# PREDICTING the outcomes of sporting events

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4 CS 229 FINAL PROJECT, AUTUMN Win Classification Algorithms Algorithm Training Accuracy Test Accuracy Benchmark Logistic Regression SVM (RBF kernel, Cost = 10) AdaBoost (65 iterations) Random Forest(500 trees, Depth = 11) Gaussian Naive Bayes game. In order to explore this theory, we partitioned our test season into 4 equal sized chronological blocks, and tested our algorithm on games occurring within each of these 4 sections using all games up to that point to calculate a teams statistic feature vector. Season Quarter Log. Regression SVM AdaBoost Random Forest Quarter Quarter Quarter Quarter Fig. 2. Results of Classification Algorithms An interesting observation of this data is that by simply comparing the win percentage of the two teams, we can accurately predict the result of the game 63.48% of the time. This is only 2% less accurate than including an additional 15 features. This result can be attributed to the fact that a teams win percentage inherently has information about how the team has been doing. Additionally, we have found that basketball is a very easy sport to predict, when compared to a sport such as baseball where chance plays a larger role and teams finish the season with win records much closer to 0.5, thus resulting in a very high baseline to surpass. After training and testing each of our classification models on the data, the resulting accuracies essentially all outperformed the baseline set by our benchmark, but by only a small margin. Some of the algorithms such as adaptive boosting and especially random forest also seemed to overfit our data, as seen by the high training accuracy. This is possibly due to the nature of our algorithms having robust decision boundaries, as well as the possibility that past season statistics and games are not a good indicator of how a team performs and how the game in general works in the test season. Fig. 3. Classification Accuracy Over the Course of a Season As seen above, the result was what we expected, with the accuracy during the first quarter of the season being extremely low compared to our results in Section 5.1, and with the accuracy during the final quarter of the season being significantly higher. The accuracy at the end of the season is much higher than the baseline utilizing simply the winloss record, indicating the the data does show potential to represent an aspect of a team not captured by one statistic alone. While our overall prediction accuracies in Section 5.1 seem only marginally better than the baseline, this trend shown by looking at each individual quarter of the season gives an indication that the accuracy can indeed be improved. Utilizing the law of large numbers, we believed that a teams long term performance would eventually regress to the mean and reflect the true ability of each team. As a result, the result of each game would likely be dictated by the difference in their average statistics each game. 5.2 Accuracy of Win Classifications Over Time One aspect of our learning models that we wanted to explore is how they performed over time. Intuitively, our statistics should vary much more at the start of the season, and slowly converge as we obtain more data to reflect a teams true ability to win a 5.3 Win Classification Without Win/Loss Record Feature selection and our baseline has shown us that a team s win-loss record is clearly the best indicator of how well the team will do in future games, but is it possible to still attain that level of accuracy in prediction by simply using the NBA

5 CS 229 FINAL PROJECT, AUTUMN box score aggregates? We tested this hypothesis by re-testing each of our learning models on a feature vector containing all 14 of the original box score statistics. Algorithm Training Accuracy Test Accuracy Benchmark Logistic Regression SVM AdaBoost Random Forest Gaussian Naive Bayes FUTURE WORK Another interesting application of this project could be understanding how the game of basketball has evolved over time and if the features selected for the seasons are the same features selected for modern day basketball. With modern basketball, there are far more advanced statistics outside of the box score that are available which could result in significantly better features to learn on. Additionally, we can further expand our data to tackle the notion that the hot hand fallacy is indeed true, by looking at the difficulty of a players shots given that they are performing well recently. REFERENCES [1] M. Beckler, H. Wang. NBA Oracle [2] A. Bocskocsky, J. Ezekowitz, C. Stein. The Hot Hand: A New Approach to an Old Fallacy Fig. 4. Results of Classification Algorithms Using Only Box Score As seen above, results show that the accuracies obtained from only using feature vectors containing the historical NBA box score aggregates performs reasonably well, but fall short of the benchmark for all models except for logistic regression and SVM. This indicates that box scores alone are not enough to represent a teams ability to win, and that further data is needed to increase our accuracy. 6 CONCLUSION We found that a basketball teams win record plays a central role in determining their likeliness of winning future games. Winning teams win more because they have the ingredients for success already on the team. However, we were surprised that removing the winning record significantly changed classification accuracy. If we consider a teams win record as representative of that teams ability to win, then this implies that the box score statistics fail to completely represent a teams success on the court. This result points to the need for advanced statistics that go beyond the boxscore in order to potentially improve prediction accuracy for close games and upsets. This need explains the growing popularity on advanced statistic sport conferences like the MIT Sloan conference.

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