Why Definitions Matter, Part 2: Demand or Quantity Demanded?

Here is my second installment on economic/business descriptive definitions and why they matter.  The first was on "bubbles".  Arguing for that distinction earned me the "pedantic" accusation on twitter from @patrick_hruby but he is just wrong, both in context and in label-slinging.  These types of distinctions are critical to communication; without them, we must always begin a conversation with, "What do you mean by that?"  And that seems inefficient and potentially quite confusing for no real reason.

Demand or Quantity Demanded?

This is an old favorite of economics professors and, judging from treatment in the press, always will be.  Just look at the two carefully:  "Demand" versus "Quantity Demanded".  They do not look the same and for good reason:  They do not mean the same thing!

Let's think about "demand" and "quantity demanded" in terms of what might be a current problem for college sports ADs, the recent decline in student attendance at football games.

If attendance falls off due to bad scheduling or ever-more-enticing TV viewing, that's a decrease in Demand.  The language is reserved for a change in attendance even at the same price, where it follows that attendance has changed at all prices that could be charged.  Responses to this type of decrease are aimed at changing Demand back to its previous levels:  If an AD brings in more air shows, flying rocket man for the pre-game, more blaring video boards, more extravagant half-time programs, or alters a non-market imposition on rights to student tickets, that is an attempt to change the product so that attendance will rebound even at the same price.  Again, if fans respond, that would be an increase in Demand.

[My friend and colleague Stef Szymanski recently turns this distinction to extremely good use by pointing out that rising EPL ticket prices will not drive fans away...when they are rising because fan demand is increasing in the first place!]

On the other hand, an increase in Quantity Demanded would follow a ticket price reduction to bring fans back, more people will come through the gate (it may take a dramatic drop as this type of consumption goes, but return they will).  The language is reserved for only the response of ticket holders to a change in the price of their ticket.  As price falls, more tickets are purchased.

The distinction is important because confusing the two descriptive definitions leads to less clear assessment of AD choices.  For example, different ideas about what to do in the case of a decrease in demand are made to appear in conflict when they are not.  One group might argue, "Lower ticket prices"; another might argue "Make the fan experience better".  Both will get more people through the gate, but with different consequences.

The Quantity Demanded for college football attendance appears quite unresponsive to price.  In such a situation, reducing price will lead to an increase in Quantity Demanded of tickets, but will also decrease revenue.  Enhancing the fan experience will require increased spending, but at the same time will increase revenue (if successful), that is, attendance will increase even at the same ticket price, an increase in Demand.

Again, to the press and casual fellow travelers, please do everybody a favor and keep this straight.  The difference between Demand and Quantity Demanded matters for judging AD choices.

Just What Do You Mean by "Bubble"?

I'm watching and reading and there is something a bit disturbing going on out there.  The language governing some economic/business outcomes in sports is being obfuscated.  Every sports price increase is a "bubble"; to fix college sports attendance demand woes, just lower price; dynamic and variable pricing are the same thing.  I can't tell whether this is just out of ignorance of well-known descriptive definitions or just sloppy use of these well-known descriptive definitions.  Maybe it is ion purpose in order to lend an added sense of urgency or judgement of the participants--people fall for bubbles, after all.  But I am concerned because the sports business can be confusing enough without this obfuscation.

Here is the first of three examples using my understanding of descriptive definitions (that match various authorities on the web).  The other two, and concluding remarks, are in subsequent entries.

Bubbles or Rising Asset Value?

A "bubble" originally described trading in an asset at higher volumes and/or price than was consistent with the ability of the asset to generate profits over time.  Eventually, a true bubble "bursts", that is, the asset's trading and price must eventually return to plausible and consistent levels based on the future return that the asset actually can generate.  In that sense, in a bubble, something is "wrong" with the asset price relative to its actual revealed value in the future.

Over time, at the level of a market or an entire economy, a bubble has also come to mean an economic cycle characterized by rapid expansion followed by a contraction.  Note especially the contraction part.

So, for a bubble, somewhere must be exaggerated expectations about the future growth of the asset value and those expectations must eventually be proven incorrect by a correction.  Now, expectations could just have been uninformed but they might also have been manipulated.

Thus, bubble logic makes us suspicious as we watch the price of the asset rise.  Pundits and market watchers may sound alarms that a bubble might be in progress.  But the seemingly unsupportable increase in price may actually be the revelation of a prolonged increase in fundamental value.  That is, the revelation that the value of some asset actually is increasing at a surprising rate.

So, a surprising increase in asset value might be a bubble, but not all increases in asset values are bubbles.  A bubble is not just a rise in the price of something.

