Binomial Distribution &
Why the Size of Your Bet Can't be Used as a
Pry-Bar to Make More Profit Than You Deserve
Even if you have a long term advantage against pointspreads
and over-under lines, you will go broke with the use of faulty money
management. For our purposes in this article, we'll say you have a 57.5%
winning expectation on each and every bet. (Of course, the actual
winning expectation is rarely the same on any two bets, - but our record
shows we expect between 55%-58% over the long term.)
many winners can you expect in the next, say, 21 bets? Well, 57.5% of 21 is
12.075, so the answer figures to be 12, producing a win-loss record of
Trouble is, a
record of 12-9 is not the only thing that can happen. There are several
other results that are also very likely, and some of these other results
are not good. The graph below shows the binomial distribution of all the
although a result of 12-9 is the most likely of all outcomes, a
result of precisely 12-9 will occur only slightly more than 17% of the
time. That's only about one time in six. In real life, you can figure on a
record of something other than 12-9 about 5 out of 6 times.
With a 55%
expectation-per-bet, you can plan on making any profit at all only
about 60% of the time over your next 21 bets. In 4 out of 10 cases,
you can expect to win less than twelve out of 21 bets.
Even with a
55% winning expectation on every bet, you must be aware that it is just as
easy to go 7-14 (or worse!) as it is to go 17-4 or better.
Once in about
8 times you can expect to lose 13 or more of your next 21 bets. By
understanding the consequences of the probabilities
involved, you can avoid the disastrous results of using such
nonsensical money management traps as the so-called 'Kelly
criterion' or the suicidal 'one-star, two-star, three-star' nonsense,
or some other progressive betting schemes.
In our book, How
Professional Gamblers Beat the Pro Football Pointspread, we explain why most
people go broke betting on sports because they don't understand the
ramifications of the probabilities; - not because they can't call winners.
They are victims of the fallacy that progressive betting schemes can
produce more profit than they deserve.
course of an entire NFL season we figure to have upwards of 210 opinions
against pointspreads and totals, - but that does not mean we can view those
210 opinions as though they were ten individual 'blocks' of 21 bets. The
210 opinions can be regarded as a continuum of bets from 1 through 210, or
a continuum of 21-block units from 21 through 210. Bets 1 through 21
comprise the first such block, bets 2 through 22 comprise the second block,
bets 3 through 23 comprise the third block, etc., within 210 consecutive
bets there are 189 blocks of 21 consecutive bets.
are 189 'blocks' of 21 consecutive bets in a series of 210 bets, it's
virtually a sure thing that we will have more than one block wherein our
record will be WORSE than 8-13, and it's also pretty much guaranteed that
we will have more than one 'block' wherein our record is better than 16-5.
Neither of these results means we are performing better or worse than our
normal level of handicapping. Such results are caused by wholly normal and
natural fluctuations from the mathematical expectation - binomial
The trick is
to be ready for the ups and downs that are bound to occur simply due to the
mathematics of the situation. With upwards of 210 opinions against NFL
lines, we do expect an overall win rate in the area of 55%-58%, but we also
fully expect a very bumpy ride along the way. Against the NFL, to ensure
that you'll still be alive in January, we highly recommend a bet size of no
more than 2% of your bankroll. Guarantees come with toasters, not football
bets, but we are confident we can offer you a pool of 55%-58% winners from
which to make your own choices over the entire NFL season. How many bets we
might win over the next ten or twenty tries, however, is hardly more than a
guess. Scale your bet sizes so you'll be alive in January. Refrain from
'jiggling' the size of your bets; keep all bets the same size.
According to expert researcher Dr. Nigel E. Turner, Ph.D., Scientist,
Centre for Addiction and Mental Health, incremental betting is one of the
telltale signs of someone with a gambling problem.
Did you get
that last paragraph? If you absolutely cannot resist betting more on some
plays than others, if you cannot resist increasing your bet size to either
catch up or to press a winning streak, you may have a gambling problem.
betting on a professional level must be approached as an investment, not a
bonanza. Understanding that fact may be the biggest difference between
successful bettors and chronic losers. Sports betting is not a means to get
rich overnight. Think "stock market," NOT "lottery."
Think "investment," NOT "Brink's truck explosion."
nearly 1,500 picks per year in Professional Gambler Newsletter. (That's against pro and NCAA
football and basketball, pro baseball and pro hockey.) We
expect a minimum of 30 units' profit per 1,000. Risking 2% of your bankroll
per bet, you figure it out. What are the chances of doing that well in the
If you are
not familiar with the vagaries of binomial distribution described above, we
recommend that you track us for at least 100 picks, and preferably
200 picks, before subscribing to Professional Gambler Newsletter. It will give you a
better sense of the winning and losing streaks we expect along the way.
J. R. Miller & Jack
Jack Painter (right)
taught us, “If you use a Star-betting system you’d better like stars
because you’re going to be sleeping under them.”
Jack was a good teacher. His insights concerning
handicapping sports and managing a bankroll are helpful to even the most
sophisticated sports bettors. Before his death in 1994 Jack taught sports
betting at Community College of Southern Nevada and on his radio show, Insider
Sports. He did a lot for us, never asking for anything in return. We
still owe him.
Could YOU Be a Professional Gambler?