Lecture 6: The “Other” Option

Stat 165, Spring 2025

Slides credit: Jacob Steinhardt

Warm-up Question

“Which NBA player will have the highest �points per game (PPG) between October �20th and October 27th, 2021?”

My Forecast

• Giannis Antetokounmpo 19%
• Steph Curry 17%
• Luka Doncic 16%
• Kevin Durant 13%
• LeBron James 12%
• Other 23%

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Does this seem reasonable to you? What would you change?

The Result

Top scorer: Ja Morant��(Second-highest scorer also �wasn’t on the list.)

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Retrospective: my forecast was pretty �bad. What could I have done better?

The “Other” Option

Two general lessons:

• The “Other” choice comprises a lot of possible outcomes, and so sometimes has surprisingly high probability.�
• Many “bad” forecasts come from not sufficiently considering the full outcome space.

Other Options in Binary Forecasts

“Will Boris Johnson be charged with a crime by 2023?”

�“Will Magnus Carlson win the 2024 Blitz chess championship?”��“Will Ukraine cede the Donbass region to Russia by Jan 1, 2026?”�

Brainstorming

Generate “Other” options for the following forecast:

• How many three-pointers will Steph Curry attempt in the February 10th, 2023 NBA game between the Golden State Warriors and the Phoenix Suns?

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What are some other prediction questions (binary, or open-choice) where thinking about “Other” options might be important?

MECE Principle

MECE: “Mutually exclusive and collectively exhaustive”

• Write down a set of outcomes that exhausts all possibilities, then consider probability of each one
• (Saw this once already: ways Biden could leave office)
• NBA top scorer: 450 total players, �not practical to list all��
• But can still be helpful…

MECE Applied to NBA Scorers

• First pass: there are 30 teams, hence 30 “best players” on a team
• The 5 superstars (Giannis / Curry / etc.) only covered ⅙ of these
• So should have assigned significant probability to the other ⅚
• To go further:
1. 5 superstars
2. 25 other “best players”
3. 30 second-best players
4. 120 other starters
5. 270 bench players
• To apply MECE, just need to assign a probability to each “category”
• What relative probability would you assign to a-e?

MECE Applied to Box Office Results

Which movie will top the box office the weekend of Nov. 13th, 2021?

Looking at reddit discussions, only 10 movies are even being discussed as major releases: Eternals, Clifford, Dune, Belfast, No Time to Die, + 5 others.

Reddit predicts Eternals $25M, Dune $5M, No Time To Die $4M, all others lower

�What do you think would be a reasonable probability to assign to everything outside these top 3?

MECE + Programming

• NBA example: Instead of explicitly splitting into tiers a-e, come up with a simple heuristic to estimate relative probabilities
• My heuristic: how many weeks last �season did that player come on top?�
• Top 5 scorers: Curry led 5x, �Beal 4x, Lillard 1x
• Other 8 weeks: PPG leader was�not in the top 5 season scorers

Another Perspective: Noise

• 1 week is a short time interval, only a few games�
• Basketball is a high-variance game�
• How could we quantify the noisiness?

Variation in Single-Game Points for Top 6 Scorers

Standard deviation: around 30 points���1 week = ~4 games. Stdev becomes �30 / sqrt(4) = 15

How much does the top scorer win by each week?

• Jan. 4th: Curry 149, Brown 137, Tatum 135
• Jan. 11th: Beal 135, LaVine 133, Hayward 117
• Jan. 18th: Lillard 133, Durant 132, Doncic 113�
• Top scorer determined by 12, 2, and 1 points, respectively�
• Much smaller than the 15-point standard deviation�
• Comparison: ~25 players have season PPG average within 10 points of top 1

Aside: Other Options and Cognitive Biases

• Narrative fallacy: “Tendency to frame events some logical coherent order”�
• Disjunction fallacy: “Whole is estimated to have lower probability than sum of parts”�
• Availability bias: “Relying on immediate examples that come to mind.”