Moneyball for Football: Early FGs For the Win

Author

Jake Stoetzner

Published

August 13, 2025

1 Introduction

Recently an NFL kicker made a 70 yard field goal in a preseason game. This is a reflection of a larger trend that teams are (1) attempting more “long” field goals and fewer “short” field goals, and (2) making these longer field goals at a higher rate. Additionally, for the 2025-26 season, the NFL is allowing teams to break-in “K-Balls” (kicking balls) before game day which may result in even longer FG attempts this year.

Then while listening to a recent Pardon My Take episode Big Cat posited the question whether an NFL team could take a Moneyball-esque approach to scoring points by only kicking field goals, maxing out defensive players and running jumbo sets until you make FG range.

This got me thinking if you could solely rely on your kicker to score points? In other words: is it possible to create a winning strategy for an NFL or NCAA football team where the offense immediately kicked field goals once inside a defined range?

I approach the question using an Expected Points (“EP”) model that I am calling the MoneyballFB Model. The challenge is that most EP models rely upon historical averages to relate field position to expected points through statistics. Since most teams in the NFL and NCAAF only kick a field goal on 4th down if they are inside of their kicker’s range (and not as a set strategy) the MoneyballFB model proposed below addresses this and other concerns.

2 Summary of Conclusions

Based on the 2018 to 2024 NFL seasons:

92% of NFL field goal attempts are on 4th down
Overall, after analyzing 35,465 drives
- Teams scored a TD 23.4% of the time for 1.64 EP per drive
- Teams scored a FG 15.2% of the time for 0.45 EP per drive
- NFL teams averaged 2.09 EP per drive
Kicking sooner (the Early FG Model) has lower EP per drive than the Traditional Model across all FG distances, FG make probabilities and starting field positions. In other words, it would never make sense to kick a FG outside of the TM limitations that current NFL teams have adopted.
There is no distance (under current NFL kicking skill levels and rules) where “kick immediately” (the Early FG Model) outperforms the Traditional Model
Although no analysis was made for NCAAF, the conclusion NOT to kick Early FGs would likely be the same

3 Traditional Model

Most teams in the NFL and NCAAF use a Traditional Model (“TM”) for offense. A TM offense will only kick a FG if they have the ball inside the field goal kicker’s range and:

it’s late in downs (4th down),
it’s at the end of either half and there is a limited amount of time to score a TD,
to win or tie a game late in the second half to send the game to overtime (“OT”), or
to win or tie a game in OT.

Traditional arguments for a TM offense are as follows:

Expected Points are higher with a TM offense. Kicking a FG early in the downs means you believe that your offense has a low likelihood of scoring and/or a high likelihood of a turnover by keeping possession.
FG is worth less than half the points of a TD. A FG is worth 3 points and a TD + PAT is worth 7. Thus, you would need to score more than twice as often to make a FG only offense work.
Kicking a FG in early downs results in more possessions and time of possession for the other team. Following a make or miss, the opposing team gets the ball after the FG attempt giving them comparatively more possessions during the game. On a made FG, the scoring team kicks off to the opposing team from the kicking team’s 35-yard line in the NFL and NCAA. If a field goal attempt is unsuccessful, possession of the ball is turned over to the opposing team where the line of scrimmage was on the field goal attempt in the NCAA, or at the spot of the kick (the spot where the placekicker made contact with the ball) in the NFL. More possessions leads to more opponent’s points and a tired defense.

4 Expected Points Modeling Overview

A short overview of Expected Points (“EP”) models is necessary. For more in-depth description, check the Notes & Research section at the end of this report. EP describes how many points, on average, a team is expected to score on a possession given a particular field position. Expected points has also been expanded to quantify the value of a particular field position given:

the down and distance,
time remaining, and
expected points on a turnover.

It is no surprise to the casual football fan to know that being closer to the opponent’s end zone and having more favorable down and distance situations increases EP. For example, consider the following:

Team with 1st & 10 at their own 20 yard line. They have a 0.7 EP.
Team makes a 20 yard completion.
Team now has 1st & 10 at their own 40 yard line with an EP of 2.06
EP modeling connects the two states by showing that the 20 yard throw added 1.36 points.

Source: What are Expected Points Added (EPA) in the NFL?

Here is a chart of EP by field position from Advanced Football Analytics for NFL teams:

Expected points for NCAAF by field position from the cfbfastR site:

EP can also be used to find the relative values of downs at particular points on the field or incorporate down and distance with field position to determine EP. Interesting comparisons arise like “1st and 10 is worth about the same as 2nd and 2 for just about every position on the field.”

EP Models generally have 7 scoring possibilities:

Touchdown (7)
Field Goal (3)
Safety (2)
No Score (0)
Opponent Safety (-2)
Opponent Field Goal (-3)
Opponent Touchdown (-7)

The scoring possibilities are combined with a probability and modeled so that EP can be calculated. From the cfbfastR site:

For each play, the multinomial logistic regression model calculates what the probability () of each of those scoring outcomes is and the expected points can be calculated by multiplying each of the scoring event probabilities by their associated point values and summing the products, like so:

As noted above, EP models are based on historical averages and do not take into account actions outside of the Traditional Model approach. Asking Bill Belichick to punt on 1st down from the opponent’s 45 yard line is like asking if the Pope poops in his hat. In other words, that shit never happened.

5 The MoneyballFB Model

The MoneyballFB model compares two approaches:

Traditional Model - play normally; kick only on 4th down per historical behavior vs.
Early-FG Model - kick immediately upon entering your defined FG range

It consists of the following components:

Probability of successfully reaching FG range from any given starting field position.
Probability of making the field goal from that range.
For the Traditional Model, you also need the EP from continuing the drive (including touchdowns, missed field goals, turnovers, punts, safeties).

5.1 Steps for the MoneyballFB Model

1. Build a “Drive Progression” Model

Use play-by-play data (e.g., NFLfastR or NCAA equivalents) to model P(next yard line | current yard line, down, distance).
Run Monte Carlo simulations to estimate:
- The probability of reaching at least the target FG line from each starting position.
- The distribution of field goal distances.

2. Define Field Goal Range & Success Probability

Gather FG attempt data by distance.
Fit a logistic regression (or smoothed curve) of FG make probability vs. distance.
Decide a cut-off (e.g., P(make) ≥ 0.85) as your “range.” This is defined in the code as fg_thresh.

3. Calculate Early FG Model EP

For each starting yard line:

Simulate drive until FG range is reached.
On entry into range, attempt FG immediately.
EP from this approach = P(reach range) × P(FG made) × 3.

