The lottery however didn’t sustain new highs. In
fact it lost ground, as lottery revenue appears to have stalled and by some
measures is somewhat lower than they were pre-pandemic. On both multi-state games of Mega Millions
and Powerball. To the degree lottery
sales do not continue to grow [real, let alone nominal] with the rest of the economy,
state education budgets relying on such income would become stressed.
In this article
we explore the concept of lottery engineering, via more complicated winning
probabilities, and other marketing. And
how the lottery, since the pandemic, has become an even worse value for those
who play. Last, how lottery odds compare
to other speculations, such as casinos and sports, and new digital investments
described above.
topic 1: growth and odds
We suspected in the previous
article that the engineered worse winning odds was leading to greater
excitement at chaotically larger jackpots. Resulting in a higher general flow
of lottery revenue. We now have 7 data
points to look at, concerning the most recent game changes.
In the summary
below, we show the change in winning probability, as well as the change in Mega
Millions and Powerball lottery revenue per draw [and total lottery revenue in
brackets]. In both cases, for the two years after the change versus the two years prior to the
change:
January 2009 Powerball
[+4 white balls, -3 red balls]
probability 1:195m
(33% harder)
$40m v $52m [$54b v $56b]
January 2012 Powerball
[unch white balls, -4 red balls]
probability 1:175m
(10% easier)
$56m v $85m [$60b v $70b]
October 2013 Mega
Millions [+19 white balls, -31 red balls]
probability 1:258m
(47% harder)
$38m vs $50m [$68b v $71b]
January 2014 Powerball
[unch white balls, unch red balls]
probability 1:175m
(0% harder)
$85m v $85m [$69b v $71b]
October 2015 Powerball
[+10 white balls, -9 red balls]
probability 1:292m
(66% harder)
$64m v $95m [$71b v $80b]
October 2017 Mega
Millions [-5 white balls, +10 red balls]
probability 1:303m
(17% harder)
$38m vs $85m [$80b v $90b]
It is plain to
see in the 7 examples above that there was never lower revenue subsequent to
each iteration of game changes. The lottery economy just rose. Of
course the general direction of the game complexity was mostly in the direction
of complexity as well, and it's always easy for leaders to conflate the two.
Also, as a
general matter, looking and counting the frequency of certain large jackpot [eg one
billion dollars] sizes isn’t useful for a statistical exercise. After all, we know what the general direction
to be, but there is ergodicity in this system and its ultimate magnitude and
specific timing could be random.
topic 2: enter covid-19
Prior to the
pandemic, the lottery was able to employ marketing tricks in order to stimulate
demand. Sometimes the buzz worked. For example engineering more
complicated winning odds, which has quietly led to ever increasing jackpots. Along with the associated excitement of a "record" jackpot"!
But this system
hasn’t changed in a while. For exmaple, the game
hasn’t changed its probabilistic chances [either Powerball or Mega Millions] in nealry five years. We’ve not had a new
state [ie #46] enter the national system since 2019.
It's worth noting that our previous article was widely cited [front page New York Times, Alabama Review,
Washington Post] and
interview [televisión española] and was used by senators to scuttle Alabama’s most recent vote in 2016 in join lottery.
Then
coronavirus hit. The world forever changed. Behaviors changed. Spending online rose. Gambling online rose. But physical spending on lottery didn’t rise. What could explain it?
People stayed
in, and turned in a different direction. They haven’t returned to lottery. The tradition of going to the local
supermarket to buy a lottery ticket, let alone food, was discouraged in the pandemic depths of 2020. Lottery revenue suddenly fell -3% in 2020
versus 2019: a slightly larger drop than during the global financial crisis.
As an instant
reaction to this unexpected new world, lottery officials had to change their
game. But given their fear over the existential lottery threat, they didn’t opt this time to reverse
their previous engineering of making the game more difficult.
The result was less revenue flow and a more difficult game, combined to make a severe
business challenge for the lottery. Making matters worse, they cannibalized their own market somewhat. They instead adjusted the minimum jackpot for
winning to something lower. And
permanently blamed coronavirus and “low interest rates” for this decision.
Lottery payouts however don’t seem to have
changed, yet [annual data comes with a lag]. An early indication that they will however will be in the coring out of the middle-prizes.
