The NBA championship is the main basketball championship in the United States. The championship is divided into two sections, the West and East coast conferences, where teams from both sections compete to become the ultimate champions. From research and simple logic, it can be deduced that the team with the least losses in the season eventually go on to win the championship in the playoffs. However, the number of losses, or wins, that a team has does not solely determine the win, since the final games determine the eventual winner. However, the record that a team has indicates the probability of it winning the championship.
This paper will determine an equation that predicts the likelihood of a team winning the championship based on the number of wins that it has. The quadratic equation that will be derived will have three main parts. The first part is the number of losses that a team has in the season, which is represented as x, the second part is the chance of winning the championship, represented as y, and the third part is a constant. For this research, the number of losses that a team has is divided into three sections.
Research indicates that between the years 1990 and 2013, the percentage of teams that won the championship with less than 20 losses was 33.33%, the percentage of teams with 20 - 29 losses was 58.4%, and the percentage of teams with 30 - 39 losses was 8.3%. To calculate this equation, the average number of losses per section is used.
As indicated above, the data collected indicated that, between the years 1990 and 2013, the percentage of teams that won the championship with less than 20 losses was 33.33%, the percentage of teams with 20 - 29 losses was 58.4%, and the percentage of teams with 30 - 39 losses was 8.3%. From this data, three data points can be located, and a quadratic equation can be formed.
Consider the chance of winning the championship as the dependent variable y and the number of losses per season as the independent variable x. From the above statistic, the data table below can be derived.
y=ax2+bx+c
Substituting the values from the above table gives the following three equations:
- 33.3 = 210.25a+14.5b+c
- 58.4=600.25a+24.5b+c
- 8.3=1190.25a+34.5b+c
Subtracting equation (ii) from equation (i) and equation (iii) from equation (ii) gives the following two equations:
- -25.1=-390a-10b
- 50.1=-590a-10b
Subtracting equation (iv) from equation (v) gives:
75.2=-200a, which is solved to give a value of -0.376 for a.
Therefore, a=-0.376.
Substituting the above in equation (iv) gives:
-25.1=146.64-10b, which when solved gives a value of 17.174 for b.
Therefore, b=17.174
Substituting the values of a and b in equation (i) gives:
33.3=210.25(-0.376)+14.5(17.174)+c, which when solved, gives a value of -136.7 for c.
Therefore, the quadratic equation for this problem is: y=-0.376x2+17.174x-136.7
The equation derived above can be used to make predictions on the probability of a team winning the NBA championship based on the number of wins it has already accumulated over the season. This means that an individual can observe the number of losses that a team has already accumulated and predict whether it has a chance of winning the championship. For example, assume that a team has 23 losses in the championship. Using the above equation, the chance of this team winning the championship is given by substituting this figure into the above equation.
y=-0.376x2+17.174x-136.7
x=23
y=-0.376*232+17.174*23-136.7
= 59.398
Therefore, a team with 23 losses has a 59.40% chance of winning the championship.
It should, however, be noted that the equation derived above is not an exact model of the relationship between the variables indicated. As previously stated, the chance of winning the championship is determined by many factors that cannot be purely explained by a mathematical equation. Some teams in the championship have had a very poor record but gone on to win the championship, while other teams have had very good records and still lost the championship in the playoffs. The final meet between the teams, the playoffs, is usually based on the resilience of the team and the win-loss record has little chance of predicting the outcome. In conclusion, it can be said that the probability if winning the championship is a mathematical equation, but other factors also come into play. The above equation can be used with relative accuracy to determine the chances of a team winning the championship, but other factors that cannot be modeled also affect the chances of winning.
