Team Cost, Profit and Winning
Here we start with definitions and
then look at idea of how a sports
owner might run the team.
1
Profit
Profit is defined as total revenue (TR) minus total cost TC. You
might see this written in shorthand as
Π = TR – TC.
In economics the is a profit maximum hypothesis that suggests
owners make decisions with the goal to have maximum profit.
What this means is if there are 2 (or more) scenarios the owner
will pick the scenario with the highest profit.
Let’s note the public will typically only see the scenario the owner
has actually taken, but not all the alternatives. Then, sometimes
what we see seems like owner didn’t maximize profit.
2
Winning Percentage
Winning percentage for a team is defined as games won divided
by the total games played.
The author will use the phrase TEAM QUALITY as a synonym
for winning percentage W. Also, sometimes W will by the
definition above multiplied by 1000.
Example: in a past year the Chicago Bulls won 72 of 82 games
for a W = 72/82 = .88 or 880.
The author tells us that sports teams produce winning or quality.
Bakeries make donuts, sports teams make wins! Let’s remember
things like athletic prowess, commonality, absolute performance
and relative performance all correlate with winning (go hand in
3
hand with).
Short Run/Long Run
In economics we typically think about resources as being either
fixed or variable.
A variable input is a resource that at any time can be changed in
amount.
A fixed input is a resource that for a least some amount of time
can not be changed in amount.
The short run is a time frame where some inputs might be
variable, but at least one input is fixed in amount.
The long run is that time frame where all inputs can be varied.
When cost of production is analyzed, the time frame is noted. In
the short run total cost (SRTC) equals the short run fixed cost
(TFC) plus the short run variable cost (TVC). In the long run we
just refer to total cost.
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Short Run/Long Run
The primary FIXED inputs are talent, on and off the field, and the
facility in which the team plays.
In the short run the owner makes decisions about the number of
tickets to sell and the price to charge and maybe the number of
games to put on local TV. All of these decisions assume the
quality of the team is fixed.
In the sports context the short run is a period of time when team
quality is held constant.
In the long run the stadium can change, coaches and management
can be replaced and the lineup may be completely altered – these
all have an impact on quality.
5
SR Production and Cost
We look at inputs to winning, see how much winning occurs and
look at the price of inputs to determine the cost of winning.
The following fixed inputs contribute to TFC:
Player roster
The stadium
Other contractual personnel like the GM, managers and coaches
Insurance
Loans
Obligations to league.
The variable inputs contribute to TVC:
Entertainment between innings/during time outs
Scouting and player development
Advertising and marketing
Labor to sell tickets, parking, concessions, ushers and clean-up.
In sports the TFC can be over 50% of the STRC
6
Example – making cookies
Fixed input Variable input cookie units TFC
TVC SRTC
Capital
labor
output
1
0
0
100
0
100
1
1
10
100
10
110
1
2
21
100
20
120
1
3
33
100
30 130
1
4
43
100
40
140
1
5
50
100
50
150
1
6
55
100
60
160
Here we have 1 oven and when labor is added we get more cookies
made per unit of time – this is all occurring in, let’s say, 1 hour. If
5 workers work in 1 hour 50 cookies are made. The oven has a
cost of $100 per hour and each worker gets paid $10.
7
Graph idea
$ costs
SRTC
TVC
TFC
Cookies
The difference between the SRTC and
TVC is the TFC. Higher TFC means
higher SRTC
Note that TVC is
always rising, but at
first the rise is at a
decreasing rate, but
then the rise is at an
increasing rate. The
rate becomes
increasing because of
the diminishing returns
to the variable input
with the fixed input.
8
Sports in SR
If you look at the graph on the previous screen and make the X
axis the attendance at games (which is correlated with winning)
then the curves are similar in the sports world.
When the team is of a certain quality, adding entertainment
during time outs, for example, might increase attendance. But the
entertainment during time outs is a small part of the time at the
game. At some point additional attendance from the time out
entertainment could only be obtained with a large increase in
cost. You would have to have really good entertainment.
