point spreads
TRANSCRIPT
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 1
Point Spreads
Changneng Xu
Sports Data Mining
Topic : Point Spreads
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 2
Overview
Introduction
Method of Spread Ratings
Example
Comparison
Conclusion
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 3
Overview
Introduction
Method of Spread Ratings
Example
Comparison
Conclusion
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 4
Introduce to Point Spreads
Spread betting - any of various types of wagering on the outcome of an event,
including in financial market(spread betting is regulated by the
Financial Conduct Authority in UK)
Point spreads - the scoring differences of a competition ( mainly in sport area)
โข Handicap
How can bookmaker makes money?
โข Vigorish/Juice: a fee that charged for the services from bookmaker
โข By setting the payout rate under 100% probabilities
โข If there is an equal amount of money that betting on each teams
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 5
Odds VS Point Spreads
If only odds betting
โข the payoff on a winning bet should tied to the odds in favor of winning(hard to predict)
โข less fovor on a weak team(skillful gambler)
โข โdecreased betting activity & less vig
โข Competition between bookmakers
point spreads betting:
For gambler: Great volatilityโ excitement, substantial losses and rewards
For bookmaker: Maximize the betting activity
Balance the amount that betting on either teams( make them equally
attractive)
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 6
Point Spread Betting
Early age: Charles K. Mcneil, a mathematics teacher, became bookmaker and offerd
betting against a published spread around 1940s in U.S.
Target: maximize and balance the activity on both sides
Operations:
โข bookmakers create a handicap against the favored team;
โข bookmakers decide the point spread that may result in an equal amount of wager;
โข gamblers betting that, the scoring differences is more/less than the offered spread;
โข adjust the spreads
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 7
Types of Point Spread Betting - Handicap
Handicap(beat the spread)
โข Underdog & favorite - the underdog(weaker/away team) receives points and favorite give points;
โข The result of wager is then determind by the adjusted score: the favorite team with original score
and the underdog plus spread on basis of primitive score;
โข โPushโ - using half-point fractions to avoid tie
โข Example of World Cup from bet365.com, in which team Holland receives 1 additional point: if
you bet on Argentina to win and Argentina wins exceeding 2 additional score, then you beat the
spread;
Asian handicap
โข range from one-quarter goal to several goals
โข originated in Indonesia
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 8
Types of Point Spread Betting - Over/Under Betting
Over/Under Bettingโข Another popular spread betting โ bet on the total score
โข Usually with a half-point fraction to avoid tie
โข Example of over/under bet of World Cup ยฝ final (Hollland VS Argentina) from
bet365.com and oddset.de showed below
โข Other stastistics โ total passing yards in football, turnovers in basketball, ect.
Over/Under Betting of a soccer game
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 9
Overview
Introduction
Method of Spread Ratings
Example
Comparison
Conclusion
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 10
Predicting Spreads with Ratings?
Difficulties:
โข The purpose of ratings are different โ usually the overall strengh of teams that related
to others
โข Details may filtered out during distillation
โข Lack of the seprate analyses of individual aspects , such as offensive/defensive
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 11
Method - Predicting Spreads with Spread data
โข Use the historical information to build rating of spreadsโข Similar to Masseyโs methodโข Build an optimal rating system that closely reflect the point spreads
Suppose that there is a perfect rating vector
r=
๐1๐2โฎ๐๐
that rating difference ๐๐ โ ๐๐ is equal to each scoring difference ๐๐ โ ๐๐
K =
0 ๐1 โ ๐2 โฏ ๐1 โ ๐๐๐2 โ ๐1 0 โฏ ๐1 โ ๐๐โฎ โฎ โฑ โฎ
๐๐ โ ๐1 ๐๐ โ ๐2 โฏ 0
, R =
0 ๐1 โ ๐2 โฏ ๐1 โ ๐๐๐2 โ ๐1 0 โฏ ๐2 โ ๐๐โฎ โฎ โฑ โฎ๐๐ โ ๐1 ๐๐ โ ๐2 โฏ 0
K = R = re๐ - er๐ (e is a column of 1)
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 12
Method - Predicting Spreads with Spread data
K =
0 ๐1 โ ๐2 โฏ ๐1 โ ๐๐๐2 โ ๐1 0 โฏ ๐1 โ ๐๐โฎ โฎ โฑ โฎ
๐๐ โ ๐1 ๐๐ โ ๐2 โฏ 0
โข Score-differential matrix K is skew symmetric K๐ = - K
โข Rank of re๐ โ er๐ is 2 Rank of K is 2
โข But actually we can only build ratings vector r that:
minimize the distance between K and R
Build a function of vector x that is minimal for Frobenius norm:
f x = โฅ K โ R(x) โฅ2 = โฅ K โ (xe๐ โ ex๐) โฅ2 (1)
as rank(K) = 2 and it is simplest and most standard
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 13
Method - Predicting Spreads with Spread data
Frobenius norm is
โฅ A โฅ๐น = ๐,๐ ๐๐๐2 = ๐ก๐๐๐๐(A๐A)
In which the trace function have these proterties:
trace (๐ผA + B) = ๐ผ trace ( A ) + trace ( B), andtrace (AB) = trace (BA)
Set๐๐
๐๐ฅ๐= 0 for each i and solve the resulting system of equations for ๐ฅ1, ๐ฅ2, โฆ , ๐ฅ๐ to minimize the
function (1)
f x = โฅ K โ R(x) โฅ2 = โฅ K โ (xe๐ โ ex๐) โฅ2
yieldsf x = trace [K โ ( xe๐ โ ex๐)]๐ [K โ (xe๐ โ ex๐)]
= trace K๐K โ ๐ก๐๐๐๐[K๐( xe๐ โ ex๐) + ( xe๐ โ ex๐)๐K] +
trace [( xe๐ โ ex๐)๐ ( xe๐ โ ex๐)]
As K is skew symmetric, then: f x = trace (K๐K) โ 4x๐Ke + 2n x๐x โ 2(e๐x)2
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 14
Method - Predicting Spreads with Spread data
f x = trace (K๐K) โ 4x๐Ke + 2n x๐x โ 2(e๐x)2
differntiate f with respect to ๐ฅ๐, we got:
๐๐
๐๐ฅ๐= โ4e๐
๐Ke + 4๐๐ฅ๐ โ 4e๐x
set๐๐
๐๐ฅ๐= 0 then: โ4(e๐
๐Ke โ ๐๐ฅ๐ + e๐x) = 0
๐๐ฅ๐ โ e๐x = e๐
๐Ke
๐๐ฅ๐ โ
๐=๐
๐
๐ฅ๐ = (Ke)๐ , ๐๐๐ ๐ = 1, 2, โฆ , ๐
This linear equation can be transfored into a matrix equation:
(n โ 1) โ1 โฏ โ1โ1 (n โ 1) โฏ โ1โฎ โฎ โฑ โฎโ1 โ1 โฏ (n โ 1)
x1x2โฎxn
=
(Ke)1(Ke)2โฎ(Ke)n
, each side divide n โ ๐ โeeT
nx =Ke
n
which I is a ideantity matrix
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 15
Method - Predicting Spreads with Spread data
๐ โeeT
nx =Ke
n(2)
As e๐Ke is a scalar and K๐ = โKyields
e๐Ke = 0,So one solution of formula (2) is the vector x that:
x = Ke
๐
Further more, ( ๐ โeeT
n) e = 0 and rank ๐ โ
eeT
n= n โ 1,
Then all solutions of the formula (2) are:
x = Ke
n+ ฮฑe , ฮฑ ๐ โ
With help of some constraint such as sum of ratings equals 0, we can determine a unique
solution: ๐ฅ๐ = e
๐x = 0
e๐Ke
n+ ฮฑe =
e๐Ke
n+ e๐ฮฑe = e๐ฮฑe = 0
yieldsฮฑ = 0
ๅจๆญคๅค้ฎๅ ฅๅ ฌๅผใ
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 16
Method - Predicting Spreads with Spread data
โข check if r=๐พ๐
๐is the actual minimizer using the Cauchy-Schwarz (or CBS) inequality method
Then the only critical point for f(x) is:
r=๐พ๐
๐(the centroid of the columns in K)
In which the set ot ratings {๐1, ๐2, โฏ , ๐๐} with constraint ๐๐๐ = 0, that the (Frobenius)
distance between K = ๐๐ โ ๐๐ and R = [๐๐ โ ๐๐] is minimized.
