UNBALANCED SCHEDULES AND THE ESTIMATION OF COMPETITIVE BALANCE IN THE SCOTTISH PREMIER LEAGUE
| DOI | http://doi.org/10.1111/j.1467-9485.2008.00463.x |
| Published date | 01 September 2008 |
| Date | 01 September 2008 |
| Author | Liam J. A. Lenten |
UNBALANCED SCHEDULES AND THE
ESTIMATION OF COMPETITIVE
BALANCE IN THE SCOTTISH PREMIER
LEAGUE
Liam J. A. Lenten
n
Abstract
Since the season ending in 2001, the Scottish Premier League (SPL) has, unlike
other European football leagues, utilised an unbalanced schedule, by which the
strongest teams in a given season play each other an extra time, mutatis mutandis
for the weakest teams. While this approach may make sense for several reasons, it
also has implications for within-season measures of competitive balance, because it
creates biases in the set of win ratios from the end-of-season league table. This
paper applies a simple log-probability rule to calculate a set of adjusted win ratios
correcting for this inherent bias. Such an adjustment is necessary if one wishes to
compare within-season competitive balance of the SPL with other European
leagues. It is shown that by correcting for the unbalanced schedule, the SPL is
consistently less competitive over the sample period. The implications of this
finding are discussed at length.
I Intro duction an d Motivation
For some time up until the conclusion of the season ending in 2000, the Scottish
Premier League (SPL) had been operating as a 10-team league, in which each
team played each other four times (twice home, twice away) over the course of
the season, resulting in a season length of 36 games. The league then expanded
to 12 teams for the commencement of the 2001 season. The problem this created
was that in order to maintain the status quo of scheduling, the season length
would have required to be extended to 44 games; however, this was considered
too long. Analogously, a schedule whereby each team was to play each other
only three times would produce merely a 33-game season.
Because most major European football leagues operate with 20 teams and a
38-game schedule (each team plays each other twice), there was a clear incentive
to construct a schedule with a season length as close to this figure as possible.
The solution to this problem was for each team to play each other on three
occasions, and then the league would be ‘split’ into two halves of six teams on
n
La Trobe University
Scottish Journal of Political Economy, Vol. 55, No. 4, September 2008
r2008 The Author
Journal compilation r2008 Scottish Economic Society. Published by Blackwell Publishing Ltd,
9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA, 02148, USA
488
the basis of the team standings from the league table after 33 games. Here, the
top six teams would form the ‘Championship’ League, and the bottom six teams
would form the ‘Relegation’ League. Finally, each team would play each other
team in their split league on an extra occasion, with a pragmatic method to
determine an equalised distribution of home and away matches, resulting in an
extra five matches, and consequently, a 38-game season length (see SPL, 2007,
pp. 53–54).
1
The SPL has persisted with this system ever since. Another
idiosyncrasy of this system is that there can be no crossover in rank-order
between Championship and Relegation teams in the final five rounds of the
season, irrespective of points earned. This rule has proven binding in all seasons
except 2001 and 2004. In the 2003 season, for instance, Dunfermline (46 points)
and Dundee (44) finished fifth and sixth, respectively, ahead of seventh-placed
Hibernian (51) and eighth-placed Aberdeen (49).
This system, until very recently unique in Europe to Scottish football, has an
arguably desirable effect of ensuring that each team plays a set of other teams
that are of a similar quality to them, more often than the remaining teams who
are either significantly more or less superior. Common sense would suggest that,
ceteris paribus, demand for games in these final five rounds at a league-aggregate
level, as calculated by common measures such as attendance or television
ratings, should be higher than if these five extra games for each team were
scheduled according to some random draw. In addition, it is also a way of
virtually guaranteeing (in a practical sense) that Celtic and Rangers will play
each other on a fourth occasion. In fact, it would not be unreasonable to suggest
that this is a major reason why the unbalanced schedule was designed in this
specific ‘power-matching’ fashion, given the huge revenues generated by ‘Old
Firm’ derbies.
2
Despite the apparent virtues of such an unbalanced schedule, it does create
the obvious problem that it becomes inappropriate to use the actual end-of-
season league table to measure within-season competitive balance. This matter is
of critical importance to sports economists because of the well-established link
from the ‘uncertainty of outcome’ hypothesis, the origins of which can be traced
as far back as Rottenberg (1956), through to the demand for sport. The reason
for this problem is that the distribution of wins after 38 games is
unrepresentatively even, that is to say, win ratios are biased upwards
(downwards) for teams in the Relegation (Championship) League. Hence, if
(average) relative performance for each team from the 38 games played were to
remain constant for another (hypothetical) six rounds of matches, in which each
team in the Championship League were to play every team in the Relegation
League a fourth time, then the distribution of wins would be more
(representatively) uneven. Therefore, accounting for the unbalanced schedule
1
Typically, these final five matches are played in proper sequencing of rounds, although there
are exceptions. For instance, in 2003, Celtic played a ‘catch-up’ fixture against Motherwell after
round 35, despite being in opposite halves of the table, and in 2004, Hibernian and Livingston
played two games in rounds 36 and 37, respectively, with the other playing none.
2
A further reason is that other common unbalanced schedule formats used elsewhere would
be considered unpalatable to the European sports market.
ESTIMATION OF COMPETITIVE BALANCE IN THE SPL 489
r2008 The Author
Journal compilation r2008 Scottish Economic Society
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