Welcome to my section on probabilities in sports betting. This and
racetrack betting are unique sections at the Wizard of Odds because
it can not be purely analyzed with mathematics. In other words you
can never know exactly what the house edge is for a certain bet because
of the human factor involved in sports. However we can look at past
bets available and their eventual outcome to make some pretty accurate
observations. We can also assume that the bookmaker's actions are
motivated by the desire to balance the action on both sides of a bet
so that he wins regardless of the outcome. In other words we can assume
that on average both sides of a bet are about equal. The organization
of this section will be to address various bets available and analyze
their return.
Straight Bets
Straight bets are the most popular and in my opinion the best kind
of bet of all sports bets. This is a simple bet on the outcome of
a game, relative to a point spread. The point spread is created to
add some fictional points to the underdog team. For example suppose
the Baltimore Ravens are playing the New Orleans Saints and New Orleans
is favored to win. The expert handicappers may determine that giving
Baltimore an extra 6 points would make it a fair bet, in other words
people would bet equally on both sides. The way this bet would look
in the papers or in the casinos is New Orleans -6 vs. Baltimore. A
way to remember what this means is that New Orleans would have a fictional
negative six points to begin the game, or that New Orleans would have
to overcome a six point handicap. If instead of a number there is
the letter P (for "pick") then there is no point spread
at all and you simply "pick" who will win the game. The
point spread is set in units of 1/2. Sometimes an apostrophe symbol
is used to designate a half, for example 6' would be a spread of 6
1/2.
When making a straight bet you must usually wager $11 to win $10.
Another way of looking at is that it is an even money bet but the
loser must pay a 10% commission. For example if you wanted to win
$50 you would have to bet $55, and if you bet $50 you would get $50*(10/11)=$45.45
if you won (subject to rounding). Assuming that the spread is truly
fair the house edge is (.5*10 - .5*11)/11 = 4.55%. In the event that
the outcome of the game is exactly on the point spread then all bets
are a push. This actually happened twice in the Super Bowl recently.
In 99 Saint Louis was favored by 7 over Tennessee and the score was
23-16. In 96 Green Bay was favored by 14 over New England and the
score was 35-21.
Sometimes the Las Vegas sport books wills have promotional 5% straight
bets. In other words the player must wager $10.50 to win $10. For
example this year (2001) the Regent casino offers 5% straight bets
during certain hours on Mondays to celebrate Monday Night Football.
The house edge on 5% straight bets for a random picker is 2.38%,
ignoring ties.
Money Lines
Money lines are another popular way to bet on sports. This is a simple
bet on the true winner of a sporting event without any point spread.
Naturally one team will be favored most of the time so if you want
to bet on the favorite you must bet more than you stand to win (laying
odds). If you bet on the underdog you stand to win more than your
bet (taking odds). Let's use the Baltimore/New Orleans from the previous
section as an example again. The money line would look something like
this: New Orleans (-210) vs. Baltimore (+170). This means that if
you prefer to bet on the favorite, New Orleans, you must wager $210
for every $100 you win if New Orleans wins. If you prefer to bet on
the underdog, Baltimore, you win $170 for every $100 you wager if
Baltimore wins.
The way a money line is established is first the bookmaker uses his
best judgment to determine the probability that the favorite will
win. For example let's assume 60%. He then converts this to a fair
money line with no house edge. If the probability is p then the money
lines are +/- 100*p/(1-p). If p is 60% then the fair money lines would
be +150 and -150. Then the bookmaker will take a constant and add
it to the amount the favorite better must bet and subtract is from
the amount the underdog better can win. A common constant is 10 points.
In this example the bookmaker would adjust the money lines to +140
and -160. This is referred to as a 20 cent line, referring the total
line movement from the theoretical fair line. For games with a strong
favorite the numbers of points will increase.
If the two money lines are x and y (for example x=+140 and y=-160)
then the house edge taking odds (or betting on the underdog) is
(x+y)/(200+x-y). The house edge on the laying odds (or betting on
the favorite) is -100*(x/y+1)/(200+x-y). In the +140/-160 example
the house edge on the taking odds is 4.00% and laying odds is 2.50%.
If the player must lay odds on either team (for example x=-105 and
y=-115) then the house edge on x is ((20000/x)+x-y+200)/(x-y+400)
and on y is ((100/y)*(x-y+200)+200)/(x-y+400). In this example the
house edge on x is 4.76% and on y is 4.24%.
Parlays
The Parlay is a way to bet on multiple sporting events with hope for
a big payoff if all of them win. All picks are relative to the same
point spread as in straight bets. If just one event doesn't win or
draw then you lose the entire bet. If one or more event is a draw
then those events are ignored. If you win all the other events you
get paid according to the number of events that you did win. In the
event all games bet on result in a push except one or none then the
entire bet becomes a push. The following table shows the payoff according
to the number of events bet on and the corresponding house edge, assuming
that the probability of winning any given event is 50%. In addition
the table presents the house edge of making the same number of straight
bets and letting the winnings ride every time. Note that the house
edge is less on the three team parlay.
Teasers
A teaser is similar to the parlay bet in that you choose multiple
events and have to win them all. However the bookmaker teases the
player with a specified number of extra points for each team bet on.
Naturally the player pays for these extra points in the form of lower
payoffs than on a parlay bet.
For example the Ravens are playing the Giants and the Ravens are favored
by 3. If you bet on the Giants are part of a 6-point teaser you will
win that game if the Ravens outscore the Giants by less then 9 points,
or if the Giants win.
The following tables show the payoff and house edge according to
the number of teaser points and number of games. Note the variation
in payoffs. For example the Fiesta Casino in Las Vegas pays 8:5
for a 3 game, 6 point, teaser, while the Suncoast casino pays 9:5
for the same thing.
Buying Half a Point
The straight bet player has the option to move the point spread
1/2 point to his advantage. The cost of this half point is laying
120, as opposed to 110. The most oportune time to buy a half point
is when one team is favored by 2.5, 3, 6.5, or 7. This is because
many games end in a 3 or 7 point difference and the extra half point
can either turn a loss into a draw or a draw into a win. However
many sportbooks do not allow purchasing a 1/2 point on these spreads
for exactly this reason. Over 1975 games during the 1993 to 2000
seasons the overall house edge by purchasing the extra half point
is 4.13%.
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