Phone 734-647-8989, Fax
734-647-2808, E-mail rodfort@umich.edu
(1.) Baade and Tiehen (1990); Bruggink and Eaton (1996); Butler
(2002); Coates and Harrison (2005); Coffin (1996); Demmert (1973);
Domazlicky and Kerr (1990); Gitter and Rhoads (2010) (MiLB); Kahane and
Shmanske (1997); Knowles and Sherony (1992); Krautmann, Lee, and Quinn
(2011); Lee (2009); Lee and Fort (2008); Lemke, Leonard, and Tlhokwane
(2007); Meehan, Nelson, and Richardson (2007); Noll (1974); Rascher and
Solmes (2007); Schmidt and Berri (2001, 2002, 2004); Siegfried and
Eisenberg, (1980) (MiLB); Soebbing (2008); Talnsky and Winfree (2010a,
2010b); Winfree et al. (2004).
(2.) Coates and Humphreys (2007); Jones and Ferguson (1988);
Leadley and Zygmont (2006); Paul (2003); Paul and Weinbach (2007);
Pivovamik et al. (2008); Schmidt and Berri (2004); Winfree and Fort
(2008).
(3.) Rottenberg never really addressed CSU in his original work,
but we estimate its importance because it is either assumed in some
earlier work (Hadley, Cieka, and Krautmann 2005; Humphreys 2002) or
there is professional interest in fan response to dynasties (Krautmann
and Hadley 2006, and references therein).
(4.) More recent investigations are also mixed on the UOH matters
(Lee and Fort 2008; Meehan, Nelson, and Richardson 2007; Rascher and
Solmes 2007; Soebbing 2008).
(5.) There is some disagreement of available data sources for NHL
attendance in certain years. For that league only, we average three
sources of game attendance for years in which multiple estimates are
available--Rod's Sports Business Data (2012), Hockey Zone Plus
(2010), and Andrew's Dallas Stars Page (2010).
(6.) We thank an anonymous referee and the editor for instructing
us to undertake the investigation of different measures of outcome
uncertainty. Our original choice was to use the same measures as in Lee
and Fort (2008) in order to maintain comparability to that earlier work.
However, as the referee put it, without an investigation of different
measures, any statement about the UOH and attendance may have more to
say about the measures chosen than about Rottenberg's idea.
(7.) Decade averages are used for exposition in Table 1. For the
NBA, the 1950s LAPG average uses only data from 1955-1956 through the
1959-1960 seasons, because of availability. However, all uncertainty
measures use all seasons in each decade included in the table.
(8.) The NHL uses a point system rather than simple winning
percentages. We convert the NHL to winning percentage, recognizing that
for our purposes the damage is light. On this issue, see Fort (2007) and
Owen (2012).
(9.) We thank the anonymous referee who first pointed out this
important distinction.
(10.) For our aim--specifying separately GU, PU, and CSU--we passed
on Humphreys' (2002) competitive balance ratio and Lenten's
(2009) top team concentration index because each is a hybrid of types of
balance and has the chance to confuse GU and PU. We also could not
determine how to calculate Owen's (2010) higher moments (range and
variance) of the ratio of standard deviations measure for the unbalanced
schedules and larger leagues/divisions of up to 15 teams in our data.
(11.) For example, while LAPG for early NHL games was nearing
15,000, league expansion reportedly decreased LAPG by 3,500. While the
Oakland Seals saw LAPG in this range (Kurtzberg 2009), it seems unlikely
that Los Angeles, Minnesota, Philadelphia, Pittsburgh, and St. Louis
did. After this short initial period of low reported attendance, reports
rebounded (just before the formation of the WHA in 1972). We return to
this issue later.
(12.) The 2008 San Francisco 49ers and 2009 Tampa Bay Buccaneers
reported attendance for only seven games, as they played one of their
home games in London, United Kingdom, leaving this number out of their
reports.
(13.) For brevity, we do not report the results of the DFGLS or
Zivot-Andrews test here; however, the results of these are available
upon request.
(14.) Bai and Perron (2006) discuss the size and power properties
of the structural break tests under certain conditions.
(15.) The caution we followed is that one cannot choose just on
goodness of fit unless the same break points are identified by
covariates under comparison because of how our chosen breakpoint method
works--breakpoint determination goes along with the choice of variables
so adjusted [R.sup.2] might go up just because another break point is
identified, not because the covariates got any stronger.
(16.) We note that the year-to-year change in GU is rather large,
highlighting the particularly economically trivial impact of
micromanaging GU in the NBA.
