CPOE, xpass, Field Goals and Fourth Downs: The Derived Models (Part VI)

Saiem Gilani, Akshay Easwaran, Jared Lee

2026-09-03

Expected points and win probability are the foundation. Everything in this article is built on top of them, and all of it ships in the same cfb_model_artifacts bundle.

There is a useful distinction to draw first. Some of these are models — they predict a thing and you read the number. Others are analytic surfaces: they build the game state that would follow a choice, score it with the WP model, and compare. Fourth down and the two-point decision are surfaces, and they are ports of cfb4th.

The bundle at a glance

Artifact	Objective	Features	Produces
ep_model	multi:softprob (7)	8	ep_before, ep_after, EPA
wp_naive	binary:logistic	12	wp_before, wpa
wp_spread	binary:logistic	13	vegas_wp
cfb_cp_model	binary:logistic	8	cp, cpoe
xpass_model	binary:logistic	7	xpass, pass_oe
fg_model	binary:logistic	5	field-goal probability
two_pt_model	binary:logistic	4	prob_2pt
fd_model	multi:softprob (76)	9	fourth-down gain distribution
qbr_model	reg:squarederror	10	QBR

Plus punt_distribution.parquet, which is not a model at all — see below.

Completion probability and CPOE

cp is the probability a given pass attempt is completed, from down, distance, field position, score, clock, home field, period and a passing-down indicator. CPOE is the difference between what happened and what was expected, on a percentage-point scale:

$$\mathrm{CPOE} = 100 \times (\text{completion} - \mathrm{cp})$$

Situation	cp
1st & 10, own 25	0.639
3rd & 3, opponent 40	0.595
2nd & 20, own 20	0.627
3rd & 12, own 30	0.489

CPOE is the standard way to separate a quarterback’s accuracy from his situation. A 65% completion rate throwing 3rd-and-12s is a much better performance than 65% throwing 1st-and-10s, and CPOE is what says so.

Note that the model has no receiver, pressure, or air-yards input — it is a situational baseline, not a throw-difficulty model. A quarterback checking down constantly will post good CPOE.

Expected pass rate (xpass and pass_oe)

xpass is the probability a play is a pass, given the situation — a model of tendency, not of quality. pass_oe (pass rate over expected) is 100 * (pass - xpass), and measures how much more pass-happy a team is than its situations warrant.

Situation	xpass
1st & goal, opponent 3	0.141
2nd & 2, own 33	0.247
3rd & 2, opponent 40	0.255
1st & 10, own 25	0.373
2nd & 8, own 27	0.536
3rd & 8, opponent 40	0.782

The spread is the point: 14% on 1st and goal from the 3, 78% on 3rd and 8. Any raw pass-rate statistic is mostly measuring which of these situations a team found itself in. pass_oe removes that.

An era-encoding trap

The xpass model uses an ordinal era feature cutting at 2006 / 2013 / 2017. The FG, two-point and QBR models use one-hot era0–era3 cutting at 2006 / 2013 / 2020.

Different encodings and different cutpoints, in the same bundle. If you score these models by hand, build each one’s era feature from its own rule — reusing one for the other is silent and wrong. cfbfastR handles this internally; it is listed here because it is exactly the kind of thing that survives a code review and fails in production.

The field goal model

Five features: yards_to_goal and the one-hot era. Kick distance is yards_to_goal + 17.

yards_to_goal	Kick	P(make)
2	19	0.956
10	27	0.893
17	34	0.809
20	37	0.754
25	42	0.675
30	47	0.614
33	50	0.542
38	55	0.455
43	60	0.366
48	65	0.366

A 50-yarder is a coin flip, which is a useful number to carry around.

Era matters, and it is not a rounding effect. Kicking has genuinely improved, and the model captures it — the same 42-yard attempt across the four eras:

Era	P(make), 42 yards
era0 (pre-2006)	0.556
era1 (2006–2012)	0.598
era2 (2013–2019)	0.612
era3 (2020+)	0.675

Twelve percentage points from the oldest era to the current one. The era features carry about 20% of the model’s gain between them, so scoring a historical kick with era3 — or a modern one with era0 — is a real error, not a nicety.