4. Calculate Traditional Model EP

Use an existing EP model (yard line → expected points) OR
Simulate traditional play progression with 4th down decision rules.

5. Compare Strategies

Compare EP curves (yard line vs. EP) for both strategies.
Identify:
- Break-even yard lines where early FG EP > traditional EP.
- Conditions that swing advantage (e.g., bad offense, elite kicker, poor weather, game state).

6. Incorporate Game Context

Variance vs. Mean: Early FG might lower variance (good for underdog or late lead protection).
Clock effects: Kicking early gives opponent the ball sooner.
Defense strength: Strong defense makes low-risk points more attractive.
Special teams quality: Elite kicker, bad punting coverage, etc.

5.2 Data

NFL data was obtained from the nflfastR package from 2018 to 2024. Note: for this post, I did not analyze NCAAF data.

Overall, NFL teams scored more points the closer they started to the endzone. For example, starting at the opponents 40-44 was worth 0.5 EP per drive vs starting at midfield or the 50-54 (3.117 vs 2.642).

FG Percentage Kicked by Down
yl_bin	n_drives	td_rate	fg_rate	avg_td_ep	avg_fg_ep	avg_total_ep
00–04	81	85.2%	8.6%	5.963	0.259	6.222
05–09	122	61.5%	27.9%	4.303	0.836	5.139
10–14	163	55.8%	32.5%	3.908	0.975	4.883
15–19	240	52.1%	38.3%	3.646	1.150	4.796
20–24	419	41.3%	29.1%	2.890	0.874	3.764
25–29	315	44.1%	37.8%	3.089	1.133	4.222
30–34	376	40.7%	35.6%	2.848	1.069	3.918
35–39	16749	22.7%	14.2%	1.590	0.426	2.015
40–44	540	33.3%	26.1%	2.333	0.783	3.117
45–49	604	30.6%	27.3%	2.144	0.820	2.964
50–54	974	29.8%	18.6%	2.084	0.557	2.642
55–59	1143	27.8%	18.3%	1.948	0.549	2.496
60–64	1486	27.9%	18.7%	1.950	0.561	2.511
65–69	1649	22.4%	15.6%	1.571	0.468	2.038
70–74	1707	23.1%	15.1%	1.616	0.453	2.069
75–79	1775	19.6%	13.0%	1.372	0.390	1.763
80–84	2759	17.7%	11.2%	1.238	0.337	1.575
85–89	1809	15.8%	9.8%	1.107	0.294	1.400
90–94	1609	16.0%	9.9%	1.122	0.298	1.421
95–99	945	15.2%	7.3%	1.067	0.219	1.286
All Starts	35465	23.4%	15.2%	1.639	0.455	2.094

5.3 Issues with EP Models

EP models are all based on a TM offense that generally won’t kick a field goal in early downs. Since no team that I could find in the NFL or NCAAF regularly kicked FGs early in downs, EP models don’t integrate the early FG approach. Based on the NFL data, almost 92% of the field goal attempts are on 4th down.

EP per Drive by Start Bin + League-wide Overall
down	fg_attempts	percentage
1	186	0.0251998
2	221	0.0299417
3	205	0.0277740
4	6769	0.9170844

5.4 Specifics of the Early FG Model

Initially, I used yardline_100 as my location variable, and restricted the analysis to non-garbage and non-overtime situations. Quick note: yardline_100 is the number of yards from the line of scrimmage to the opponent’s end zone. It’s always from the offense’s perspective, so:

100 = your own goal line (i.e., you’re about to snap from your own 0-yard line).
50 = midfield.
1 = the opponent’s 1-yard line (almost a TD).
0 = the opponent’s end zone (used for scoring plays).

Field goal distance was estimated using the kick_dist variable. In the NFL, the distance of a field goal is equal to the line of scrimmage plus the length of the endzone (10 yards) plus where the hold occurs (estimated at 7 yards). So a total of 17 yards was added to the line of scrimmage.

As a baseline, kick distance is modeled as a smoothed logistic where only the kick distance predicts the make probability.

Then, the minimum make percentage is input using the fg_thresh parameter. This is the minimum probability (based on the logistic model) where a FG could be made a required minimum percentage of the time. If fg_thresh is set to 0.85, kickers in the model must make at a minimum 85% of their kicks from that distance. The Early FG model then is “in range” when the the yards to the opponent’s endzone is within the models required minimum range (yardline_100 ≤ fg_range_min_yd100) and a field goal is kicked. For example, if the the user sets a minimum threshold of 85% makes and that is at the opponents 33 yard line, then once the Early FG model is within this range, the kick is attempted regardless of the down or time remaining in the game.

I used a coarse Markov model for “normal plays” by (down, to-go bucket, yardline bucket) that captures where the offense ends up next and which terminal events occur (TD, INT, FUM, SACK-fumble leading to turnover, Punt, FG attempt, TO on downs, etc.) to end the drive. For the Traditional Model, historical 4th-down behavior governs (i.e., the transition matrix already embeds real-world kick/punt/go for it behavior). That keeps the baseline honest without hard-coding any specific 4th-down model.

Then, compute an EP curve directly from nflfastR’s ep column. For simulation we’ll just roll forward with the empirical transitions until we hit a terminal outcome and assign points:

TD = +7 (the extra point was assumed)
FG_ATT is not guaranteed points; if historical next play is FG_ATT, we’ll simulate the FG using our kicker model (instead of blindly awarding 3).
PUNT, TURNOVER, SAFETY → opponent ball; here we’ll stop the drive and return 0 points for the offense. (This can be expanded to opponent-return EP later.)

Next, simulate the Early FG model. As discussed above, the instant the Team crosses into FG range (yardline_100 ≤ fg_range_min_yd100), attempt a FG. Note: I still use the same empirical transitions to “walk” the ball down the field prior to the fg_thresh, but I intercept when FG range is reached. This means that prior to the early FG zone, both models should look the same.

Finally, I ran head to head simulations calculating the expected points per drive (“EPD”) from a set of starting yard lines for both the Traditional Model and the Early FG Model. Simulations for each model were repeated 10,000 times and the results were compared.

6 Model Outputs

Much of the comparisons between the Early FG model and the Traditional Model are dependent on the minimum FG make probability.

The chart below shows the model and the actual historical FG make probability vs field position. For example, if you set a 50% make probability, then you need to kick from the Opponent’s 40 yard line of closer.

The second chart relates the make probability to the kick distance rather than field positon. Recall that since 17 yards are added for the holder and end zone to the line of scrimmage, a 50% probability of a make equates to a kick distance of 57 yards.