(17.) The question does not extend to the NBA (founded 1946-1947)
since it was founded during World War II and we do not know whether the
NHL (founded 1917-1918) would be included in the question because our
data do not go that far back.
(18.) The subsequent upward trend in hockey attendance coincides
with further expansion to Buffalo and Vancouver for the 1970-1971
season. The two outdrew some of the most prominent teams in the league
like the Detroit Red Wings and Boston Bruins after only 2 years in the
league.
(19.) There are two complicating factors for the NBA. The first is
related to the move of some teams to new arenas. Second, Magic Johnson
and his L.A. Lakers teammate Kareem Abdul Jabber would retire shortly
after the 1987-1988 break point and the Celtics' Larry Bird just
after them, ending a long-running charismatic NBA episode. While
entering the league for the 1984-1985 season, the Bulls' Jordan
matured as the previous era ended. As rosters are so much smaller than
in any other sport, charismatic (as well as proficient) stars may have
larger individual impacts than in any other sport.
(20.) One explanation for the lack of a similar break point in the
NL is that NL expansion occurred with Florida (the Marlins) and Colorado
(the Rockies) beginning play in 1993. The Rockies topped the attendance
chart in both leagues while the Marlins were a respectable 5th in the
NL.
(21.) Due to the constraints on estimating breaks near endpoints,
the BP method is unable to detect anything about the NHL lockout in
2004-2005. Visual inspection does not raise any concern about changes
due to the lockout, and it could be that rule changes adopted after the
lockout, added enough excitement to the game as to counteract any
backlash that may have occurred. We suspect, instead, that it is worth
returning to the question after a few years more of data are generated.
(22.) There were other things going on in the NFL as well (the
Oilers' move from Houston to Tennessee, rule changes, the entry of
FOX into the broadcast market, and improved on-screen TV viewing
innovations). However, the league had an earlier occurrence of a 42-day
training camp strike in 1974 that may have soured the fans for that
season, with some evidence for fan substitution between football and
baseball.
TABLE I
LAPG, Outcome Uncertainty Measures, and Decade Averages
NBA LAPG GU PU CSU
1950s 4,778 0.241 0.060 0.410
1960s 5,714 0.022 0.052 0.558
1970s 9,644 0.201 0.047 0.285
1980s 12,110 0.052 0.052 0.654
1990s 15,836 0.044 0.047 0.605
2000s 17,204 0.105 0.046 0.488
Avg. 11,436 0.112 0.050 0.501
NFL LAPG GU PU CSU
1930s 18,205 0.189 0.046 0.647
1940s 26,521 0.167 0.043 0.483
1950s 31,211 0.495 0.048 0.382
1960s 44,349 0.470 0.046 0.428
1970s 54,326 0.862 0.051 0.518
1980s 54,048 1.363 0.059 0.357
1990s 57,732 1.041 0.061 0.354
2000s 64,478 0.998 0.059 0.345
Avg. 47,432 0.725 0.052 0.428
NHL LAPG GU PU CSU
1960s 12,658 0.174 0.051 0.527
1970s 12,837 0.081 0.050 0.762
1980s 13,842 0.521 0.058 0.631
1990s 15,539 0.647 0.057 0.483
2000s 16,879 0.660 0.051 0.457
Avg. 14,351 0.417 0.053 0.572
AL LAPG GU PU CSU
1900s 4,809 0.038 0.020 0.499
1910s 4,997 0.045 0.015 0.458
1920s 7,796 0.064 0.015 0.628
1930s 6,445 0.018 0.011 0.747
1940s 11,235 0.103 0.017 0.616
1950s 13,360 0.055 0.015 0.742
1960s 12,606 0.166 0.014 0.638
1970s 14,824 0.267 0.021 0.558
1980s 22,100 0.364 0.024 0.433
1990s 27,906 0.395 0.026 0.337
2000s 29,160 0.167 0.029 0.560
Avg. 14,198 0.154 0.019 0.568
NL LAPG GU PU CSU
1900s 4,366 0.006 0.012 0.690
1910s 4,203 0.101 0.012 0.396
1920s 7,248 0.090 0.020 0.690
1930s 6,686 0.072 0.020 0.685
1940s 10,478 0.047 0.015 0.631
1950s 13,348 0.146 0.017 0.693
1960s 15,578 0.148 0.019 0.494
1970s 18,215 0.294 0.022 0.603
1980s 23,191 0.393 0.024 0.298
1990s 28,016 0.339 0.026 0.178
2000s 31,304 0.543 0.031 0.429
Avg. 14,881 0.200 0.020 0.520
LAPG: League annual average attendance per game.
