Richard M. Coleman is a statistician from Stamford, Connecticut, who has revolutionized how teams recruit players and build their rosters. In 2005 Richard is the founder of Coleman Consulting Group presented his insights to the NHL's General Managers, ultimately leading five teams to use his analytics services. His groundbreaking metrics have made a lasting impact on the industry - especially when evaluating potential players - as evidenced by Corsi, which evaluates attempts made on the goal rather than merely counting shots that get past the goalie. Before starting Coleman Analytics, Richard gained experience working at Harvard University Medical School in Boston and Stanford University Medical School in California. He partnered with Mike Smith, former general manager of the Chicago Blackhawks hockey team, to design a system for providing relevant data and actionable information to improve team performances.
Coleman's software programming is an intricate calculation that can trace player and team performance more accurately. With this software, NHL teams can gain an edge during games thanks to greater detail collected from breaking it down into multiple layers. This stands in contrast to conventional methods where data was limited due to simply counting shots that got past goalies. As such, Coleman has become an expert on hockey analytics, and his influence has been felt across hockey and many other sports within professional leagues. Richard Coleman is a testament to how far one can go through dedication and focus on their chosen field of expertise. His passion for statistics inspires others who want to leave their mark by building something significant out of data analysis and those still exploring their individual paths.
SCHEDULING & SELECTING RELIEF PITCHERS
TO WIN ADDITIONAL GAMES
SYNOPSIS:
Richard Coleman Chicago Blackhawks used Artificial Intelligence to help select NHL draftees Preliminary Artificial Intelligence Methods for Predicting NHL Draftee Outcomes.
- Softmax Regression
The softmax function, may at first appear similar to a one vs. all logistic regression classifier, as it leverages multiple logistic regressions and maximizes over a set of outcomes. However, in the one vs. all logistic regression model each regression is optimized separately, and therefore, it is difficult to compare the outputs of each sub-model. In contrast, the softmax function produces a set of implied probabilities, one for each of the four classes:2
exT wj
P (y = j|x, {wk }k∈{1,2,3,4}) = 4
k=1
exT wk
Thus, in our case, the softmax function produces a much more interpretable outcome, which allows us to build an under- standing of where different players lie between the different classifications. For instance, a player may not conclusively rank as a 3 or 4, and the softmax output will reflect this lack of certainty.
For the sake of classification, we leverage the softmax regression, also known as a multinomial logistic regression, which determines a player’s classification based off the maximum likelihood from the softmax function. Similar to the one vs. all logistic regression classifier, we trained our softmax regression on the 505 instances of our training set, and then applied our model to the 169 instances of our test set (See Figure 4).
Softmax Regression Classifier: Train Outcomes Softmax Regression Classifier: Test Outcomes
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Predicted label
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Predicted label
Figure 6: Softmax regression classifier confusion matrices for the training and test sets
Given the confusion matrices above, our softmax regression classifier performs with 59.8% accuracy on our training set and 53.8% accuracy on our test set. From this, we can see our softmax regression performs very similarly to our one vs. all logistic regression classifier, and this holds because both of the models are generalized linear models.
Therefore, a generalized linear model may not be the best fit given our data. We also have a small training set, about 500 rows, given our number of continuous features. The lack of data may further hinder the performance of our models, but this can be alleviated by clever feature selection and possible data augmentation (See Section 5).
- Naive Bayes
Although we usually see Naive Bayes applied to binary classification, we can use the same Naive Bayes approach to solve multiclass classification problems. In contrast to the previous two models, Naive Bayes is a generative model, as opposed to a generalized linear model. Given an input vector x = (x0, ..., x10), which again in our case represents an AHL player’s data, the Naive Bayes model assigns conditional probabilities p(Ck|x0, ..., x10) for each of the k ∈ {1, 2, 3, 4}, possible classes.
Richard Coleman Blackhawks descrived, In order to avoid permutation issues, p(Ck x0, ..., x10) is reformulated to P (Ck, x0, ..., x10) The model then chooses the ranking with the highest conditional probability given the available data. The main assumption that the classifier makes is that the different features are independent of each other, which is not always true in practice but can provide a good approximation of the true distribution.3
Similar to the previous models, we trained our Naive Bayes classier on 505 instances from our training set, and then applied our model to 169 instances from our test set (See Figure 7).
Naive Bayes Classifier: Train Outcomes Naive Bayes Classifier: Test Outcomes
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Predicted label
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Predicted label