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Long Run – production of winning or
quality
The main idea presented is that the more stars there are on a team
the higher will be the quality of the team. So, winning is produced
by stars. Adding a few stars when the team has none has a great
impact on the winning, but at some point adding even more stars
will increase winning, but the rate of increase in winning will slow
down.
In the long run when the team
adds stars the winning percent
Winning
increase slows down because it
percent
is thought that the management
function is limited and can not
effectively deal with a large
amount of stars. So, at some
# of stars
point adding a star does not add
10
as much to the winning percent.
Long Run Cost
Cost $
Relatively
large
Relatively
small
increment to
cost
Total Team
Salary Cost
+ other costs
Equal
increments to
winning.
Winning
%
Here we see winning
can be increased, but
eventually the costs
begin to rise rapidly
due to the same thing
we saw before. The
management
function has a
difficult time
handling all the stars.
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Connecting short run and long run
On the previous slide we have winning % on the horizontal axis.
Once a level of winning percentage is picked (by going after the
appropriate number of star players) we have a short run situation.
Back on slide 8 we have one short run situation.
The connection between the short run and the long run is that the
greater the number of star players purchased in the long run, the
higher the cost in the long run. This means in the short run there
will be higher fixed costs and the SRTC is thus higher.
In other words, with 5 star players, for example, the SRTC is
higher than it would be if there were just 4 star players.
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Profit in the SR
$
An owner may be
dissatisfied with this
range of profit and decide
to dump talent. This
would have the impact of
lowering SRTC (which
really is a long run idea –
to which we turn next)
SRTC
TR
A
Range of attendance where profit is positive. Quality of
team is fixed. In this example revenue max is at an
attendance level above the profitable range. Owner won’t
13
go to revenue max point.
Profit in the LR
In economics we often say that the long run is simply a series of
short run situations. Recall that Profit = TR – TC = TR – SRTC
in the short run. Also recall the short run is the time frame in
which quality is held constant. Since player salary is the major
part of SRTC and is a fixed cost, the more stars on the team the
higher the fixed cost and SRTC. SO, each number of stars on a
team sets a quality of team and results in a different SRTC.
On slide 13 if you took the whole SRTC and moved it you would
really be talking about a different quality team. You can see if the
SRTC shifted up a lot because of a team deciding to get a high
quality team, then maybe the profit is a negative number.
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Profit in the LR
The story on the previous slide is incomplete. The reason is that
when the owner decides to have a higher quality team the TR also
shifts up (and moves a little to the right). The TR shifting up
increases the range of attendance that would give profit.
So, we have a couple of things to think about when the owner of a
team attempts to change team quality. Both TR and TC change.
The way it is thought to play out is what we see on the next slide.
The idea is that when quality is really low and an attempt is made
to increase it TR will grow more than TC will grow and profit will
rise. But, at some point, increasing quality will have TR increase
by less than TC increases and thus profit will begin to fall.
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Profit in LR
$
π*
π1
Q1
Q*
1.000
Quality or winning %
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Profit in LR
Let’s note some things about the previous slide
1) The graph is of profit and not just TR.
2) Each quality level has a graph similar to slide 13 representing
it.
3) The profit is maximized in the graph with quality level Q*
because it has the highest profit level π*.
4) Different teams will have a different profit function but will
have the general shape as the one shown.
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Profit in the LR
Conclusions
1) Profits can constrain winning – the profit max level for some
owners will be at a low Q – either they are high cost owners
and/or the market for the team is low revenue,
2) Profits can influence competitive balance – If only a few teams
have relatively high revenue and low cost operations, then the
few will have high winning %’s and the rest will be low winning
percentage teams. Caution – you are about to enter a no spin
zone! Now, some years high winning % teams will have injuries
and other bad luck which will make them look bad. But over the
long haul they will win more games!
3) A small market is only a problem if it can only generate a
small revenue (Is Green Bay a problem market?).
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