GU: We compared three measures but "tail likelihood" ([TL.sub.t])
became the main focus (it is the only GU variable covered in this
table). [TL.sub.t] is the excess of observed tail frequencies of
high or low winning percentages over "idealized" frequencies that
would occur if all teams were of equal playing strength (supposing
the probability that any team will defeat any other equals 0.5). If
[TL.sub.t] increases, the tails of the distribution are moving closer
to the league average winning percentage, that is, outcome uncertainty
increases. We also examined the ratio of standard deviations. Let
[ASD.sub.t] be the actual standard deviation of winning percentages
for a league in a given year. Let [ISD.sub.t] be the standard
deviation of an "idealized" league where the probability that any team
beats any other team is 0.5, namely for the binomial, 0.5/[square root
m], where m is season length. The ratio of standard deviations is
[RSD.sub.t] = [ASD.sub.t]/[ISD.sub.t]. As [RSD.sub.t] increases,
outcome uncertainty declines. We also examined [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE IN ASCII], where [N.sub.t] is the number of teams in
the league in year t, [w.sub.i] is wins by team i, and r is the total
number of games in the season in year t. Outcome uncertainty declines
with higher values of [HICB.sub.t].
PU: We use a variant of the measure cited in the text since we can
only evaluate at season's end for our annual league-level aggregate of
attendance. The measure is given by, [PLU.sub.t] = 1/N
[[summation].sup.N.sub.i = 1] f ([GB.sub.i,t] max(G)/[G.sub.t]. N is
the number of teams other than division winners in a league, f is n
~(0,6), and max(G) is the maximum number of games played over the
sample period for the league. For [GB.sub.i], let [GB.sub.id] be the
number of games back for a team that is i wins behind the division
winner and let [GB.sub.iw] be the number of games back for a team that
is i wins behind the wild-card winner. [GB.sub.i] = min([GB.sub.id],
[GB.sub.iw]). As [PLU.sub.t] increases, outcome uncertainty declines.
CSU: [CORR.sub.t] is the correlation across teams between
[WPs.ub.i,t], winning percentage for team i, year t, and 1/3
[[summation].sup.t-1.sub.s=t-3] [WP.sub.i,s]. Outcome uncertainty
declines as [CORRs.ub.t] increases.
TABLE 2
Results of Unit-Root Tests
League NBA NFL NHL
T (seasons) 55 76 50
ADF (p) Constant -0.883 (1) -2.017 (1) -1.210 (1)
ADF (p) Trend -1.287 (1) -2.233 (1) -2.682 (1)
pp (l) Constant -0.965 (3) -1.774 (3) -1.399 (3)
pp (l) Trend -1.406 (3) -1.905 (3) -2.987 (3)
2-Break LM
[??] 7 3 6
[[??].sub.b1] 1972/1973 1972 1973/1974
[[??].sub.b2] 1996/1997 2000 1985/1986
Test Stat. -5.714 ** -6.076 ** -6.323 **
1-Break LM
[??] 7 8 3
[[??].sub.b] 1992/1993 1980 1976/1977
Test Stat. -5.182 *** -3.431 -4.580 **
p. the number of lags: l, lag truncation: [??] is the optimal number
of lagged first-difference terms included in the unit-root test to
correct for serial correlation. [[??].sub.b] denotes the estimated
break points. See Table 2 of Lee and Strazicich (2003) for critical
values. ***, **, * = significant at 99%, 95%, and 90% critical
levels, respectively. See Lee and Fort (2008) for unit roots of MLB
American and National Leagues.
TABLE 3
Bai and Perron Model 1 Break Test Results
League [T.sub.1] [T.sub.2]
NBA 1987-1988 1997-1998
[1986-1987, 1988-1989] [1996-1997, 2000-2001]
NFL 1973 1997
11972, 1974] [1996, 2000]
NHL 1966-1967 1975-1976
[1965-1966, 1967-1968] [1974-1975, 1976-1977]
AL 1918 1945
[1917, 1919] [1944, 1946]
NL 1918 1945
[1917, 1919] [1944, 1946]
League [T.sub.3] [T.sub.4] [T.sub.5]
NBA
NFL
NHL 1994-1995
[1993-1994, 1995-1996]
AL 1963 1978 1994
[1962, 1964] [1977, 1981] 11993, 1996]
NL 1976
[1975, 1979]
Notes: 90% confidence intervals are in []. Lee and Fort (2008) break
points were as follows: AL: 1918, 1945, 1962, 1987; NL: 1918, 1945,
1967.