This is an
illustration of median Mega Millions and Powerball jackpot changes over 5-quarter increments:
We used quartile
charts here to illustrate the impact of random jackpot surges within a small
sample size. For example, we saw a $1.7 billion
dollar combined jackpots in January 2021. The next largest combined jackpots
from 2019 onwards were in 2019 and earlier this year. And both of them were near the high-$800 million range [just half of the $1.7 billion from early 2021!]
And peeling back
one level down in jackpot sizes, we see in the 2.5 years
pre-pandemic [which equal the first two periods of the four-period chart above] versus the latter 2.5
years post-pandemic:
Mega Millions went down from 7 -to 6- jackpots of at least $300m
Powerball went down from 7 -to 5- jackpots of at least $300m
Also bear in
mind this trend towards smaller and fewer jackpots mildly overlaps with the tail-effect of the late-2017 Mega Millions engineering we discussed in the previous section. Is it likely we don't see another billion dollar jackpot for some time?
Meanwhile we
have education budgets that are statistically misrepresenting [and likely fooling themselves] that everything is back to normal. The presentation of lottery revenue data shows things are relatively back only by looking at the statistics with the inclusion of the early-2021 jackpot outlier.
If one instead assumes steady state is the vast amount of known median data [as we have done above], then we see that there has been no rebound and the post-pandemic data above [eg past 12 months] is lower than the pre-pandemic data [eg 2019].
By this point the economy has already recovered briskly. Stay-home and mask restrictions long lifted. So too have been interest rates. And yet the lottery still has not
been able to recover their revenue as easily.
And at these ssemingly crucial crossroads, the lottery continues to weaken under the
surface. Perhaps materially. One example
of detrimental changes was the lack of reversal to the Covid-19 era decision to cut minimums based on interest rates.
It’s difficult to see the actuarial math now working back in its favor given
other market headwinds. And as a result, the consumer's ticket value is perpetually weaker.
topic 3: the 1% actuarial change
Do small changes in the
long-term rates actually matter? Let's use a simple example of the 30-year interest rate i, which fell from
2.4% pre-coronavirus, to near 1.4% months later at the 2020 lows.
If one was
“promised” a 30-year annuity-due lottery prize for example [in lieu of an equally-valued lump sum payment] of
$500m, the actuarial model is straightforward [assuming no sudden deaths, credit issues, etc] at i=2.4%:
Where v=1/[1+i]=0.977,
and d=1-v=0.023. Or a X=500m/21.8, and an
annual annuity of $23 million [versus $24 million if receiving a typical deferred annuity].
The issue here is continuing to offer a $23 million annuity when i falls to 1.4%,
implies an impossibly larger jackpot size [and associated proportional revenue increase] of $570m
in order to offset this collapse in government rate.
This of course
wasn’t an issue previously as rates have fallen for many decades, including a 2019 1% drop in i from 3.4%, to the pre-coronavirus 2.4%. The reason this wasn't a business isue before is, as we noted, the lottery
revenue was generally increasing during this falling rate regime and could still sustain the
prizes.
What the
lottery did to now mask this issue for players is to simply [and quickly] lower the
minimum jackpot sizes blaming it on i. But now, interest rates have since increased not only from those 1.4% lows in the 2020 pandemic depths, but back through the 2.4% pre-coronavirus level, and all the way towards 3.4%.
So a 2% interest range change! And meanwhile the lottery has simply unbudged themselves at their
reduced minimums. Evidencing stress in maintaining the pre-coronavirus revenue levels to sustain the high hundreds of millions [or even a billion] dollar jackpot they've gotten the public accustomed to.
We have a lower value ticket now as a part of a stymied system. Offering only a slower -and less exciting- runway to achieving any sort of medicore jackpot, assuming one eventually wins.
topic 4: risks in digital growth
At these
crossroads, the lottery has had to be inventive in forging new growth avenues
and opportunistically capitalizing on trends in innovation. Unfortunately given its size, these other
sources of income are not enough to make-up for the loss of the core business
model.
As noted, only 1 new state has been added to the national system since our last article. And the remaining states are mostly modest in
their economic size. Mobile operators
such as the early pre-acquisition start-ups have sprung up to offer a new channel for
states to play lottery [eg 8 cent charge per 10 tickets].