6.1 85% FG Percentage Threshhold

At fg_thresh = 0.85, the range starts around the opponent’s 22 yard line. From those distances, the Traditional Model drives still have a solid chance to convert first downs and push for a TD. This simulation compared kicking a FG immediately once the ball was within range vs the Traditional Model.

85% FG Percentage Threshhold
yardline_100	EP_traditional	EP_earlyFG	EP_diff	pr_3plus_trad	pr_3plus_early
85	3.9605	2.5235	-1.4370	0.5675	0.6725
80	3.9170	2.6570	-1.2600	0.5610	0.6970
75	4.1485	2.5320	-1.6165	0.5935	0.6800
70	4.1500	2.6035	-1.5465	0.5940	0.6865
65	4.0475	2.6085	-1.4390	0.5785	0.6975
60	4.2030	2.5725	-1.6305	0.6020	0.6995
55	4.2825	2.6300	-1.6525	0.6125	0.7120
50	4.3965	2.7085	-1.6880	0.6285	0.7475
45	4.5255	2.7470	-1.7785	0.6475	0.7510
40	4.5910	2.8955	-1.6955	0.6570	0.7885
35	4.8625	2.8915	-1.9710	0.6955	0.8105
30	4.7720	2.8780	-1.8940	0.6820	0.8360
25	5.1495	3.0060	-2.1435	0.7365	0.8800

The table output columns are defined as follows:

yardline_100 Starting field position (yards from opponent’s end zone). Lower numbers = better starting position.
EP_traditional Expected points per drive using historical 4th-down behavior (drive until stopped or choose FG).
EP_earlyFG Expected points if you kick as soon as you’re within range for an ~85% make rate.
EP_diff EP_earlyFG − EP_traditional. Negative means the early FG strategy is worse.
pr_3plus_trad Probability the drive ends with ≥ 3 points under Traditional Model.
pr_3plus_early Same probability under Early FG Model strategy.

6.2 75% FG Percentage Threshhold

75% FG Percentage Threshhold
yardline_100	EP_traditional	EP_earlyFG	EP_diff	pr_3plus_trad	pr_3plus_early
85	4.0385	2.6250	-1.4135	0.5785	0.6930
80	4.2040	2.5775	-1.6265	0.6010	0.6925
75	4.1145	2.5520	-1.5625	0.5885	0.6780
70	4.0300	2.5550	-1.4750	0.5770	0.6950
65	4.1515	2.6355	-1.5160	0.5935	0.6945
60	4.3440	2.6785	-1.6655	0.6220	0.7115
55	4.2570	2.7180	-1.5390	0.6090	0.7360
50	4.3705	2.7240	-1.6465	0.6255	0.7460
45	4.4015	2.7120	-1.6895	0.6305	0.7380
40	4.5100	2.8145	-1.6955	0.6450	0.7975
35	4.8275	2.8380	-1.9895	0.6905	0.8080
30	5.0190	2.9915	-2.0275	0.7170	0.8545
25	5.0940	3.0180	-2.0760	0.7280	0.9020

6.3 65% FG Percentage Threshhold

65% FG Percentage Threshhold
yardline_100	EP_traditional	EP_earlyFG	EP_diff	pr_3plus_trad	pr_3plus_early
85	3.8595	2.5915	-1.2680	0.5525	0.6965
80	3.8760	2.4630	-1.4130	0.5550	0.6590
75	4.2010	2.5565	-1.6445	0.6010	0.6915
70	3.9690	2.5760	-1.3930	0.5690	0.6920
65	4.1435	2.6400	-1.5035	0.5925	0.7160
60	4.2310	2.6120	-1.6190	0.6050	0.7080
55	4.4840	2.7045	-1.7795	0.6410	0.7335
50	4.3200	2.6985	-1.6215	0.6180	0.7415
45	4.3375	2.7810	-1.5565	0.6205	0.7610
40	4.5260	2.8415	-1.6845	0.6480	0.7845
35	4.7970	2.8825	-1.9145	0.6860	0.8155
30	4.7830	2.8875	-1.8955	0.6840	0.8285
25	4.9675	3.0685	-1.8990	0.7105	0.8915

6.4 50% FG Percentage Threshhold

50% FG Percentage Threshhold
yardline_100	EP_traditional	EP_earlyFG	EP_diff	pr_3plus_trad	pr_3plus_early
85	4.0225	2.5815	-1.4410	0.5765	0.6645
80	4.0560	2.5760	-1.4800	0.5800	0.6820
75	4.1775	2.6405	-1.5370	0.5975	0.6875
70	4.0895	2.5535	-1.5360	0.5855	0.6905
65	4.1300	2.5645	-1.5655	0.5910	0.6955
60	4.2970	2.5900	-1.7070	0.6150	0.7060
55	4.2460	2.6705	-1.5755	0.6080	0.7295
50	4.4515	2.6860	-1.7655	0.6365	0.7380
45	4.3155	2.7425	-1.5730	0.6175	0.7555
40	4.6265	2.8590	-1.7675	0.6615	0.7870
35	4.6960	2.8900	-1.8060	0.6720	0.8120
30	4.9795	2.9175	-2.0620	0.7125	0.8305
25	5.0930	2.9860	-2.1070	0.7280	0.8880

7 Minimum FG Make Probability

Having struck out defining specific fg_thresh values, I decided to expand my view to see if the Early FG model ever had higher EP than a Traditional Model. The steps were as below:

Pick a grid of fg_thresh values (0.50 → 0.95).
Pick a set of starting yardline_100 values which is the Team starting field position (30 → 75)
Run both the Traditional Model and Early FG strategies for each combination.
Find the cross-over point (where EP_diff is positive).
Plot the curves an tables so you can visually see where the Early FG starts to make sense.

8 Break-Even Calculation for Early FG Model

To this point, I failed to find a situation where the Early FG model beat the Traditional Model when comparing points per drive. My initial explanation was that NFL kickers aren’t making a high engough percentage of field goals from far enough away. Which brings me to the last question: what make percentage would be required for the Early FG model to break even versus the TM model from a given start, if we commit to kicking at a particular field position? How good would a kicker have to be to make the MoneyballFB Model better than the existing NFL approach?

Turns out there is no real limit.

The plot below is showing that for every tested starting field position and kick distance, the minimum make percentage required for “Early FG” ≥ “Traditional EP” is 100%.

