Sports Betting Charts: 2013

Wednesday, December 25, 2013

Soccer - Converting 1x2 Moneyline Into Asian Handicap

Variables
P(Aw) = Probability of team A winning
P(d) = Probability of draw
P(Bw) = Probability of team B winning
P(A|1) = Probability of Team A winning by exactly 1 goal = 0.191856-0.30565416*x+1.42165*x^2-1.21885522*x^3, where x=P(Aw)
P(A|2) = Probability of Team A winning by exactly 2 goals = 0.13482-0.553848*x+1.71645*x^2-1.08417508*x^3, where x=P(Aw)
TO(A|X) = True decimal odds of team A with handicap X

True Odds, A^[1]
$TO(A|0)=\frac{1-P(d)}{P(Aw)}$
$TO(A|-0.25)=\frac{(1-\frac{P(d)}{2})}{P(Aw)}$
$TO(A|-0.50)=\frac{1}{P(Aw)}$
$TO(A|-0.75)=\frac{1-\frac{P(A|1)}{2}}{P(Aw)-\frac{P(A|1)}{2}}$
$TO(A|-1)=\frac{1-P(A|1)}{P(Aw)-P(A|1)}$
$TO(A|-1.25)=\frac{1-\frac{P(A|1)}{2}}{P(Aw)-P(A|1)}$
$TO(A|-1.5)=\frac{1}{P(Aw)-P(A|1)}$
$TO(A|-1.75)=\frac{1-\frac{P(A|2)}{2}}{P(A|1)-\frac{P(A|2)}{2}}$
$TO(A|-2)=\frac{1-P(A|2)}{P(Aw)-P(A|1)-P(A|2)}$

Notes and Sources
[1] To find true odds of Team B, use the following equation: 1-TO(A|X).

Tuesday, November 26, 2013

NBA - Home Win Probability Using SRS

The following equations can be used to determine true money-line and true point spreads for the NBA. The basis of them are using Adjusted Simple Rating System (aSRS), which can be calculated by:

$aSRS = \frac{G * SRS}{G+12}$

Where:

aSRS = adjusted simple rating system
G = games played
SRS = simple rating system

Simple Rating System—from what I've seen—is only published on Basketball-Reference, and is calculated by adding the team's margin of victory and strength of schedule. Justin Kubatko of Statitudes compiled the results of the 1976–1977 through 2012–2013 NBA seasons using aSRS, and created the following logit equation to predict the probability of the home team winning:

$P(W_{H})=\frac{1}{1+e^{-(0.613230+0.167546*dSRS)}}$

Where:

e = Euler's number, the base of natural logarithm
dSRS = Home team's aSRS – Away team's aSRS

This answer will produce a decimal (i.e. 0.5277) which can be multiplied by 100 to get the implied probability (i.e. 52.77%). This implied probability can be converted into a true money-line by using a convertor. Finally, this probability can be converted into a point spread using the following equation:

$Spread(H)=\frac{ln(\frac{1}{P(H_{W})}-1)}{0.13959}$

Sources:
Kubatko, Justin (November 13, 2013). "Home Win Probability Using SRS." Statitudes. Retrieved November 26, 2013.

NFL Playoff Predictions - Week 12

Methodology:
At NFL-Forecast, there is a program that uses a monte carlo simulator to simulate the remainder of the season 5,000 times. It also takes the team efficiency ratings from Advanced NFL Stats.

Division Standings:

AFC East
New England	96.18%
NY Jets	1.32%
Miami	1.30%
Buffalo	1.20%

AFC North
Cincinnati	95.40%
Pittsburgh	3.50%
Baltimore	1.08%
Cleveland	0.02%

AFC South
Indianapolis	96.90%
Tennessee	3.10%
Houston	0.00%
Jacksonville	0.00%

AFC West
Denver	89.88%
Kansas City	10.08%
San Diego	0.04%
Oakland	0.00%

NFC East
Philadelphia	65.86%
Dallas	34.04%
NY Giants	0.10%
Washington	0.00%

NFC North
Detroit	51.22%
Green Bay	32.64%
Chicago	16.14%
Minnesota	0.00%

NFC South
New Orleans	90.04%
Carolina	9.96%
Tampa Bay	0.00%
Atlanta	0.00%

NFC West
Seattke	98.74%
San Francisco	1.06%
Arizona	0.20%
St. Louis	0.00%

Tuesday, October 15, 2013

CBB - Middling Totals

Difference	Middle	EV @ -110
0	1.24%	-$7.39
0.5	3.25%	-$3.17
1	5.87%	$2.32
1.5	7.74%	$6.25
2	10.23%	$11.48
2.5	12.21%	$15.64
3	14.72%	$20.91
3.5	16.69%	$25.04
4	19.42%	$30.78

Source: Detroit, Johnny (January 18, 2012). "Middling Totals." Pregame.com. Retrieved October 11, 2013.

CBB - Middling Sides

Difference	Middle
0.0	2.04%
0.5	5.71%
1.0	9.60%
1.5	13.20%
2.0	17.23%
2.5	20.99%
3.0	24.90%
3.5	28.85%
4.0	32.51%

Source: Detroit, Johnny (January 18, 2012). "Middling Totals." Pregame.com. Retrieved October 15, 2013.