TABLE 4
Breakpoint Regression Results
League [[alpha].sub.1] [[beta].sub.1] [[alpha].sub.2]
NBA 281 3.927 312
t-value (29.18) *** (5.42) *** (6.76) ***
NFL 1.107 6,662 286
t-value (39.60) *** (2.24) ** (4.83) ***
NHL 587 9,787 103
t-value (7.85) *** (9.68) *** (1.70) *
AL -69 5.641 -5
t-value (-1.04) (5.77) *** (-0.19)
NL -104 5,085 22
t-value (-1.20) (4.60) *** (0.64)
League [[beta].sub.2] [[alpha].sub.3] [[beta].sub.3]
NBA 4,977 71 14,277
t-value (2.55) ** (1.72) * (6.73) ***
NFL 32,474 448 25,602
t-value (8.94) *** (2.79) *** (2.16) **
NHL 11,344 224 7,226
t-value (10.67) *** (10.71) *** (5.89) ***
AL 7.546 -194 24,671
t-value (7.41) *** (-3.74) *** (8.67) ***
NL 5.583 127 6.756
t-value (4.45) *** (4.40) *** (3.77) ***
League [[alpha].sub.4] [[beta].sub.4] [[alpha].sub.5]
NBA
t-value
NFL
t-value
NHL 107 11,442
t-value (4.28) *** (7.28) ***
AL 324 -9,453 705
t-value (4.89) *** (-2.02) ** (11.01) ***
NL 397 -11,080
t-value (14.62) *** (-4.61) ***
League [[beta].sub.5] [[alpha].sub.6] [[beta].sub.6]
NBA
t-value
NFL
t-value
NHL
t-value
AL -37,388 222 5,685
t-value (-6.71) *** (3.33) *** (0.84)
NL
t-value
League [gamma]TL (GU) [gamma]PLU (PU) [gamma]Corr3 (CSU)
NBA 1,619 -9.696 -708
t-value (2.75) *** (-0.72) (-1.95) *
NFL 101 157,186 -260
t-value (0.11) (2.46) ** (-0.25)
NHL 244 -302 921
t-value (0.95) (-0.02) (2.83) ***
AL -516 31,852 -836
t-value (-0.59) (1.64) (-1.45)
NL -338 44,961 -200
t-value (-0.40) (1.93) * (-0.39)
League [[bar.R].sup.2] ([R.sup.2])
NBA 0.990
t-value (0.992)
NFL 0.986
t-value (0.988)
NHL 0.954
t-value (0.964)
AL 0.984
t-value (0.986)
NL 0.977
t-value (0.979)
*** Significant at the 99% critical level.
** Significant at the 95%c critical level.
* Significant at the 90% critical level.
[[alpha].sub.M] and [[beta].sub.M] refer to the slope and intercept
coefficients for regime M. respectively.
TABLE 5
UOH Summary
League GU PU CSU
NBA Fail to reject (a) Reject (b) Reject
NFL Reject Fail to reject Reject
NHL Reject Reject Reject (-) (c)
MLB (d) Reject Reject Reject
(a) "Fail to reject": Estimated coefficient yields statistically
significantly positive relationship between the given measure
of outcome uncertainty and attendance.
(b) "Reject": Estimated coefficient yields statistically
insignificant relationship between the given measure of out
come uncertainty and attendance.
(c) "Reject (-)": Estimated coefficient yields statistically
significantly negative relationship between the given mea
sure of outcome uncertainty and attendance.
(d) Lee and Fort (2008) found the following: GU = Reject,
PU = Fail to reject, CSU = Reject.
TABLE 6
Economic Significance of Outcome Uncertainty
(Statistically Significant Coefficients Only)
NBA NFL NHL
Value calculation GU PU CSU
2009 LAPG 17,132 67,426 17,476
2009 Variable 0.030 0.058 0.378
Coef. est. (a) 1,619 157.186 921
Elasticity 0.0028 0.1352 0.0199
[DELTA] Variable (b) 0.064 0.004 0.184
Inc. Factor 213.3% 6.9% 48.7%
[DELTA] LAPG 102.3 629.0 169.4
% [DELTA] LAPG 0.60% 0.93% 0.97%
Rev. Per Attend (c) $71.93 $103.16 $75.14
[DELTA] Game Rev. $7,358 $64,887 $12,729
(a) Coefficient taken from Model 1 and follows the
approach of Lee and Fort (2008, 291).
(b) All measures interpreted by definition, not coefficient
sign in the model.
(c) Revenue per attendee data come from Team Marketing
Report, Fan Cost Index data, 2009.