That means:

Even if a kicker could make every single attempt from those distances, the Early FG strategy just barely ties the traditional strategy at best.
At any real-world FG% (<100%), Early FG is always worse in terms of expected points.
The reason is that a traditional drive has upside beyond 3 points (touchdowns, closer FGs, penalties in your favor), while Early FG caps you at 3 points and adds the risk of a miss.

Thus, there is no distance (under current NFL kicking skill levels and rules) where “kick immediately” outperforms the traditional strategy.

Break-even make% for Early-FG to exceed Traditional EP (by start & distance)
start_yl100	kick_dist	frontier_yl100	EP_traditional	pi_reach	p_required_pct	p_model_pct	EP_diff_model	EP_positive
85	45	28	3.500	0.800	100.0%	75.5%	-1.688	NO
85	50	33	3.500	0.767	100.0%	70.6%	-1.876	NO
65	55	38	3.733	0.867	100.0%	62.3%	-2.113	NO
75	50	33	3.900	0.833	100.0%	70.6%	-2.135	NO
65	45	28	3.733	0.700	100.0%	75.5%	-2.148	NO
55	50	33	3.967	0.833	100.0%	70.6%	-2.201	NO
75	45	28	3.900	0.733	100.0%	75.5%	-2.239	NO
85	55	38	3.500	0.667	100.0%	62.3%	-2.253	NO
65	50	33	3.733	0.667	100.0%	70.6%	-2.321	NO
85	60	43	3.500	0.767	100.0%	43.6%	-2.497	NO
55	45	28	3.967	0.633	100.0%	75.5%	-2.532	NO
55	55	38	3.967	0.733	100.0%	62.3%	-2.595	NO
65	60	43	3.733	0.867	100.0%	43.6%	-2.600	NO
95	55	38	4.133	0.800	100.0%	62.3%	-2.637	NO
95	50	33	4.133	0.700	100.0%	70.6%	-2.650	NO
75	55	38	3.900	0.633	100.0%	62.3%	-2.716	NO
95	45	28	4.133	0.567	100.0%	75.5%	-2.850	NO
75	60	43	3.900	0.800	100.0%	43.6%	-2.853	NO
45	45	28	4.900	0.867	100.0%	75.5%	-2.937	NO
95	60	43	4.133	0.900	100.0%	43.6%	-2.956	NO
85	65	48	3.500	0.700	100.0%	23.5%	-3.006	NO
55	60	43	3.967	0.733	100.0%	43.6%	-3.007	NO
65	65	48	3.733	0.967	100.0%	23.5%	-3.051	NO
85	100	83	3.500	1.000	100.0%	11.3%	-3.161	NO
85	75	58	3.500	0.933	100.0%	11.3%	-3.184	NO
85	85	68	3.500	0.933	100.0%	11.3%	-3.184	NO
85	95	78	3.500	0.933	100.0%	11.3%	-3.184	NO
85	70	53	3.500	0.900	100.0%	11.3%	-3.195	NO
75	65	48	3.900	0.900	100.0%	23.5%	-3.265	NO
45	50	33	4.900	0.767	100.0%	70.6%	-3.276	NO
45	55	38	4.900	0.867	100.0%	62.3%	-3.279	NO
55	65	48	3.967	0.867	100.0%	23.5%	-3.355	NO
65	85	68	3.733	1.000	100.0%	11.3%	-3.395	NO
65	95	78	3.733	1.000	100.0%	11.3%	-3.395	NO
65	100	83	3.733	1.000	100.0%	11.3%	-3.395	NO
65	75	58	3.733	0.967	100.0%	11.3%	-3.406	NO
65	70	53	3.733	0.900	100.0%	11.3%	-3.428	NO
75	95	78	3.900	1.000	100.0%	11.3%	-3.561	NO
75	100	83	3.900	1.000	100.0%	11.3%	-3.561	NO
45	60	43	4.900	1.000	100.0%	43.6%	-3.592	NO
95	65	48	4.133	0.767	100.0%	23.5%	-3.592	NO
75	75	58	3.900	0.900	100.0%	11.3%	-3.595	NO
75	85	68	3.900	0.867	100.0%	11.3%	-3.606	NO
55	70	53	3.967	1.000	100.0%	11.3%	-3.628	NO
55	75	58	3.967	1.000	100.0%	11.3%	-3.628	NO
55	85	68	3.967	1.000	100.0%	11.3%	-3.628	NO
55	95	78	3.967	1.000	100.0%	11.3%	-3.628	NO
55	100	83	3.967	1.000	100.0%	11.3%	-3.628	NO
75	70	53	3.900	0.800	100.0%	11.3%	-3.629	NO
95	85	68	4.133	0.967	100.0%	11.3%	-3.806	NO
95	100	83	4.133	0.933	100.0%	11.3%	-3.817	NO
95	75	58	4.133	0.900	100.0%	11.3%	-3.828	NO
95	95	78	4.133	0.867	100.0%	11.3%	-3.840	NO
95	70	53	4.133	0.833	100.0%	11.3%	-3.851	NO
45	65	48	4.900	1.000	100.0%	23.5%	-4.194	NO
45	70	53	4.900	1.000	100.0%	11.3%	-4.561	NO
45	75	58	4.900	1.000	100.0%	11.3%	-4.561	NO
45	85	68	4.900	1.000	100.0%	11.3%	-4.561	NO
45	95	78	4.900	1.000	100.0%	11.3%	-4.561	NO
45	100	83	4.900	1.000	100.0%	11.3%	-4.561	NO

9 Notes & Research

american football - Could an immediate field goal be advantageous in NFL? - Sports Stack Exchange - Link - DB
Field Goal Success Probabilities by Direction | NFL Football Operations - Link - DB
Visualizing NFL Kicker Accuracy Trends (1999-2024) // Conor McLaughlin - Link - DB
Using Ridgeline Plots to Visualize the NFL’s Shift Towards Longer Field Goal Attempts // Conor McLaughlin - Link - DB
Field goal - Wikipedia - Link - DB
Mathematically If a Team Invests in a kicker, could they kick it every drive? : r/NFLNoobs - Link - DB
What are Expected Points Added (EPA) in the NFL | nfelo - Link - DB
Operations research on Football - Link - DB
College Football Expected Points Model Fundamentals - Part I • cfbfastR - Link - DB
College Football Expected Points Model Fundamentals - Part II • cfbfastR - Link - DB
College Football Expected Points Model Fundamentals - Part III • cfbfastR - Link - DB
What is the Predicted Probability of a Field Goal Given Yards - Link - DB
Advanced Football Analytics (formerly Advanced NFL Stats): Expected Point Values - Link - DB
An R package to quickly obtain clean and tidy NFL play by play data • nflfastR - Link - DB