The first bubble logic I saw misapplied was when MLB player salaries began rising at a surprising rate in the early 1990s.  "When will this crazy bubble burst?"  My response was that there was no bubble, it was just expanding cable network coverage and increasing venue revenues driving the rise in salaries.  In other words, it was easy to see salaries tied to an increase in the fundamental that creates that value in the first place--fan spending in the stadium and upward pressure on rights fees due to expanded cable coverage.

Lately, it's bubbles in franchise values and TV rights fees (again) despite the many historical instances where sports asset values have increased based on an entirely believable increase in an underlying fundamental.  [As far as I know, MLB player salaries have yet to decline.]  So, just saying some sports price rising over time is a bubble doesn't make it so.  And instilling in readers that any sports values that are rising over time all are bubbles, as if everybody paying higher prices is crazy, may make for good press but it is poor factual reporting.

So, to the press, please do everybody a favor and just note that prices of some sports properties are increasing for an interestingly long period of time (if that is even true) and then either 1) claim that bubbles sometimes, but not always, look like this so be alert, or 2) go ask somebody in the know to define a bubble and comment on whether or not the price in question is a bubble or not, and why.  And if you think the people involved with any asset are behaving in a crazy fashion, just say so; it doesn't take bubble logic to make that case.

Don't just state that an increasing price is a bubble and then have it go into the press-repetition process that imprints a potentially harmful false truth in the minds of readers.  Bubbles do suggest that participants have gotten carried away with themselves and some are bound to lose possibly large amounts.  But sometimes the value of sports assets just rise over time.

Kids Sports Should Be Kept In Their Place, Indeed

I was inspired to think about this again after reading Bruce Feiler's "There's no off in this season, Team Sports Are Taking Over Kids’ Lives" in the NYT. The article is nicely done and the point is important. The line quoting Pastor James Emery White, "Sports is a wonderful thing to do for kids, but it should be kept in its place", returned me to my time as a high school athlete, and the treatment of my own kids when they went through the same thing.  I also offered some thoughts in the press a while back and I thought I'd do a bit more on it.

I see and hear the following on occasion:  "At least we got a tuition break out of it." Other versions voice the actual pursuit of a "scholarship" as part or all of the point of kids’ sports. Some even voice pro pipe dreams (yes, pipe dreams, I watched a couple of athletes I played against go all the way through to the pro level and, trust me, your kid isn't good enough.)

These claims got me thinking.  How much money and time went into that pursuit?  We had our own youth athletes in football and swimming and the money costs are clear—memberships, fees, tournament fees, equipment, travel, “fundraisers” (that actually came mostly out of our pocket) and never forget the value of time. I can’t even look back and estimate the time spent by our kids and us.

And it gets even more expensive for the parents of more athletically talented kids. All of the preceding occur nearly year round, plus now there may need to be individual coaching, getting on the right "travel" (elite) teams, or into the right academy. Don't forget having to get into the elite private school where rules are more favorable to sports participation—good coaches are there especially in basketball and football.

It's pretty easy to see that the "get the scholarship" claim really can't make monetary sense for nearly anybody. [I'll return to a more complete consideration of other benefits later.]

We could start an analysis at any point in time, but I find it easiest to present for a youth athlete at the college entry point.  The net present value (NPV) of an upcoming four-year offer can be characterized generally as:

NPV = (aG – e)/(1 + i) + (aG – e)/[(1 + i)^2]

                    + (aG – e)/[(1 + i)^3] + (aG – e)/[(1 + i)^4]

Here, G would be a full ride, the Holy Grail.  But a grant-in-aid (the NCAA definition of an athletic "scholarship") can be partial (as all you baseball, women’s basketball, softball, and soccer parents should by know if you don’t already).  Let a be the offered portion of an annual full ride.  Since right now G is less than full cost of attendance, there will be out-of-pocket expenses, e.

So the numerator is just the annual net value of the offer.  The denominator brings the next four years back to present value using the interest rate i. I’m fully aware that all of the elements in the numerator under the summation can vary each year, but no harm is really done to the point I am trying to make by assuming they are constant over the four years. [Yes, I know that occasionally eligibility is longer (grad school) or shorter (by injury) but, again, I’ll sacrifice that characterization to make the point.]  So, with constant numerator:

NPV = (aG – e){1/(1 + i) + 1/[(1 + i)^2] + 1/[(1 + i)^3] + 1/[(1 + i)^4]}

If i = 5%, then the sum in braces is 3.55.

