How to Follow Probabilities to Win More Bets

The outcomes of the games have been assumed to be independent. The following probabilities were identified and defined:

P (Yankees win at home in New York) = 0.55

P (Phillies win at home in Philadelphia) = 0.53

P (Yankees win away in Philadelphia) = (1-0.53) = 0.47

P (Phillies win away in New York) = (1-0.55) = 0.45

The three probabilities are given by:

P (a) = Yankees 1 (Yankees win first home game) * Yankees 2 (Yankees win game 2 away).

P (a) = 0.55 * 0.47 = 0.2585.

P (a) = 0.2585.

P (b) = Yankees 1 (Yankees win first home game) x Phillies 1 (Phillies win home game) x Yankees 3 (Yankees win 3rd game in New York).

P (b) = 0.55 * 0.53 * 0.55 = 0.1603

P (b) = 0.1603

P (c) = Phillies 1 (Phillies win the first away game) x Yankees 2 (win in away game) x Yankees

3 (win home game).

P (c) = (1-0.55) x (1- 0.53) x 0.55 = 0.45 * 0.47 * 0.55 = 0.1163

P (c) = 0.1163 

P (a + b + c) = P (a) + P (b) + P (c)

P (a + b + c) = 0.2585 + 0.1603 + 0.1163 = 0.5351

The probability that Yankees win the series is = 0.5351 

Objective Probability 2 

For the analysis of the objective probability, the statistics data that was used was the PGA data sample for 2017. The events player completed in 2017 was analyzed through the variable cuts made (“Professional Golfers’ Association of America”, 2017). The data was imported into JASP (Version 0.13.1; JASP Team, 2020) for descriptive analysis. The results were as shown.

Table 1 

Frequency Tables 

Cuts Made		Frequency		Percent		Valid Percent		Cumulative Percent
1		1		0.500		0.500		0.500
3		2		1.000		1.000		1.500
4		2		1.000		1.000		2.500
5		1		0.500		0.500		3.000
6		9		4.500		4.500		7.500
7		10		5.000		5.000		12.500
8		8		4.000		4.000		16.500
9		9		4.500		4.500		21.000
10		11		5.500		5.500		26.500
11		10		5.000		5.000		31.500
12		12		6.000		6.000		37.500
13		13		6.500		6.500		44.000
14		14		7.000		7.000		51.000
15		13		6.500		6.500		57.500
16		13		6.500		6.500		64.000
17		12		6.000		6.000		70.000
18		15		7.500		7.500		77.500
19		9		4.500		4.500		82.000
20		16		8.000		8.000		90.000
21		5		2.500		2.500		92.500
22		8		4.000		4.000		96.500
23		4		2.000		2.000		98.500
24		3		1.500		1.500		100.000
Missing		0		0.000
Total		200		100.000

Figure 1 

Distribution Plots 

The probability (%) that PGA players make cut in 10 or more events is given by:

= 1- % in cumulative at 10

= 100% - 26.5%

= 73.5% 

The probability (%) that PGA players make cut in 21 or more events is given by:

= 1- % in cumulative at 21

= 100% - 92.5%

= 7.5% 

Table 1  Descriptive Statistics
		Cuts Made
Valid		200
Missing		0
Mean		14.155
Std. Deviation		5.106

Z = (x - µ) / σ 

where z = standard core

x = observed value

µ = mean of the sample

σ = standard deviation of the sample

Z for x = 10

= (10 – 14.155)/5.106

= -0.8137 

Z for x = 21

= (21 – 14.155)/5.106

= 1.3405 

Subjective Probability – NCAA 

From the analysis of the college sports data, gender equity is likely to improve. There is an 80% chance that gender equity will be improved in the sports. The expected growth is expected to be 2 percent growth within the next 5 years. The data that can be used to support this is the number of women’s coaching jobs that has been increasingly steadily over the past five years. Between 2008 and 2014, the number of female coaches increased by 1.6% (Acosta & Carpenter, 2015). The next data that can be used to support the growth in gender equity is that the number of teams that are available for women has also grown remarkably over the years. Most of the sports have experienced a rise of between 1 to 2 percent. The percentage of schools that lack any female administrator has also decreased from 13.2 percent in 2010 to 11.3 percent in 2014 which represents a decrease by 2.1 percent (Acosta & Carpenter, 2015). Such a rise can be forecasted to occur in the next five years.

In conclusion, there has been a consistent increase in the number of female opportunities over the past five years. Based on the analysis of the past data, it can also be forecasted that there is an 80 percent chance that the data will increase by 2 percent within the next five years.

References 

Acosta, V. R., & Carpenter, J. L. (2015). Women in Intercollegiate Sport: A Longitudinal, National Study, Thirty-Seven Year Update. 1977-2014. Acosta Carpenter. www.acostacarpenter.ORG 

JASP Team (2020). JASP (Version 0.13.1) [Computer software].

Professional Golfers’ Association of America. (2017). 2017 PGA Tour Top 200 Honored Golfers season datasets. [Data file]. University of Florida, https://ufl.instructure.com/courses/414261/files/52446630/download?wrap=1