Take the result of World Cup in group G for example:
K =
0 4 0 1โ4 0 1 00 โ1 0 โ1โ1 0 1 0
Germany Portugal Ghana United States
Germany 0 4 - 0 2 - 2 1 - 0
Portugal 0 - 4 0 2 - 1 2 - 2
Ghana 2 - 2 1 - 2 0 1 - 2
United States 0 - 1 2 - 2 2 - 1 0
r =
1.2โ0.75โ0.50
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 17
Overview
Introduction
Method of Spread Ratings
Example
Comparison
Conclusion
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 18
Example : NFL 2009 - 2010
โข 267 games in 2009 โ 2010 NFL season
โข If two teams meet more than once, use the average
score respectively
โข Hindsight prediction percentage : 71.54%
โข High efficiencyโ only averaging the score differences
โข
Spread ratings NFL 2009-2010
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 19
Example : NFL 2009 - 2010
Absolute-spread error โ with linear regression approach
Parameters: โhome-field advantageโ , ๐ผ, ๐ฝ, ๐พ
Expected[(home-team score) โ (away-team score)] =๐ผ + ๐ฝ๐โ โ ๐พ๐๐
๐โ and ๐๐ are the ratings for home and away teams;
In this euqation:
๐ผ + ๐ฝ๐โ๐ โ ๐พ๐๐๐ = ๐โ๐ โ ๐๐๐, i = 1,2,โฆ,267
๐ผ, ๐ฝ, ๐พ are determined by computing least squares solution within equation above,
Where ๐โ๐ and ๐๐๐ are the ratings for home and away team in game i, ๐บ๐๐ and ๐บ๐๐ is the scores at
home or away in game i,
Computing LS of linear system Ax = b โ the 3 X 3 system of normal equations ๐ด๐Ax = ๐ด๐b,
Where
A267ร3 =
1 rh1 ra11 rh2 ra2โฎ โฎ โฎ1 rh267 ra267
, x =
ฮฑฮฒฮณ, and b =
Sh1 โ Sa1Sh2 โ Sa2โฎ
Sh267 โ Sa267
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 20
Example : NFL 2009 - 2010
Result:
๐ผ = 2.3671
๐ฝ = 2.4229
๐พ = 2.2523
โ ๐ก๐๐๐๐ ๐๐๐ ๐๐๐ข๐ก๐-spread error:
Which the spread error per game is 10.59
๐=1
267
| 2.3671 + 2.4229๐โ๐ โ 2.2523๐๐๐ โ (๐โ๐ โ ๐๐๐)| = 2827.6
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 21
Overview
Introduction
Method of Spread Ratings
Example
Comparison
Conclusion
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 22
Compare with other Methods
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 23
Compare with other Methods
Comparisons of popular rating systems with 2009-2010 NFL data
Compare the hindsight win accuracy and spread error
โข Spread ratings method is in the similar efficiency area as the other 4 rating systems
โข Spread (centroid) ratings are more easier to compute
Hindsight Win Accuray: Average Spread Error(Points per Game)
Spread Ratings = 71.5% Spread Ratings = 10.59 points per game
Sagarin Ratings = 70.8% Sagarin Ratings = 10.53 points per game
Elo Ratings = 75.3% Elo Ratings = 10.71 points per game
Keener Ratings = 73.4% Keener Ratings = 10.54 points per game
Massey Ratings = 72.7% Massey Ratings = 10.65 points per game
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 24
Overview
Introduction
Method of Spread Ratings
Example
Comparison
Conclusion
09.07.14 | TU Darmstadt| Knowledge engineering | Prof. Johnannes Fรผrnkranz | Changneng Xu | 25
Conclusion
Gambling is sometimes an art (of psychology) โ gamblers, bookmakers
are betting on the expectation that their โpredietedโ point spread will
generate an equal amount of money,
Using simple method may also receive a good result.