Win Probability in College Football: wp, WPA and vegas_wp (Part V)

Saiem Gilani, Akshay Easwaran, Jared Lee

2026-09-03

Win probability (WP) is the chance the team with the ball wins the game, given the score, time, field position, down, distance and timeouts. Where expected points asks “how many points is this situation worth”, win probability asks the question that actually settles games — and the two can disagree sharply.

WPA — win probability added — is the change in WP across a play, exactly parallel to EPA:

$$\mathrm{WPA} = \mathrm{WP}_{\text{after}} - \mathrm{WP}_{\text{before}}$$

Why not just use EPA?

Because points and wins are the same thing only in the middle of a game.

Down 3 with a minute left, a 12-yard completion to the opponent’s 30 is worth modest EPA — a few tenths of a point. It is worth enormous WPA, because it moves a field goal from unlikely to routine. Conversely, a 60-yard touchdown while up 28 in the fourth quarter is worth large EPA and almost exactly zero WPA. You had already won.

The distinction matters whenever you rank plays or evaluate decisions. EPA is the better measure of performance, because it is not distorted by score and clock. WPA is the better measure of leverage, precisely because it is — a play is worth more WPA exactly when the game state makes it matter more.

What the model uses

The naive model is a gradient-boosted binary classifier over twelve features:

Feature	What it carries
pos_score_diff_start	current score margin
ExpScoreDiff_Time_Ratio	expected margin per second remaining
adj_TimeSecsRem	seconds left in the game
TimeSecsRem	seconds left in the half
is_home	home field
pos_team_receives_2H_kickoff	who gets the ball after halftime
down, distance, yards_to_goal	the situation
pos_team_timeouts_rem_before, def_pos_team_timeouts_rem_before	clock control
period	quarter

Gain-based importance from the shipped booster:

Feature	Gain
pos_score_diff_start	53.1%
ExpScoreDiff_Time_Ratio	25.6%
is_home	11.5%
pos_team_receives_2H_kickoff	3.5%
yards_to_goal	2.0%
adj_TimeSecsRem	1.5%
everything else	< 1% each

Nearly 80% of the model is score margin and score margin scaled by time. That is the correct shape for the problem — football win probability is overwhelmingly about the lead and how long the opponent has to erase it — but it is worth knowing before you over-interpret a WP swing on a 2nd-and-7.

Expected points is an input to win probability

The second-most important feature is built from EP:

adj_TimeSecsRem          <- ifelse(half == 1, 1800 + TimeSecsRem, TimeSecsRem)
ExpScoreDiff             <- pos_score_diff_start + ep_before
ExpScoreDiff_Time_Ratio  <- ExpScoreDiff / (adj_TimeSecsRem + 1)

ExpScoreDiff is the current margin plus what the current drive is worth — in effect, the score once this possession resolves. Dividing by time remaining turns it into “how big is the effective lead, relative to how long is left to do something about it.”

So the four articles before this one are not a detour. The EP model feeds the WP model directly: a better EP estimate is a better WP estimate.

What the numbers look like

Scoring the naive model for a home team with all timeouts:

Situation	WP
1st & 10 own 25, tied, opening drive	0.573
1st & 10 own 25, down 7, Q1	0.318
1st & 10 own 25, up 7, Q1	0.792
1st & 10 own 25, tied, Q4 5:00	0.648
1st & 10 own 25, down 3, Q4 2:00	0.255
4th & 2 opp 35, down 2, Q4 1:00	0.400
1st & goal opp 5, down 4, Q4 0:30	0.846
1st & 10 own 25, up 21, Q4 10:00	0.998

Two of these are worth pausing on.

The opening drive is 0.573, not 0.500. That is home-field advantage, and it is why is_home carries 11.5% of the model’s gain. A tied game is not a coin flip if you are the home team.