--- title: "Moneyball for Football: Early FGs For the Win" author: "Jake Stoetzner" date: 2025-08-13 format: html: theme: flatly # Bootstrap theme toc: true # Table of contents toc-depth: 3 fig-cap-location: top # Place captions above or below code-fold: false # Don't fold code unless you want to self-contained: true # Embed everything into a single HTML file smooth-scroll: true df-print: paged # Paginate large data frames number-sections: true # Number sections in TOC code-overflow: wrap # Wrap long code lines code-tools: true # Show copy/download buttons for code execute: echo: false # Hide code by default warning: false # Suppress warnings in output message: false # Suppress messages in output cache: true # Cache computations editor: source # Quarto visual editor - source or visual --- ```{r load required packages} #| output: false # install.packages(c("nflfastR","tidyverse","data.table","arrow","mgcv","yardstick")) library(tidyverse) library(lubridate) library(data.table) library(knitr) library(kableExtra) library(nflfastR) library(tidyverse) library(mgcv) library(yardstick) set.seed(42) ``` ```{r custom functions} ``` ## Introduction Recently an [NFL kicker made a 70 yard field goa](https://www.youtube.com/watch?v=2Ofwp5x65C0)l in a preseason game. This is a reflection of a larger trend that teams are (1) [attempting](https://conormclaughlin.net/2025/01/using-ridgeline-plots-to-visualize-the-nfls-shift-towards-longer-field-goal-attempts/) more "long" field goals and fewer "short" field goals, and (2) [making](https://conormclaughlin.net/2025/01/visualizing-nfl-kicker-accuracy-trends-1999-2024/) these longer field goals at a higher rate. Additionally, for the 2025-26 season, the [NFL is allowing teams to break-in "K-Balls"](https://operations.nfl.com/updates/the-rules/approved-2025-playing-rules-bylaws-and-resolutions/) (kicking balls) before game day which may result in even [longer FG attempts this year](https://www.reddit.com/r/nfl/comments/1mmo3n5/cam_littles_improbable_70yard_kick_for_jaguars_is/). Then while listening to a recent [Pardon My Take episode](https://youtu.be/E5ayJ_I4Lro) Big Cat posited the [question](https://youtube.com/clip/Ugkxzpox1dV0FZVm3v52DyV01La-czvzch7r?si=v63WIM9ZYePE89tG) whether an NFL team could take a [Moneyball-esque](https://en.wikipedia.org/wiki/Moneyball_(film)) approach to scoring points by only kicking field goals, maxing out defensive players and running jumbo sets until you make FG range. ```{=html} <iframe width="560" height="315" src="https://www.youtube.com/embed/E5ayJ_I4Lro?si=v63WIM9ZYePE89tG&clip=Ugkxzpox1dV0FZVm3v52DyV01La-czvzch7r&clipt=EJD_Qxjw00c" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen> </iframe> ``` This got me thinking if you could *solely* rely on your kicker to score points? In other words: **is it possible to create a winning strategy for an NFL or NCAA football team where the offense immediately kicked field goals once inside a defined range?** I approach the question using an [Expected Points](https://www.sportsinfosolutions.com/2025/08/13/a-new-expected-points-model/) ("EP") model that I am calling the MoneyballFB Model. The challenge is that most EP models rely upon historical averages to relate field position to expected points through statistics. Since most teams in the NFL and NCAAF only kick a field goal on 4th down if they are inside of their kicker's range (and not as a set strategy) the MoneyballFB model proposed below addresses this and other concerns. ## Summary of Conclusions Based on the 2018 to 2024 NFL seasons: - 92% of NFL field goal attempts are on 4th down - Overall, after analyzing 35,465 drives - Teams scored a TD 23.4% of the time for 1.64 EP per drive - Teams scored a FG 15.2% of the time for 0.45 EP per drive - NFL teams averaged 2.09 EP per drive - Kicking sooner (the Early FG Model) has lower EP per drive than the Traditional Model across all FG distances, FG make probabilities and starting field positions. In other words, it would never make sense to kick a FG outside of the TM limitations that current NFL teams have adopted. - There is no distance (under current NFL kicking skill levels and rules) where “kick immediately” (the Early FG Model) outperforms the Traditional Model - Although no analysis was made for NCAAF, the conclusion NOT to kick Early FGs would likely be the same ## Traditional Model Most teams in the NFL and NCAAF use a Traditional Model ("TM") for offense. A TM offense will only kick a FG if they have the ball inside the field goal kicker's range **and**: - it's late in downs (4th down), - it's at the end of either half and there is a limited amount of time to score a TD, - to win or tie a game late in the second half to send the game to overtime ("OT"), or - to win or tie a game in OT. Traditional arguments for a TM offense are as follows: - **Expected Points are higher with a TM offense.** Kicking a FG early in the downs means you believe that your offense has a low likelihood of scoring and/or a high likelihood of a turnover by keeping possession. - **FG is worth less than half the points of a TD.** A FG is worth 3 points and a TD + PAT is worth 7. Thus, you would need to score more than twice as often to make a FG only offense work. - **Kicking a FG in early downs results in more possessions and time of possession for the other team.