Modeling  ·  Applied statistics  ·  Machine learning

Measure uncertainty. Manage risk.

Build and employ apps and methodologies to deliver solutions and solve problems.

Products

Research

Research in progress

Inference workbench

Regression and Bayesian methods.

Research future

Cliodynamics

Quantitative modeling in theoretical history.

Sample output

Real output from the models, 2025 NFL season. Static snapshot.

Weekly player projections

2025 · Week 20 · DK
Player Pos Team Opp Salary Pred 70% interval Value
Puka NacuaWRLARCHI $9,00023.113.6 – 32.72.6
Christian McCaffreyRBSFSEA $8,80022.612.8 – 32.32.6
Drake MayeQBNEHOU $6,30020.39.8 – 30.83.2
Matthew StaffordQBLARCHI $6,60019.311.4 – 27.22.9
Jaxon Smith-NjigbaWRSEASF $8,50019.39.7 – 28.82.3

Every projection carries a 70% interval. Value is points per thousand of salary.

Interval honesty

holding

A 70% interval should contain the real result 70% of the time. Across the 2025 mid-season weeks it averaged 0.60.

promised 0.70 W4 W17

Reported openly — 13 mid-season weeks, averaging about 10 points below the promise.

Where the model leans

watch

Season-average gap between prediction and result, per player. Negative means the model under-predicted — these five it was most cautious about.

  • Puka Nacua WR · LAR−4.8
  • DJ Moore WR · CHI−3.3
  • Colston Loveland TE · CHI−2.9
  • Drake Maye QB · NE−2.6
  • Christian McCaffrey RB · SF−2.6

545 players tracked · 64 lean-in · 215 fade. The model over-predicts more often than not, which is what the watch flag tracks.

The approach

Applied statistics and machine learning methods for problem-solving. Distribution sampling, conformal prediction, regression, and various other statistical techniques.