1st and goal from the 5, trailing by 4, with thirty seconds left is 0.846. Down by more than a field goal, needing a touchdown, with almost no time — and you are a heavy favourite, because you are five yards from the win with four downs to get there. No expected-points figure conveys that. This is precisely the kind of situation where EPA and WPA part company.

library(cfbfastR)
library(dplyr)

pbp <- cfbfastR::load_cfb_pbp(2025)

pbp |>
  dplyr::filter(!is.na(wpa)) |>
  dplyr::select(pos_team, period, clock.minutes, pos_score_diff_start,
                play_text, wp_before, wp_after, wpa, vegas_wp) |>
  dplyr::arrange(dplyr::desc(abs(wpa))) |>
  dplyr::slice_head(n = 10)

Sorting by abs(wpa) is the quickest way to find the plays that decided a season.

WPA and its edge cases

wp_after = wp_before + wpa, and the defensive view is simply 1 - wp_after — win probability is zero-sum in a way expected points is not.

Two overlays are applied that a naive difference would get wrong:

• Turnovers. Possession changes hands, so the raw model output is for the other team. WPA is computed against the complement, the same way EPA negates expected points across a change of possession.
• End of half and end of period. A play that ends a half does not hand the next situation to anyone in the usual sense; wpa_half_end handles the transition so the last snap of a half is not credited with a phantom swing.

These are the same two places EPA needs care, for the same reason.

vegas_wp: what the market knew

The naive model treats both teams as anonymous. Kickoff between the best team in the country and the worst is 50/50 plus home field, because nothing in those twelve features says who is playing.

That is a defensible choice — it measures in-game leverage without prejudice — but it is wrong as a forecast. So a second model adds one feature:

elapsed_share <- pmax((3600 - adj_TimeSecsRem) / 3600, 0)
spread_time   <- pos_team_spread * exp(-4 * elapsed_share)

spread_time is the pre-game line, exponentially decayed as the game runs down. The market’s opinion should dominate before any football has been played, and count for less once sixty minutes of evidence exist. This is a faithful port of the nflfastR / sportsdataverse-py construction, decay constant included.

Game point	adj_TimeSecsRem	Elapsed	spread_time (7-point line)
Kickoff	3600	0.00	7.00
End of Q1	2700	0.25	2.58
Halftime	1800	0.50	0.95
End of Q3	900	0.75	0.35
2:00 left	120	0.97	0.15
Final gun	0	1.00	0.13

The feature decays much faster than its influence

It is tempting to read that table as “by halftime the spread counts for 13% of what it did at kickoff.” That is wrong, and it is worth understanding why.

spread_time is an input. What matters is the model’s response to it, which is a learned, non-linear function — and a tree ensemble is free to react sharply to small values. Measuring the actual effect, as the gap between vegas_wp and the naive wp in an otherwise identical state, expressed as a share of the same gap at kickoff:

Line	Kickoff	Q1 end	Halftime	Q3 end	Q4 10:00
+7	100%	61%	62%	27%	−15%
+10	100%	70%	55%	28%	16%
+14	100%	84%	64%	36%	23%
+21	100%	85%	67%	43%	31%
−14 (underdog has ball)	100%	99%	82%	61%	50%

Roughly 55–80% of the spread’s influence survives to halftime, not 13%. The model compensates for the shrinking feature by responding to it more steeply. The exponential decay sets the scale the model trains against; it does not set the weight the model gives it.

The two models do not share a baseline

That table has a trap in it, and it is worth being precise because the obvious reading is wrong.

wp_spread is well behaved in spread_time. Sweeping the feature from −20 to +20 with the state held fixed, win probability rises essentially monotonically at every point in the game — 0.11 to 0.91 at kickoff — with only a handful of tiny decreasing steps out of eighty. A bigger favourite does not get a lower win probability. There is no reversal.

What actually happens is that the two models disagree about the pick’em case. Setting spread_time to exactly zero and comparing:

Game point	wp (naive)	wp_spread at spread_time = 0	Gap
Kickoff	0.573	0.499	−0.074
Halftime	0.595	0.517	−0.077
End of Q3	0.617	0.537	−0.080
Q4 10:00	0.624	0.547	−0.078
Q4 2:00	0.694	0.636	−0.058

A constant offset of roughly −0.08, present everywhere.

