Economics of Point Spread Betting

I. Implications of Efficient Pricing for Point Spreads

A. How the Point Spread Market Works

1. Notation:

DP = score difference of the game

e.g. Bulls 100, Bucks 93 => DP = 7

PS = point spread

Suppose Bulls are favored by 4 points over the Bucks => PS = 4

2. Outcome of the bet is determined by the score difference of the game

Let PS = 4

Bets on the Bucks win if they beat the Bulls or lose by less than 4

Ex: Score is Bulls 76, Bucks 74

Bets on the Bulls win if they win by more than 4

Score: Bulls 112, Bucks 74

If score difference is the point spread all money is refunded to bettors

Score: Bulls 112, Bucks 108

3. Odds are fixed at 10-11; bettors bet $11 to win $10 (net)

Bookmakers make money if their book is "balanced"

i.e. they take in $11 on both the Bulls & the Bucks ($22);

pay out $21 to whichever side wins the bet for a net of $1

4. Efficient Point Spreads: No Profitable Wagering Opportunities

Two implications of efficient point spreads

a) at the spread, all bets are a coin flip

If PS=4 is efficient

=> 50% chance Bulls win by 4 or more

& 50% chance Bulls win by 4 or less, or lose to the Bucks

Math Equivalent: PS is the median of the distribution of DP

b) PS is the Optimal Prediction of DP

--PS is unbiased

--no public information exists which allows one to construct a better prediction of DP than PS

Math Equivalent: PS is the Expected Value of DP given information I

PS = E(DP | I)

II. Simple Tests of Efficiency

Score differences defined on home team minus away team basis

Use 6 seasons of NBA games (5636 games)

A. Test: Is PS is the Median of DP?

Table 7A

B. Test: Is PS an unbiased predictor of DP?

Table 7B

C. Pictures of Point Spread & Score Difference Distributions

III. Are There Profitable Wagering Rules?

Profitable Wagering Rules are like the Loch Ness Monster:

Periodic reports claim to have found one, but these claims dissolve under further investigation

A. Score-Difference Model of NFL Football Games (Zuber et al, 1985)

Linear Regression Model: DP = f(Rush, Pass, Prior Wins, Fumbles, Interceptions, Yards Penalized, % Plays Passing, # Rookies)

These variables are differences between the home team and visiting team during the game being played.

Variable Coefficients

Constant (Home Team) 1.6

Rush Yards 0.04

Pass Yards 0.05

# Prior Wins 0.57

Fumbles -2.0

Interceptions -2.8

Yards Penalized -0.31

% Plays Passing -0.24

# Rookies -0.31

RSquare 0.73

Example: Let the Cowboys and Redskins play in Dallas; the Cowboys run for 50 yards more than the Redskins, pass for 100 more yards, and have 1 fewer fumble during the game. Let all other variables be the same for each team. The model "predicts" that

DP = 1.6 + .04(50) + .05(100) -2(-1) = 1.6 + 2 + 5 + 2 = 10.6

What is good about the Zuber model:

These performance measures are surely related to score differences.

The coefficient estimates make sense.

What is not so good:

The performance measures & DP are contemporaneous - what happened in a game that has already been played.

To have a profitable betting rule, you must be able to predict DP in advance. To make use of this model, you must thus be able to predict the variables in advance.

B. Zuber's Wagering Rule:

Use past averages of rushing yards, passing yards etc. to serve as predictors of next week's figures.

Difference the home & visiting teams' predictor variables. Apply the coefficients estimates (from the Table above) to obtain

MODEL DP = f(predicted differences in the explanatory variables)

Compare MODEL DP to PS from the market

If MODEL DP >> PS bet on the home team

If MODEL DP << PS bet on the visitor

Zuber's Claim: Bets won 60% of the time. This violates the rule that point spreads don't yield profit opportunities. Conclude market is inefficient.

C. The Zuber Rule on Subsequent investigation (Sauer et al, 1988)

1. The success rate is +/- 50% in the following (& subsequent) years

2. Sauer runs the Zuber regression using DP - PS as the dependent variable with the performance predictors as independent variables

Question: do these performance predictors predict PS forecast errors?