We also see a new entrant -Jackpocket- [covering
15 large states and recently valued at only $200 million] has made an introduction with
sports tie-ins and perhaps sustainable independent branding. We’ve also seen a flush of money used to facilitate
sports gambling mobile apps getting state licenses.
The gamification of sports gambling, combined
with dynamic sports bets [which adjust games and odds, live during the game] makes it
difficult to both understand the traditional odds [see my previous math on NCAA brackets]
for anyone, including major bookies. As we note below, this makes the lowered customer value of playing, even more terrible.
Add to this a 9% fee on
initial deposits for Jackpocket, and it is almost
assuredly similar to the high fees that would reduce the payouts from the
lottery [see comment above about distributions from mobile lottery operators].
But in this growth era across the economy, sometimes leveraged money circulates to give the appearance of growth. For examle, along with online
casinos, we’ve seen a tsunami of sports-betting advertising in major travel locations and at
sporting venues.
The economics of these new gaming [gambling?] models are egregious to everyone. From high "convenience" fees for the customer, and onerous for the
technology companies [eg currently double-digit “fees” paid back to the lottery for
casino games that should have higher payouts].
Also the mobile experience provides greater and more frequent access to games [a frightening five times initial maximum spend on Jackpocket versus what high lottery spenders and already spending]. Since our 2016 lottery article, new surveys of consumer lottery spending suggest some randomness across income strata, though a typically high share coming from older citizens. Still, as we noted in that article, the level of spending across the population is extraordinarily high and ill-advised.
The total
lottery market share loss [versus the nominal economic growth of the economy
post-coronavirus] isn’t fully made up for by the triple-digit revenue growth
from these small mobile casinos and sports games. But the numbers are close when you also include the other
market based froth [described at the start of the article] of the past couple years.
topic 5: gaming odds with casinos and sports
Different types of speculation each come with its own chances of winning large or small prizes. Casinos are slightly simpler than sports,
though probability mathematics could be generally challenging for most people. But casinos and sports probabilities are similar enough to
be able to describe together, here.
We discussed
one example above for a complex sports bet being a 1:20m chance of winning [eg perfectly
selecting early March Madness brackets]. And note that you would need a 1:30m range chance
of winning lottery game in order to have the same basic ticket value [given the
reduced lottery payouts].
But let’s
consider the fundamtntal two-team sporting game odds. For example, who will win the World Cup, between two evenly matched countries? Similar to who will win a national election. If we assumed the sports games the and
lottery payouts were the same [we know they are not, but this is for mathematical illustarion] then the expected value over the course of a single game or bet would be equal.
However there
is also the consideration of taxes on the winning, which would always tilt the
“value” towards a loss. Leaving that aside, we have the compounded nature similar to the disproportional gambler's ruin problem, famous among the most renowed probablists over a century ago while playing in Casino de Monte-Carlo.
And other complications such as the fact that the original “evenly matched”
odds one assumes is actually only a guess. The actual chance could be more or less than this due to the individual game/team randomness, and
also estimation errors in the the odds themselves for the unique game you [and only you] are interested in betting on.
Of course even
in the most basic sports betting, speculators generally bet on lopsided odds
match-ups. Implying the compounded
effect of gambling [chapter 6 of Statistics Topics] is even
greater. And returning to the more
exotic game bets, the confidence intervals are generally wider due to the
nature of artificial intelligence models being solved. Instead of the preferred closed-form probability theory, on small and unique sample sizes.
The flawed
overconfidence of the gamer would almost certainly be matched by larger and
less efficient waging. And everything
above works for sports as well as casinos.
The most elementary casino game is roulette [with bare options such as a
number or color], followed by Black Jack [with bare options such as a single
draw, single player, and large shoes].
Last, there's generally a flawed mentality of gaming [or gambling entertainment] when it
comes to casinos and sports, while there's more of a retirement mentality when it
comes to the simpler lottery. Though one rarely realized. Perhaps
why more money is wasted on the lottery. And why
money has also flowed into other speculative [and perhaps fraudulent], new market-based products recently. For example the mirage of pumped-up cryptocurrencies being the get-rich quick scheme, which many in society could retire on.
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