MLB - Various Proposition Equations

Batter's True Batting Average Against Certain Pitcher:^[1]

$TBA=\frac{\frac{BA*BAA}{LBA}}{\frac{BA*BAA}{LBA}+\frac{(1-BA)*(1-BAA)}{(1-LBA)}}$

     Where:
          BA = Player's Batting Average
          BAA = Pitcher's Batting Average Against
          LBA = League's Batting Average

Total Number of Hits in a Game by Player X:

$H_{Total}=TBA*\frac{AB}{G}$

   Where:
   TBA = True Batting Average
   ^AB/_G = At Bats Per Game

Park Factor:

$PF=\frac{\frac{OBP_{home}+OBPA_{home}}{N_{home}}}{\frac{OBP_{away}+OBPA_{away}}{N_{away}}}$

   Where:
   OBP = On Base Percentage
   OBPA = On Base Percentage Against
   N = Number of Games

Probability of Team Scoring Run in First Inning:[2]

$PR\left \{A,R \right \} = \sum_{r=1}^{\infty}e^{-0.1219*A-0.3865r-\frac{1.813r}{A}-1.042}$

Where:
A = Team's Runs/Game

Sources:
[1] Sugano, Adam (2008). A Player-Based Approach to Baseball Simulation (Dissertation). University of California, Los Angeles. p. 50.
[2] Woolner, Keith (n.d.) An Analytic Model for Per-Inning Scoring Distributions (Report.) Baseball Prospectus. pp. 8–10.

Monday, October 14, 2013

Pythagorean Theorem for Season Wins

$Expected Wins = \frac{Runs Scored^x}{Runs Scored^x+Runs Allowed^x}$

x = 1.83 - MLB, 2.37 - NFL, 16.50 - NBA, 10.00 - CBB, 2.00 - NHL, 1.70 - MLS

Sunday, October 13, 2013

Golf - Probability of Hole-In-One

According to US Hole-In-One Insurance,^[1] the odds of this even occurring in a four-round, 144-player PGA tournament is approximately 1/1 (50%, +100). The probability of a single professional golfer getting a hole-in-one has been estimated to be 3,000/1 (0.03%, +300,000).^[2]

Using this number of 3,000/1 the following equation can be created to find the odds of a hole-in-one in a tournament:

${TO_{yes}}=\frac{N_{par 3 holes}*(P_{before cut}+P_{after cut})}{1,500}$

Sources:
[1] "What are the Odds That My Event Has a Hole In One Winner?" HoleInOneInsurance.com. Retrieved October 13, 2013.
[2] Kelley, Brent. "What Are the Odds of Making a Hole-In-One?" About.com. Retrieved October 13, 2013.

NFL - Wong Teasers

Wong Teasers are teasers when a bettor passes through the "key numbers" of 3 and 7 in the NFL. Normal 6-point teasers would require favorites of -7.5 to -8.5 and underdogs of +1.5 to +2.5. Below is the cover percentage of a single leg of a Wong Teaser covering. (At -110, 72.34% of legs have to cover to have +EV.)

	6-pt	6.5-pt	7-pt
1990-1999^[1]	76.00%	77.00%	76.00%
2000-2008^[1]	70.60%	72.44%	73.28%
2000-2010^[2]	72.54%	—	—

Sources:
[1] Wong, Stanford (2011). Sharps Sports Betting. Las Vegas, NV: Pi Yee Press. pp. 258-262. ISBN: 0-935926-24-0.
[2] "NFL Teasers: Wong Teasers." WizardOfOdds.com. October 12, 2013. Retrieved October 13, 2013

NCAAF, NFL, NBA - Spread to Fair Money Line

Spread	NCAAF	NFL	NBA
0	100	100	100
1.5	120	122	113
2	127	130	119
2.5	135	139	129
3	143	149	141
3.5	152	159	153
4	161	170	167
4.5	171	181	182
5	182	194	198
5.5	193	207	216
6	205	221	236
6.5	217	236	258
7	231	252	283
7.5	245	269	310
8	260	288	342
8.5	276	307	377
9	293	328	419
9.5	311	351	466
10	330	375	523
10.5	350	400	579
11	372	427	645
11.5	395	457	720
12	419	488	807
12.5	445	521	910
13	472	557	1033
13.5	501	595	1179
14	532	635	1358
14.5	565	678	1579
15	599	725	1857
15.5	636	774	2216
16	675	827	2693
16.5	717	883	3351
17	761	944	4305
17.5	808	1,008	N/A
18	858	1,077	N/A
18.5	910	1,150	N/A
19	966	1,229	N/A
19.5	1,026	1,313	N/A
20	1,089	1,402	N/A
20.5	1,156	1,498	N/A
21	1,227	1,600	N/A
21.5	1,303	1,709	N/A
22	1,383	1,826	N/A
22.5	1,468	1,950	N/A
23	1,558	2,083	N/A
23.5	1,654	2,226	N/A
24	1,756	2,377	N/A
24.5	1,864	N/A	N/A
25	1,978	N/A	N/A
25.5	2,100	N/A	N/A
26	2,229	N/A	N/A
26.5	2,366	N/A	N/A
27	2,512	N/A	N/A
27.5	2,666	N/A	N/A
28	2,830	N/A	N/A
28.5	3,004	N/A	N/A
29	3,189	N/A	N/A
29.5	3,385	N/A	N/A
30	3,594	N/A	N/A
30.5	3,815	N/A	N/A
31	4,049	N/A	N/A

Sources:
[1] "College Football Money Lines." WizardOfOdds.com. Retrieved October 13, 2013.
[2] "Betting on the NBA." WizardOfOdds.com. Retrieved October 16, 2013
[3] "Betting on the NFL." WizardOfOdds.com. Retrieved October 16, 2013