Answer: No. Not even in the original Zuber sample!

RSQ is 0.00.

Conclusion: the 60% rate in the Zuber paper was a Nessie.

D. No Profitable Wagering Rule Has Survived Subsequent Scrutiny

(See Table 8 for another example)

IV. Noise, Information, and Economic Models

A. Do Changes in PS Represent Noise or Information?

1. Brown and Sauer (1993)

Basketball spreads are used to estimate

PS = H + S_i - S_j

Where H is the home court advantage, S_i is the estimated strength of team i (the home team) and S_j is the estimated strength of team j.

See table with coefficient estimates.

The estimates of H, S_i, and S_j are then used to predict that the point spread will be when team j plays at team i out of sample.

Suppose the market PS differs substantially from that predicted by this model. This corresponds to an unexplained component of a stock price. Studies of the stock market call these unexplained components "noise." Often these studies hypothesize that the source of noise is trading by uninformed agents. Their trading is alleged to move prices away from fundamental values.

Brown & Sauer show the "noise" component in point spreads is essential to unbiased prediction of the score difference. (Table 9)

Hence "noise" is actually "news". It is something real that is simply difficult to place in a parsimonious model.

2. Gandar et al (1998)

Gandar et al apply the Brown & Sauer method to changes in PS from the opening of the market to the close of the market.

They show that had PS not changed, it would have been a biased predictor of the outcome of the game.

Gandar et al thus show that trading creates information.

In the absence of trading, the ability of PS to predict DP would have been worse. Trading results in improved prediction, hence relevant information is added to the market during the trading period.

B. Point Spread Changes When Players are Injured

Let team 1 have an injured player, and define the score difference as points scored by this team less points scored by the opponent.

PS should decline by the impact of the player on DP.

Example: Bulls with Jordan beat Bucks by 10 (on average)

Bulls w/o Jordan beat Bucks by 6 (on average)

If the above is true, PS should drop by 4 points when MJ is injured.

Tests using incapacitating injuries:

1. Calculate: PS without player - PS with player

this estimates the impact of "good" players (= 2 points )

2. Calculate Mean(DP without - PS without) = 0 points

Conclusion: The PS market efficiently responds to situations in which players are injured. The strength of the team with the injured player is adjusted downward by the right magnitude, on average.

V. Conclusion

Sports wagering markets enable tests of efficient pricing that are not possible in ordinary financial markets such as stock and bond markets.

The principal difference is the simplicity of this market. The betting contracts are specific to a single event, and the outcome of this event is determined once and for all when the race is run or the game is played. This contrasts with most financial contracts which are open ended and remain in force for long periods of time. Because of this, the price of a stock may be affected on any given day by anticipations of events that might take place at any of a number of future dates. This makes it hard to determine just what moves a stock price on a given day.

Observable events and market prices are more tightly linked in the wagering markets. We can thus run cleaner tests of efficient pricing here than in financial markets.

For the most part, these tests indicate that prices in the wagering market are efficient.

To summarize our basic findings:

--At the racetrack, win pool shares are good estimates of the probability that a horse wins the race, the favorite-longshot bias notwithstanding.

--In the NFL and NBA, point spreads are unbiased, best optimal predictors of score differences.

--Changes in point spreads point to changes in the distribution of outcomes. Player injuries are an obvious observable case when we observe point spread responses that match the deterioration in a team's performance. In other cases we do not know what causes point spreads to change, but when we see them changing we know that this change is necessary to unbiased prediction of the score difference.

--Trading in the market creates information and results in improved forecasts of outcomes. This finding is unique to wagering markets - it can't be tested as precisely and powerfully in markets where contracts are open ended.

In general, wagering markets provide a useful window to important issues which have been difficult to resolve in other financial markets. On balance, studies of wagering markets add to the case that market prices are efficient, and are driven by informed evaluation of fundamentals, as opposed to waves of irrational sentiment. This is certainly ironic given the popular images of sports fans as sentimental supporters of their teams and gamblers as psychopaths in need of therapy.