Chapter 21: Quiz - Win Probability Models

Instructions

Choose the best answer for each question. Questions cover WP model fundamentals, calibration, and applications.

Section 1: Win Probability Fundamentals (Questions 1-10)

Question 1

Win probability at any point in a game is:

A) The historical frequency of similar situations B) A conditional probability given the current game state C) Always 50% at game start D) Only dependent on the score

Question 2

Which factor has the LARGEST impact on win probability?

A) Down and distance B) Score differential C) Field position D) Timeouts remaining

Question 3

At the start of an evenly-matched game, the home team's win probability should be:

A) Exactly 50% B) Slightly above 50% due to home field advantage C) Dependent only on the pregame spread D) Unable to be determined

Question 4

The game state space in football includes all EXCEPT:

A) Score differential B) Time remaining C) Player fatigue levels D) Field position

Question 5

Why is logistic regression commonly used for win probability?

A) It's the most accurate model B) It naturally outputs probabilities between 0 and 1 C) It requires the least data D) It's the newest algorithm

Question 6

A team leading by 14 with 2 minutes remaining should have WP:

A) Exactly 100% B) Very high but not 100% (upsets can happen) C) 50% (anything can happen) D) Depends only on field position

Question 7

The relationship between score differential and WP is:

A) Linear B) Non-linear (sigmoid shape) C) Exponential D) Constant

Question 8

Which game state change typically causes the LARGEST WP swing?

A) Gaining 5 yards on first down B) A touchdown when trailing by 7 C) A punt from midfield D) Using a timeout

Question 9

Time remaining affects WP by:

A) Making score differential more important late in games B) Making all situations equally important C) Only mattering in the 4th quarter D) Having no effect on WP

Question 10

Pregame win probability should be influenced by:

A) Only home field advantage B) Team strength differential and home field C) Only the Vegas line D) Historical head-to-head record only

Section 2: Model Building (Questions 11-17)

Question 11

Which features are MOST important for a WP model?

A) Player names and jersey numbers B) Score differential, time, field position, possession C) Stadium capacity and weather D) Conference affiliation

Question 12

Feature engineering for WP models should include:

A) Raw features only B) Interaction terms (e.g., score × time remaining) C) Only linear transformations D) Player-specific features

Question 13

Gradient boosting WP models compared to logistic regression:

A) Are always worse B) Can capture non-linear relationships automatically C) Require less training data D) Are more interpretable

Question 14

The "possession_score_diff" feature represents:

A) Total points scored in possession B) Score difference from possessing team's perspective C) Historical possession efficiency D) Time of possession

Question 15

When training a WP model, the target variable is:

A) Final score differential B) Whether the home team won (binary) C) Total points scored D) Margin of victory

Question 16

Which regularization is appropriate for WP logistic regression?

A) L1 only B) L2 only C) L1 or L2 depending on feature count D) No regularization needed

Question 17

Neural network WP models should have output:

A) Raw score B) Probability via sigmoid activation C) Integer class label D) Confidence interval

Section 3: Calibration (Questions 18-24)

Question 18

A well-calibrated WP model means:

A) High accuracy on test set B) Predicted probabilities match observed frequencies C) Low computational cost D) Simple interpretability

Question 19

If a model predicts 70% WP for 100 situations, how many should result in wins for good calibration?

A) Exactly 70 B) Approximately 70 C) At least 90 D) Between 50 and 100

Question 20

Expected Calibration Error (ECE) measures:

A) Average absolute calibration error across bins B) Maximum prediction error C) AUC score D) Log loss

Question 21

Isotonic regression for calibration:

A) Retrains the entire model B) Maps raw predictions to better-calibrated ones C) Only works with logistic regression D) Requires new features

Question 22

The Brier Score for WP models measures:

A) Average squared error between prediction and outcome B) Calibration only C) Discrimination only D) Feature importance

Question 23

A model with good AUC but poor calibration:

A) Is useless B) Ranks situations well but gives wrong probability values C) Should be retrained from scratch D) Has overfitting issues