This is not a bug — it is the two models answering different questions. A pick’em line for the home team means the market rates the visitor as the better side by about a field position’s worth of home advantage. So wp_spread is right to say 0.50, and wp is right to say 0.573 for an average home team. They disagree because “no spread information” and “a spread of zero” are different statements.

The consequence is the practical one:

vegas_wp − wp is not the market’s contribution. It is the market’s contribution plus a −0.08 baseline difference between two separately-trained models. For a modest line late in a game, where the decayed spread_time is worth only a few hundredths, the offset dominates and the difference goes negative — which looks like the spread reversing sign and is nothing of the kind.

Practical guidance:

• Use wp or vegas_wp for a question, and stay in one of them. They are two coherent models, not a model and an adjustment.
• Do not difference them. The quantity that comes out is dominated by a baseline offset, not by the spread.
• vegas_wp adds the most where the line is large and the game is young, which is exactly where you would want it.

This is the same split nflfastR draws between wp and vegas_wp, and cfbfastR keeps wp_before completely unchanged — vegas_wp is added alongside rather than replacing it, with vegas_wpa and vegas_wp_after derived using the same turnover and half-end overlays.

Two sign conventions that must agree

This is the sort of thing that produces a confidently backwards win probability chart:

• CFBD’s spread is negative when the home team is favoured.
• The model reads positive spread_time as the team in possession being favoured.

Those are not the same convention, and the conversion depends on who has the ball. The mapping was verified across 83 games rather than assumed — worth knowing if you build spread_time yourself.

When is vegas_wp NA?

Wherever the game has no pre-game line: the ESPN play-by-play path, and CFBD before 2013. The column is added as NA rather than the stage failing, so filter on it rather than assuming it is populated.

# in-game leverage, team-agnostic -- use for play and decision evaluation
pbp$wp_before

# forecast that knows who is playing -- use for "should they have won?"
pbp$vegas_wp

Which should you use? For evaluating a decision or a play’s leverage, the naive wp is usually right: it asks what this situation is worth to anybody. For “how surprising was this result”, vegas_wp is right, because a 14-point comeback against a 21-point favourite is a different event from the same comeback against an even opponent.

Limits

• Neither model knows anything about the teams beyond the spread. The naive model knows nothing at all; vegas_wp knows only the market’s pre-game number.
• No injury, weather, or personnel information enters either.
• Overtime is not modelled in the same framing.
• The tails are the hardest part. A model trained on 2.2 million plays sees very few genuine 0.99 → 0.20 collapses, so extreme values are the least well-estimated. Treat 0.997 and 0.999 as “almost certainly won”, not as a meaningful ordering.
• Timeouts are in the model but carry under 1% of gain, which is probably an underweight relative to how much late-game coaches agonise over them.

Seeing it applied

Every game page on Game on Paper renders the win probability chart for that game, with the play-by-play beneath it showing the WP swing on each snap — the plays with the largest |wpa| are the ones the chart’s cliffs correspond to.

Frequently asked

What is a good WPA for a single play? Anything above ±0.10 is a genuinely big play; ±0.30 is a game-turning one. Regular-season games are usually decided by a handful of plays above 0.15.

Why is win probability not 50% at kickoff? Home-field advantage. The naive model puts the home team near 0.57 in a tied game on the opening drive. With vegas_wp, the spread moves it further.

What is the difference between wp and vegas_wp? wp ignores who is playing; vegas_wp adds the pre-game spread, decayed as the game progresses. vegas_wp is NA when no line is available.

Can win probability be wrong? It is a probability, not a prediction. A team at 0.95 loses one time in twenty, and over a season that will happen many times. The model is wrong only if teams at 0.95 fail to win about 95% of the time.

Next

Part VI covers the derived surfaces built on these two models — completion probability and CPOE, expected pass rate (xpass / pass_oe), the field goal and two-point models, fourth-down decisions, and QBR.

Data and artifacts

• Models — cfb_model_artifacts (wp_naive.ubj, wp_spread.ubj)
• Season play-by-play — cfbfastR-data
• Source — cfbfastR · sportsdataverse-py
• 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.