The tail runs out at 57 yards. From yards_to_goal 40 outward the model returns a constant 0.3656 — a 57-yard and a 70-yard attempt get identical probabilities. Nobody attempts many 65-yarders except in desperation, so there is nothing to learn from and the model extrapolates flat. Treat anything past a 57-yard kick as “the model has run out of evidence” rather than an estimate.

Two small monotonicity violations. Across 58 steps the curve rises twice where it should fall: a 49-yard kick is rated 0.5882 against 0.5647 for a 48-yarder, and 51 yards beats 50. Both are sub-3-point artifacts of tree splitting rather than anything meaningful, but if you are differencing adjacent yard lines — as the fourth-down surface does when it weighs a make against a miss — be aware the curve is not strictly monotone.

The model also has no kicker identity, weather or altitude input. A kick in Laramie and a kick in a dome get the same number.

The two-point model, and an honest caveat

Four features: posteam_spread, posteam_total, pos_score_diff, era. It produces prob_2pt, which feeds the two-point decision surface — two_pt_wp, xp_wp, two_pt_wp_diff and two_pt_recommendation.

This model does not work, and it is worth showing exactly how rather than gesturing at a caveat.

Sweeping each feature with the others held at realistic values:

Feature	Values swept	prob_2pt
pos_score_diff	−14 → +14	0.487 … 0.578 … 0.557
posteam_spread	−28 → +28	0.572 … 0.592
posteam_total	35 → 75	0.578 at every value
era	0 → 3	0.578 at every value

The whole model moves between 0.487 and 0.592. It is very nearly a constant.

Three specific problems, from the tree dump:

1. era is never split on. It appears in the feature list and in no tree. Two-point conversion rates have moved over twenty years; this model cannot express that.
2. The posteam_total splits are at 21.375 and 31.875. College football game totals live between about 45 and 65. Every realistic game takes the same branch, which is why sweeping the total from 35 to 75 changes nothing. Those thresholds suggest the training feature was not the game total on the scale it is scored with — a scaling or fill problem upstream, not a modelling choice.
3. The first split is pos_score_diff < -6. Almost every genuine two-point decision happens within a touchdown either way, so in the region that matters the model is flat by construction.

And the level is wrong: it centres on 0.578 where real college two-point conversion rates run closer to 45%. Note its own base_score is 0.4816 — the trees push the prediction above the base rate for every realistic input.

Practical consequence. prob_2pt feeds two_pt_wp, so an optimistic and nearly-constant conversion probability biases the decision surface toward going for two, everywhere, regardless of situation. cfb4th’s rule has no margin — it will recommend two on a difference of 0.0001 — so read two_pt_wp_diff and treat anything under a couple of percentage points as a coin flip, or supply your own conversion probability.

To be clear about where the fault lies: the surface’s arithmetic is sound and was verified bit-identical to sportsdataverse-py to eight decimal places. The problem is entirely the input model. It is a retrain candidate, and until then the recommendation column should not be used on its own.

The fourth-down decision

This is the most elaborate surface in the package, and the 76-class model is the interesting part.

fd_model is a multi:softprob classifier over 76 classes: yards gained, from −10 to +65. It does not predict whether a fourth down is converted. It predicts the whole distribution of what happens if you go for it.

The go branch then:

1. Scores the 76-class distribution for the fourth-down state.
2. Expands the play into one hypothetical game state per outcome — every yardage result gets its own down, distance and field position.
3. Scores each with the win probability model.
4. Averages, weighted by the distribution.

That average is go_wp — the win probability of going for it, integrated over everything that could happen.

The punt branch is different again. cfb4th does not model punts. It joins an empirical distribution of punt end-yardlines from punt_distribution.parquet, expands to one state per landing spot, scores each, and averages. The field-goal branch uses the FG model above, weighting a make against a miss and the field position each produces.

