1. Introduction

This is a statistical analysis of who has the highest probability of winning. Will it be the people’s champion Manny “Pacman” Pacquiao or the reigning WBC super featherweight champion Juan Manuel Marquez. This study will evaluate through statistical analysis what are the percentages by which one person will win over the other. It will also try to evaluate the percentage that the game will end up as a draw.

The procedure of the analysis will be as follows:

1. Search in the internet the available data regarding the fight records of Manny Pacquiao and Juan Manuel Marquez

2. From these available data, derived the logical formulas needed to analyze the given data. This may also involve doing research in the internet about statistical formulas.

3. Record the required data and calculate the percentage by which Manny Pacquiao will win, the percentage by which Juan Manuel Marquez will win, the percentage by which Manny will win through KO, and the percentage by which the fight will end up a draw.

2. Data Collection

After doing a thorough research on the web, it was found out that http://www.boxrec.com provided the most complete data for the analysis. The data regarding all their fights were recorded including the judges scoring at the end of the fight, the fight records of their opponent, and the type of win. The concept of percentage, which is per 100 (MathSisFun.com, 1), is best way to express the amount of wins relative to the other fighter because they have different number of fights. Based on the individual records of Manny Pacquiao and Juan Manuel Marquez, we can calculate their percentage of wins (Pwin) according to the following formula:

where:

Pwin is the percentage of wins

Wins is the total number of wins

TotalFights is the total number of fights.

To know their chances of winning against each other, it was decided that this percentage alone is not sufficient. First we must look at the quality of their opponents by looking at the opponent’s percentage of wins. Then we must look by how many points they win over their opponent in terms of the average score of the three judges at the end of the game. Here we apply the concept of average, which is the measure of central tendency and more specifically the arithmetic mean (Wikipedia, 1). In formula this can be expressed as

where:

Wonpointsn is the number of points by which a fighter wins over his opponent, average of three judges

Sfj1 is the score of the first judge to the fighter

Soj1 is the score of the first judge to the opponent

Sfj2 is the score of the second judge to the fighter

Soj2 is the score of the second judge to the opponent

Sfj3 is the score of the third judge to the fighter

Soj3 is the score of the third judge to the opponent

This is where it was decided to add some qualitative approach to the quantitative data because if a fight ends in a KO or TKO, the scores are incomplete. It was noticed that if the fights ends in either unanimous or split decision, the average difference of scores would just be in the range of 1 to 13. So it was decided that if one wins by TKO, the points with which they win over their opponent (Wonpoints) is set to 15. Then through this we defined a qualitative value called Effective Winning Value (EWV) which is the product of the score by the fighter wins over his opponent (Wonpoints) multiplied by the percentage of win of the opponent.

If the fighter wins:

If the fighter looses the Wonpoints becomes negative:

Since this is a measure of how effectively the fighter wins over his opponent, the average of all the EWV is obtained. It was decided to use only half of the fight record of the fighter as entry to the average EWV because the records of their very old fights were already missing. For Manny Pacquiao, we included only 25 fights out of his 50 fights. For Juan Manuel Marquez, we included only 26 of his 52 fights. The product of EWV and the fighter’s percentage of winning Pwin is proportional to his probability of winning over his next opponent (K*EWVA*PwinA). If we divide this by the sum of their (K*EWVA*PwinA+ K*EWVB*PwinB+ K*EWVA*PdrawA+ K*EWVB*PdrawB), then we get their probability of winning against the other. If we cancel the constant of proportionality K then we arrive at the following equation:

Where:

WinprobA is the probability that fighter A wins over fighter B

The probability that the outcome will be a draw is based on the idea that neither of them wins and can be calculated according to the following formula:

The probability that the outcome will be a knockout (KOprobA) by fighter A is proportional to the probability of winning of fighter A WinprobA multiplied by the fighters knockout percentage.

Results:

Table 1. Analysis fo Manny Pacquiao Records

Table 2. Analysis for Juan Manuel Records

3. Interpretation of Results

Table 3. Summary of Results

From the calculation, it says that Manny Pacquiao will have a better chance of winning over Juan Manuel Marquez. He has 50.84% of winning the fight over Juan Manuel Marquez who just have 45.94% of winning over him. There is a 3.22% that the game will be draw. The probability that Manny Pacquiao will knock out Juan Manuel Marquez is 35.59%, while the probability that Juan Manuel Marquez will win over Manny through a knockout is just 30.92%.

4. Validity

The formulas used are based on mostly quantitative data from http://www.boxrec.com and logical interpretation of percentage and probability of occurrence. The additional qualitative data which is the introduction of an Effective Winning Value (EWV) per opponent fought is based on a logical formula. It is based on direct and indirectly proportionality of a variable to another set of variables. Therefore there is a very strong logical basis of the formulas being used even if it was just logically derived by the author from the concepts of percentage and probability of events.

5. Conclusion

Through statistical analysis it is possible to predict the outcome of future events to some degree of accuracy. This is done by using the principles of probability of events and concepts of percentage.

References

“Percentage %.” 2005. MathSisFun Website. 13 February 2008 <http://www.mathsisfun.com/percentage.html>.

“Average.” October 2005. Wikipedia, the free encyclopedia website. 13 February 2008 <http://en.wikipedia.org/wiki/Average>.