Let’s have G = $25,000 annually, say, good old State U, and e = $3,500 (the midpoint given what I read in the press coverage on the issue).  Using these choices, NPV becomes pretty tractable (and you can choose other values and do your own analysis if you like):

NPV = ($25,000a – $3,500)(3.55) = $88,750a – $12,425

We also need to include the fact that there is only a probability of getting an offer, let's call it p. Multiplying NPV by p gives Net Expected Value (NEV):

NEV = pNPV = p($88,750a – $12,425)

Let's run a few different scenarios on a and p. Let a and p both run to 1.00 in equal 0.25 increments. It's an easy Excel task to use the formulae to generate the following table of NPV and then NEV:

a	NPV	NEV p=.25	NEV p=.5	NEV p=.75	NEV p=1.0
0.25	$9,763	$2,441	$4,881	$7,322	$9,763
0.50	$31,950	$7,988	$15,975	$23,963	$31,950
0.75	$54,138	$13,534	$27,069	$40,603	$54,138
1.00	$76,325	$19,081	$38,163	$57,244	$76,325

Now, let's suppose you started “investing” in your kid’s sports prospects starting at age 9 (for us, that was the start of youth baseball and then on to football and swimming later). That's 10 years to get the kid into position for the big offer. The table shows that if the offer is a low partial a = 0.25, with low chances of p = 0.25, then no more than $2,441/10 = $244 per year (in today's dollars) should ever have been spent in the pursuit of the offer. Anybody with a youth athlete knows they spend far more than that on memberships, fees, tournament fees, equipment, “fundraisers”, travel, and the value of time.  We used to easily drop that much on a weekend swim meet.

Of course, at the other end of the spectrum, the prospects for a sure thing full ride student were worth spending of up to $76,325/10 = $7,633 per year. And it's a good thing NEV goes up since, in order to generate that higher p, spending will surely have gone up anyway! Of course the payoff at higher tuition colleges (G >$25,000) increases the rational spending for any a and p.

But on the other hand, and these would be the parents I’m talking to most, an even lower probability is strikingly revealing, regardless of the size of a or G. This second table was taken from NCAA.org on their research showing historical average chances of advancing to different levels of play (Pros are included just to drive the point home):

Level	WBB	MBB	Baseball	MHockey	FB	MSoccer
HS-NCAA	3.3%	3%	6.1%	11%	5.7%	5.5%
NCAA-Pro	0.02%	0.03%	0.45%	0.32%	0.08%	0.07%

This is just the NCAA calculating the total slots available at the next level relative to the number of participants at the lower level.  But it shows that the idea that p = .25, the lowest value in the previous analysis, is probably way too high for nearly everybody!  For nearly everybody who doesn’t have an elite athlete identified at an early age, the chances are more like the ones in the table.

At p = 0.05 (a 5% chance), like for football or men’s soccer, we can use the calculations in the NPV/NEV Table to adjust the value of spending on a developing youth athlete since everything is linear in p (5% is 1/5 of 25%).  For a = 0.25, we can just multiply the $244 per year by 0.2 and see that student now should only draw spending of $49 per year.  Even investment in a full G (a = 1.0) falls to $1,527 per year, which seems a hefty enough amount, but a few sessions of individualized coaching would eat that up pretty quick.

Realistically, if your kid is low p, the financial component cannot be about “getting that ‘scholarship’”.  Indeed, hitting the “jackpot” lessens the blow but does not cancel it.  So for the typical "pretty good" youth athlete, that is, one with low p, these meager NEV results raise the question, "What really goes on with parents and youth sports?"

We can't forget some kids are innately better than others (you can’t teach speed or size) so that some have lower investment for large outcomes than others. Also, long shots pay off occasionally but remember the real problem is whether your kid really is even a long shot. And the calculations are pretty hard and fast on what these dreams cost. If it is far-fetched in monetary return, either the investment is irrational or there is a broader explanation.

Surely it's the latter and early on I promised to return to all those other “values”.  The alternative explanations I've seen include the not so seemly—peer pressure, permissive (generous? indulgent?) parenting, or overbearing parenting. But there are also other more seemly—sports kids also keep busy and maybe out of trouble. Sports build other values. [My experiences were more along the lines of a quote I’ve seen tracked back to Grantland Rice, “Sports doesn’t build character, it reveals it.”]  And you probably heard seen some I have not seen.

But nearly all parents should stop using (hiding behind?) the money value of a "scholarship" as an explanation for their spending on their kids’ sports. What else could have been done with these resources for the vast majority of kids? If we’re talking about a relatively richer parent, maybe it's no biggie but then time spent still weighs in. If the parent is less well off, this could be a biggie for parents, depending on next best possibility. [See Roger Noll's 1998 piece, "Economic perspectives on the athlete's body," on the rationality of investment in sports by those without much in terms of other prospects. I also cover this in my Sports Economics 3d, p. 226.]

As if this weren't enough, sports economics offers another important insight on this spending. All of the other parents are out there spending the same or more than you! And your chance for success depends on what they are spending on their kid as well as what you spend on yours. [This is the logic of something called the "contest success function", a mainstay in sports economics.]

So, fun is fun and there are many types of values created (some enviable, some not so much). But spending is spending and those dollars invested at a young age are the dollars that eventually pay off the most. Here's to investing those earliest dollars wisely.