Modeling and Computing Probabilities of NBA Players Shooting Averages: Empirical and Theoretic Distributions
Bibliographic record
Abstract
For our statistic analysis we chose the sports area, namely basketball and NBA. NBA is the most popular basketball association and league in the world. It includes 29 teams - 27 U.S.A. teams and 2 Canadian ones. Besides observing each team's and players' performance there are also many commercial activities related to the NBA games like advertising, selling tickets, selling basketball gears & accessories which serve as a broad field for statistic analysis. Our objective was to collect raw data of 150 randomly chosen NBA players quantitatively, qualitatively and graphically analyze the data and make conclusions which could be used in decision-making process of the NBA association, each coach or for other business related activities. There are many categories NBA players' statistics are collected on. We chose the shooting percentage of a player which means the percentage proportion of made shots over total shots that a player takes in games. In the first part of the project we are analyzing the gathered data to obtain descriptive statistics of our sample and histograms help us to understand the distribution of the data. In the next step we are providing the probabilities of shooting percentages falling into determined intervals. One of the challenges of the project was to hypothesize 3 possible continuous probability distribution functions which we eventually compare to our empirical histogram. In the last part of the project we discuss our observations and make conclusions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".