Question 24

Maximum Calibration Error (MCE) identifies:

A) Average model error B) The worst-calibrated prediction bin C) Computational limits D) Overfitting degree

Section 4: Win Probability Added (Questions 25-28)

Question 25

Win Probability Added (WPA) is calculated as:

A) WP_before - WP_after B) WP_after - WP_before C) (WP_before + WP_after) / 2 D) Final WP - Initial WP

Question 26

A play with WPA = +0.25 means:

A) The team gained 25 yards B) Win probability increased by 25 percentage points C) The play was 25% successful D) The team scored

Question 27

WPA differs from EPA because:

A) WPA is context-dependent, EPA is context-neutral B) EPA is better for player evaluation C) WPA only applies to scoring plays D) Both A and B

Question 28

Total game WPA for the winning team should be:

A) +1.0 (started at 0.5, ended at 1.0) B) Variable depending on game C) +0.5 always D) Dependent on margin of victory

Section 5: Applications (Questions 29-35)

Question 29

Fourth-down decision analysis using WP compares:

A) Go, punt, and field goal expected WP values B) Only go vs. punt C) Historical success rates D) Coach preferences

Question 30

The "break-even" conversion rate is:

A) Where going for it equals punting in expected WP B) Historical average conversion rate C) 50% always D) League average

Question 31

WP-based analysis suggests going for it on 4th down more often because:

A) Coaches are too conservative B) The WP cost of failed attempts is often less than punt WP loss C) All fourth downs should be conversion attempts D) Field goals are never optimal

Question 32

Leverage index in WP analysis measures:

A) Physical force of plays B) How much a situation magnifies play importance C) Betting odds D) Player strength

Question 33

Late-game scenarios have high leverage because:

A) Players are tired B) Each play has larger WP impact C) More penalties occur D) Crowds are louder

Question 34

Real-time WP systems require:

A) Only final scores B) Play-by-play data with game state C) Only pre-game predictions D) Player tracking data

Question 35

WP models are useful for ALL EXCEPT:

A) In-game decision making B) Identifying clutch performances C) Predicting exact final scores D) Post-game analysis

Answer Key

Section 1: Fundamentals

  1. B - Conditional probability given game state
  2. B - Score differential has largest impact
  3. B - Slightly above 50% for home team
  4. C - Fatigue not typically modeled in game state
  5. B - Naturally outputs probabilities
  6. B - Very high but not 100%
  7. B - Non-linear sigmoid relationship
  8. B - Touchdown when trailing
  9. A - Score diff more important late
  10. B - Team strength and home field

Section 2: Model Building

  1. B - Score, time, field position, possession
  2. B - Include interaction terms
  3. B - Captures non-linear relationships
  4. B - Score diff from possessor's view
  5. B - Binary win outcome
  6. C - L1 or L2 depending on situation
  7. B - Sigmoid for probability

Section 3: Calibration

  1. B - Predictions match observed frequencies
  2. B - Approximately 70
  3. A - Average absolute calibration error
  4. B - Maps raw predictions
  5. A - Average squared error
  6. B - Ranks well but wrong values
  7. B - Worst-calibrated bin

Section 4: WPA

  1. B - WP_after - WP_before
  2. B - Increased by 25 percentage points
  3. D - Both A and B are correct
  4. A - From 0.5 to 1.0 = +0.5 (or pregame WP to 1.0)

Section 5: Applications

  1. A - Go, punt, field goal comparison
  2. A - Where options are equal in expected WP
  3. B - Failed attempt cost often < punt WP loss
  4. B - Situation importance magnification
  5. B - Larger WP impact per play
  6. B - Play-by-play data required
  7. C - Can't predict exact final scores

Scoring Guide

  • 30-35 correct: Excellent! Ready for WP system development
  • 24-29 correct: Good understanding, review weak areas
  • 18-23 correct: Solid foundation, more practice needed
  • Below 18: Review chapter material before proceeding