The outputs:

Column	Meaning
go_wp, fg_wp, punt_wp	win probability of each choice
go_wp_diff, fg_wp_diff, punt_wp_diff	each against the best alternative
go_boost	how much going for it gains over the best kicking option
first_down_prob	conversion probability from the distribution
wp_succeed, wp_fail	WP after converting / failing
fourth_down_recommendation	the call

library(cfbfastR)
library(dplyr)

pbp <- cfbfastR::load_cfb_pbp(2025)

pbp |>
  dplyr::filter(down == 4, !is.na(go_boost)) |>
  dplyr::select(pos_team, distance, yards_to_goal, go_wp, fg_wp, punt_wp,
                go_boost, first_down_prob, fourth_down_recommendation) |>
  dplyr::arrange(dplyr::desc(go_boost)) |>
  dplyr::slice_head(n = 20)

Sorting by go_boost finds the fourth downs where going for it was most clearly right — and, sorted the other way, the punts that cost the most.

As with the two-point surface, go_boost is more useful than the recommendation: a 0.001 edge and a 0.08 edge are different decisions, and only the magnitude distinguishes them.

QBR

A regression (reg:squarederror) on ten features, all of which are already EPA components: qbr_epa, sack_epa, pass_epa, rush_epa, pen_epa, plus spread and the one-hot era.

This is worth being clear about, because QBR is often described as a black box. Here it is not a new measurement of anything — it is a re-scaling of EPA components onto the 0–100 scale people recognise, fit to reproduce the published QBR values. Everything it knows, it knows from EPA. If you want to understand why a quarterback’s QBR is what it is, look at his EPA splits; there is nothing else in there.

Everything degrades to NA

A design decision worth knowing about: none of these surfaces fail the pipeline. If a model artifact cannot be fetched, or arrow is missing, or the punt table is unavailable, or the game has no pre-game line, the columns are added as NA rather than the stage erroring.

This means you must check for NA rather than assuming a column is populated — particularly vegas_wp and the two decision surfaces, which need a spread. The upside is that a network problem degrades your play-by-play instead of destroying it.

pbp |>
  dplyr::summarise(dplyr::across(
    c(EPA, wpa, vegas_wp, cpoe, xpass, go_boost),
    ~ mean(is.na(.x))
  ))

Seeing it applied

Game on Paper surfaces most of this per game: the win probability chart, per-play EPA, and fourth-down decision context. Its glossary defines the derived metrics in the same terms used here.

Frequently asked

What is CPOE in college football? Completion percentage over expected — the gap between a passer’s actual completions and what the situation predicted, in percentage points. It separates accuracy from difficulty of situation.

What is pass rate over expected (pass_oe)? How much more often a team passes than its down, distance, score and clock suggest. It measures aggression, not effectiveness.

How accurate is the college field goal model? In the modern era (era3, 2020+) it gives about 81% at 34 yards and 54% at 50. Older eras are materially lower — 42 yards is 0.68 in era3 against 0.56 in era0. It has no kicker, weather or altitude input, and flattens beyond roughly 57 yards where data runs out.

Should I trust two_pt_recommendation? No, not on its own. The underlying prob_2pt model is nearly constant at about 0.578, against real college rates closer to 45%, so the surface is biased toward going for two. Read two_pt_wp_diff and treat small margins as coin flips.

Should I trust fourth_down_recommendation? Use go_boost instead. The recommendation has no margin, so it treats a 0.0001 edge as a decision.

The series

1. Expected points: how the model works
2. How the model is built
3. A history of expected points models
4. What is EPA?
5. Win probability, WPA and vegas_wp
6. CPOE, xpass, field goals and fourth downs — this article

Data and artifacts

• Models — cfb_model_artifacts
• Season play-by-play — cfbfastR-data
• Source — cfbfastR · sportsdataverse-py · cfb4th
• Applied, live — Game on Paper
• Raw API — CollegeFootballData.com, courtesy of @CFB_data

Citation

Gilani, S., Easwaran, A., Lee, J., and Hess, E. (2026). cfbfastR: Access College
Football Play by Play Data. R package version 3.0.0.9000.
https://cfbfastr.sportsdataverse.org

Authors, contributors and related SportsDataverse packages are listed on the package home page.