** Following a make or miss, the opposing team gets the ball after the FG attempt giving them comparatively more possessions during the game. On a made FG, the scoring team kicks off to the opposing team from the kicking team's 35-yard line in the NFL and NCAA. If a field goal attempt is unsuccessful, possession of the ball is turned over to the opposing team where the line of scrimmage was on the field goal attempt in the NCAA, or at the spot of the kick (the spot where the placekicker made contact with the ball) in the NFL. More possessions leads to more opponent's points and a tired defense. ## Expected Points Modeling Overview A short overview of Expected Points ("EP") models is necessary. For more in-depth description, check the Notes & Research section at the end of this report. EP describes how many points, on average, a team is expected to score on a possession given a particular field position. Expected points has also been expanded to quantify the value of a particular field position given: - the down and distance, - time remaining, and - expected points on a turnover. It is no surprise to the casual football fan to know that being closer to the opponent's end zone and having more favorable down and distance situations increases EP. [For example](https://www.nfeloapp.com/analysis/expected-points-added-epa-nfl/), consider the following: - Team with 1st & 10 at their own 20 yard line. They have a 0.7 EP. - Team makes a 20 yard completion. - Team now has 1st & 10 at their own 40 yard line with an EP of 2.06 - EP modeling connects the two states by showing that the 20 yard throw added 1.36 points. ![](https://www.nfeloapp.com/_next/image/?url=https%3A%2F%2Fimages.ctfassets.net%2Fwwdoup4surp5%2F3cBQ6fY4WA4DVfgQxrmwEP%2F2b569630da2b4f30f07dc0415ae72eca%2FScreen_Shot_2021-10-23_at_5.24.03_PM.png&w=1920&q=75) [Source: What are Expected Points Added (EPA) in the NFL?](https://www.nfeloapp.com/_next/image/?url=https%3A%2F%2Fimages.ctfassets.net%2Fwwdoup4surp5%2F3cBQ6fY4WA4DVfgQxrmwEP%2F2b569630da2b4f30f07dc0415ae72eca%2FScreen_Shot_2021-10-23_at_5.24.03_PM.png&w=1920&q=75) Here is a chart of EP by field position from [Advanced Football Analytics](https://www.advancedfootballanalytics.com/2009/12/expected-point-values.html) for NFL teams: ![](img1.png) Expected points for NCAAF by field position from the [`cfbfastR` site](https://cfbfastr.sportsdataverse.org/articles/college-football-expected-points-model-fundamentals-part-i.html): ![](img2.jpeg) EP can also be used to find the [relative values of downs at particular points on the field](https://www.nfeloapp.com/analysis/expected-points-added-epa-nfl/) or incorporate down and distance with field position to determine EP. Interesting comparisons arise like "[1st and 10 is worth about the same as 2nd and 2 for just about every position on the field](https://www.nfeloapp.com/analysis/expected-points-added-epa-nfl/)." ![](img3.png) [EP Models](https://cfbfastr.sportsdataverse.org/articles/college-football-expected-points-model-fundamentals-part-i.html) generally have 7 scoring possibilities: - Touchdown (7) - Field Goal (3) - Safety (2) - No Score (0) - Opponent Safety (-2) - Opponent Field Goal (-3) - Opponent Touchdown (-7) The scoring possibilities are combined with a probability and modeled so that EP can be calculated. From the [`cfbfastR` site](https://cfbfastr.sportsdataverse.org/articles/college-football-expected-points-model-fundamentals-part-i.html): > For each play, the multinomial logistic regression model calculates what the probability () of each of those scoring outcomes is and the expected points can be calculated by multiplying each of the scoring event probabilities by their associated point values and summing the products, like so: ![](img4.png) As noted above, EP models are based on historical averages and do not take into account actions outside of the Traditional Model approach. Asking Bill Belichick to punt on 1st down from the opponent's 45 yard line is like asking if the Pope poops in his hat. In other words, that shit never happened. ## The MoneyballFB Model The MoneyballFB model compares two approaches: 1. **Traditional Model** - play normally; kick only on 4th down per historical behavior vs. 2. **Early-FG Model** - kick immediately upon entering your defined FG range It consists of the following components: - **Probability of successfully reaching FG range from any given starting field position.** - **Probability of making the field goal from that range.** - For the Traditional Model, you also need the **EP from continuing the drive** (including touchdowns, missed field goals, turnovers, punts, safeties). ### Steps for the MoneyballFB Model **1. Build a "Drive Progression" Model** - Use play-by-play data (e.g., NFLfastR or NCAA equivalents) to model **P(next yard line \| current yard line, down, distance)**. - Run Monte Carlo simulations to estimate: - The probability of reaching at least the target FG line from each starting position. - The distribution of field goal distances. **2. Define Field Goal Range & Success Probability** - Gather FG attempt data by distance. - Fit a logistic regression (or smoothed curve) of **FG make probability vs. distance**. - Decide a cut-off (e.g., P(make) ≥ 0.85) as your "range." This is defined in the code as `fg_thresh`. **3. Calculate Early FG Model EP** For each starting yard line: 1. **Simulate drive until FG range is reached**. 2. On entry into range, **attempt FG immediately**. 3. EP from this approach = P(reach range) × P(FG made) × 3. **4. Calculate Traditional Model EP** - Use an existing EP model (yard line → expected points) *OR* - Simulate traditional play progression with 4th down decision rules. **5. Compare Strategies** - Compare EP curves (yard line vs. EP) for both strategies. - Identify: - Break-even yard lines where early FG EP \> traditional EP. - Conditions that swing advantage (e.g., bad offense, elite kicker, poor weather, game state). **6. Incorporate Game Context** - **Variance vs. Mean**: Early FG might lower variance (good for underdog or late lead protection). - **Clock effects**: Kicking early gives opponent the ball sooner. - **Defense strength**: Strong defense makes low-risk points more attractive. - **Special teams quality**: Elite kicker, bad punting coverage, etc. ### Data NFL data was obtained from the [`nflfastR` package](https://www.nflfastr.com/) from 2018 to 2024. Note: for this post, I did not analyze NCAAF data. ```{r data prep helper} #| echo: false #| output: false seasons <- 2018:2024 # adjust as you like # pbp <- load_pbp(seasons) # write_csv(pbp, file = "/Users/jstoetz/Library/CloudStorage/Dropbox/@projects/p2025-09-moneyball-football/nfl-2018-2024.csv") pbp <- read_csv("/Users/jstoetz/Library/CloudStorage/Dropbox/@projects/p2025-09-moneyball-football/nfl-2018-2024.csv") clean_pbp <- pbp %>% filter(!is.na(yardline_100), !is.na(down), !is.na(ydstogo), qtr <= 4, # ignore OT for first pass !is.na(play_type)) %>% mutate( # standard field goal distance approximation kick_dist = if_else(play_type == "field_goal", yardline_100 + 17, NA_real_), # binning for empirical transitions yl_bin = pmin(20L, pmax(0L, floor((100 - yardline_100)/5))) # 0=own goal line … 20=opp EZ ) ``` Overall, NFL teams scored more points the closer they started to the endzone. For example, starting at the opponents 40-44 was worth 0.5 EP per drive vs starting at midfield or the 50-54 (3.117 vs 2.642). ```{r actual outcomes} # 1) Build drive-level outcomes directly from plays # - start_yl100: yardline_100 on the first offensive snap of the drive # - td_for: did the offense that started the drive score a TD on this drive? # - fg_for: did they make a FG on this drive? drives <- pbp %>% filter(qtr <= 4) %>% # (optional) regulation only group_by(game_id, drive) %>% summarise( start_yl100 = { x <- yardline_100[!is.na(yardline_100)] if (length(x)) x[1] else NA_real_ }, drive_offense = dplyr::first(posteam), # posteam is constant within a drive td_for = any(touchdown == 1 & if ("td_team" %in% names(cur_data_all())) td_team == dplyr::first(posteam) # prefer td_team when available else TRUE), # otherwise touchdown==1 is for the offense fg_for = any(play_type == "field_goal" & field_goal_result == "made" & posteam == dplyr::first(posteam)), .groups = "drop" ) %>% filter(!is.na(start_yl100)) # 2) Compute EP components per drive drives <- drives %>% mutate( ep_td = if_else(td_for, 7, 0), ep_fg = if_else(!td_for & fg_for, 3, 0), # mutually exclusive on a drive ep_total = ep_td + ep_fg ) # 3) Bin by 5-yard increments of the starting field position drive_ep_binned <- drives %>% na.omit() %>% mutate(yl_bin = cut( start_yl100, breaks = seq(0, 100, by = 5), include.lowest = TRUE, right = FALSE, labels = sprintf("%02d–%02d", seq(0,95,5), seq(4,99,5)) )) %>% group_by(yl_bin) %>% summarise( n_drives = n(), td_rate = mean(td_for), fg_rate = mean(fg_for), avg_td_ep = mean(ep_td), # expected points from TDs only avg_fg_ep = mean(ep_fg), # expected points from made FGs only avg_total_ep = mean(ep_total), .groups = "drop" ) %>% arrange(as.numeric(sub("–.*", "", yl_bin))) # sort by bin start # 4) Pretty table #drive_ep_binned %>% # mutate( # td_rate = scales::percent(td_rate, 0.1), # fg_rate = scales::percent(fg_rate, 0.1), # across(starts_with("avg_"), ~round(.x, 3)) # ) %>% # knitr::kable( # align = "c", # caption = "League-wide EP per Drive by Starting Field Position (TD vs FG components)" # ) # Overall (drive-weighted) league averages across ALL starts overall_ep <- drives %>% na.omit() %>% summarise( n_drives = n(), td_rate = mean(ep_td > 0), # proportion of drives that scored a TD fg_rate = mean(ep_fg > 0), # proportion of drives that scored a (made) FG avg_td_ep = mean(ep_td), # expected points from TDs only avg_fg_ep = mean(ep_fg), # expected points from FGs only avg_total_ep = mean(ep_total) # TD + FG (by design here) ) #overall_ep overall_row <- overall_ep %>% mutate(yl_bin = "All Starts") %>% select(yl_bin, n_drives, td_rate, fg_rate, avg_td_ep, avg_fg_ep, avg_total_ep) drive_ep_binned_with_overall <- drive_ep_binned %>% bind_rows(overall_row) %>% mutate( td_rate = scales::percent(td_rate, 0.1), fg_rate = scales::percent(fg_rate, 0.1), across(starts_with("avg_"), ~round(.x, 3)) ) knitr::kable(drive_ep_binned_with_overall, align = "c", caption = "FG Percentage Kicked by Down") %>% kableExtra::kable_classic(full_width = FALSE) ``` ### Issues with EP Models EP models are all based on a TM offense that generally won't kick a field goal in early downs. Since no team that I could find in the NFL or NCAAF regularly kicked FGs early in downs, EP models don't integrate the early FG approach. Based on the NFL data, almost 92% of the field goal attempts are on 4th down. ```{r issues with EP models} fg_by_down <- clean_pbp %>% filter(play_type == "field_goal") %>% group_by(down) %>% summarise( fg_attempts = n(), .groups = "drop" ) %>% arrange(down) knitr::kable(fg_by_down %>% mutate(percentage = fg_attempts / sum(fg_attempts)), align = "c", caption = "EP per Drive by Start Bin + League-wide Overall") %>% kableExtra::kable_classic(full_width = FALSE) ``` ### Specifics of the Early FG Model Initially, I used `yardline_100` as my location variable, and restricted the analysis to non-garbage and non-overtime situations. Quick note: `yardline_100` is the number of yards from the line of scrimmage to the opponent's end zone. It's always from the offense's perspective, so: - *100* = your own goal line (i.e., you're about to snap from your own 0-yard line). - *50* = midfield. - *1* = the opponent's 1-yard line (almost a TD). - *0* = the opponent's end zone (used for scoring plays). Field goal distance was estimated using the `kick_dist` variable. In the NFL, the distance of a field goal is equal to the line of scrimmage plus the length of the endzone (10 yards) plus where the hold occurs (estimated at 7 yards). So a total of 17 yards was added to the line of scrimmage. As a baseline, kick distance is modeled as a smoothed logistic where *only* the kick distance predicts the make probability. Then, the minimum make percentage is input using the `fg_thresh` parameter. This is the minimum probability (based on the logistic model) where a FG could be made a required minimum percentage of the time. If `fg_thresh` is set to 0.85, kickers in the model must make at a minimum 85% of their kicks from that distance. The Early FG model then is "in range" when the the yards to the opponent's endzone is within the models required minimum range (`yardline_100` ≤ `fg_range_min_yd100`) and a field goal is kicked. For example, if the the user sets a minimum threshold of 85% makes and that is at the opponents 33 yard line, then once the Early FG model is within this range, the kick is attempted regardless of the down or time remaining in the game. ```{r Field-goal make model} fg_data <- clean_pbp %>% filter(play_type == "field_goal", !is.na(field_goal_result), !is.na(kick_dist)) %>% mutate(make = as.integer(field_goal_result == "made")) # Smooth logistic via GAM fg_mod <- gam(make ~ s(kick_dist, k = 8), data = fg_data, family = binomial()) p_make_fg <- function(kick_dist) { kick_dist <- pmin(pmax(kick_dist, 15), 70) # clamp reasonable bounds as.numeric(predict(fg_mod, newdata = data.frame(kick_dist), type = "response")) } fg_thresh <- 0.85 # configurable yd100_grid <- 1:80 mk <- p_make_fg(yd100_grid + 17) fg_range_min_yd100 <- max(yd100_grid[mk >= fg_thresh], na.rm = TRUE) ``` I used a coarse [Markov model](https://en.wikipedia.org/wiki/Markov_decision_process) for "normal plays" by (down, to-go bucket, yardline bucket) that captures where the offense ends up next and which terminal events occur (TD, INT, FUM, SACK-fumble leading to turnover, Punt, FG attempt, TO on downs, etc.) to end the drive. For the Traditional Model, historical 4th-down behavior governs (i.e., the transition matrix already embeds real-world kick/punt/go for it behavior). That keeps the baseline honest without hard-coding any specific 4th-down model. ```{r Empirical play progression transitions} # Bucket to-go and yardline: binner <- function(x, cuts) pmin(length(cuts)-1L, pmax(1L, as.integer(cut(x, breaks = cuts, labels = FALSE, include.lowest = TRUE)))) togo_cuts <- c(0, 2, 4, 6, 8, 10, 15, 99) # buckets yl_cuts <- c(seq(0, 100, by = 5)) # 5-yard increments # Identify "next state" after the play: # We'll map the next snap state (or terminal outcome) from nflfastR columns. trans_df <- clean_pbp %>% # Exclude pure special-teams and penalties for the progression matrix; we keep FGs to learn range but remove them here filter(play_type %in% c("run","pass")) %>% mutate( togo_bin = binner(ydstogo, togo_cuts), yl_next = lead(yardline_100), # next snap location (from nflfastR sequence) down_next = lead(down), togo_next = lead(ydstogo), # terminal outcomes td_for = touchdown, turnover = if_else(interception == 1 | fumble_lost == 1, 1L, 0L), to_on_downs = if_else(first_down == 0 & play_type %in% c("run","pass") & (down == 4), 1L, 0L), punt_next = as.integer(lead(play_type) == "punt"), fg_next = as.integer(lead(play_type) == "field_goal"), # score events on *this* play: td_now = as.integer(touchdown == 1), safety_now = as.integer(safety == 1) ) %>% filter(!is.na(togo_bin), !is.na(yl_bin)) # Build empirical transition choices: # We record either: (A) terminal outcome, or (B) a continued state (down_next, togo_next, yl_next). transitions <- trans_df %>% mutate( terminal = case_when( td_now == 1 ~ "TD", safety_now == 1 ~ "SAFETY", turnover == 1 ~ "TURNOVER", to_on_downs == 1 ~ "TODS", punt_next == 1 ~ "PUNT", fg_next == 1 ~ "FG_ATT", TRUE ~ "NONE" ), continue = terminal == "NONE" ) %>% filter(!(is.na(yl_next) & continue)) %>% mutate( togo_bin_next = if_else(continue, binner(togo_next, togo_cuts), NA_integer_), yl_bin_next = if_else(continue, pmin(20L, pmax(0L, floor((100 - yl_next)/5))), NA_integer_), down_next2 = if_else(continue, down_next, NA_real_) ) %>% group_by(down, togo_bin, yl_bin) %>% summarise( n = n(), # Probabilities of terminal outcomes p_TD = mean(terminal == "TD"), p_SAF = mean(terminal == "SAFETY"), p_TOV = mean(terminal == "TURNOVER"), p_TODS = mean(terminal == "TODS"), p_PUNT = mean(terminal == "PUNT"), p_FG = mean(terminal == "FG_ATT"), # Distribution over continued next states next_states = list(tibble( down_next = down_next2[continue], togo_bin_next = togo_bin_next[continue], yl_bin_next = yl_bin_next[continue] )) ) %>% ungroup() sample_next <- function(down, togo_bin, yl_bin) { row <- transitions %>% filter(down == !!down, togo_bin == !!togo_bin, yl_bin == !!yl_bin) if (nrow(row) == 0) return(list(type = "ABSORB", state = NULL)) row <- row %>% slice(1) probs <- c(row$p_TD, row$p_SAF, row$p_TOV, row$p_TODS, row$p_PUNT, row$p_FG) names(probs) <- c("TD","SAFETY","TURNOVER","TODS","PUNT","FG_ATT") p_cont <- max(0, 1 - sum(probs, na.rm = TRUE)) draw <- sample(c(names(probs), "CONTINUE"), size = 1, prob = c(probs, p_cont), replace = TRUE) if (draw != "CONTINUE") return(list(type = draw, state = NULL)) # continue: sample a next (down, togo_bin, yl_bin) from empirical pool pool <- row$next_states[[1]] if (nrow(pool) == 0) return(list(type = "ABSORB", state = NULL)) ix <- sample(seq_len(nrow(pool)), 1) list(type = "CONTINUE", state = pool[ix, ]) } ``` Then, compute an EP curve directly from `nflfastR`'s `ep` column. For simulation we'll just roll forward with the empirical transitions until we hit a terminal outcome and assign points: - `TD` = +7 (the extra point was assumed) - `FG_ATT` is not guaranteed points; if historical next play is `FG_ATT`, we'll simulate the FG using our kicker model (instead of blindly awarding 3). - `PUNT`, `TURNOVER`, `SAFETY` → opponent ball; here we'll stop the drive and return 0 points for the offense. (This can be expanded to opponent-return EP later.) ```{r A simple traditional EP baseline} # helper: map yl_bin back to center yardline_100 estimate for FG distance if needed ylbin_to_yardline100 <- function(yl_bin) { # yl_bin was built from (100 - yardline_100)/5; invert approximately # We'll map to the *mean* inside the bin: yl_lo <- yl_bin*5 yl_hi <- yl_lo + 5 # these are yards FROM own GL to LOS; we want yardline_100 (to opp EZ) yard_from_own <- (yl_lo + yl_hi)/2 yardline_100 <- 100 - yard_from_own yardline_100 } simulate_drive_traditional <- function(start_yl100, max_plays = 100, xp_points = 1, td_points = 6) { # start state: 1st & 10 at start_yl100 down <- 1L togo_bin <- binner(10, togo_cuts) yl_bin <- pmin(20L, pmax(0L, floor((100 - start_yl100)/5))) points <- 0 for (i in 1:max_plays) { res <- sample_next(down, togo_bin, yl_bin) if (res$type == "ABSORB") break if (res$type == "CONTINUE") { down <- as.integer(res$state$down_next) togo_bin <- as.integer(res$state$togo_bin_next) yl_bin <- as.integer(res$state$yl_bin_next) next } if (res$type == "TD") { points <- td_points + xp_points # keep simple; plug your PAT/2pt model if desired break } if (res$type == "FG_ATT") { # Approx kick distance from current yl_bin yl100_now <- ylbin_to_yardline100(yl_bin) kd <- yl100_now + 17 make <- rbinom(1, 1, p_make_fg(kd)) if (make == 1) points <- 3 else points <- 0 break } # PUNT / TURNOVER / TODS / SAFETY -> end drive with 0 for offense (expand later if modeling next-possession EP) points <- ifelse(res$type == "SAFETY", -2, 0) # if you want to charge the offense; usually just 0 EP for offense viewpoint break } points } ``` Next, simulate the Early FG model. As discussed above, the instant the Team crosses into FG range (`yardline_100` ≤ `fg_range_min_yd100`), attempt a FG. Note: I still use the same empirical transitions to "walk" the ball down the field prior to the `fg_thresh`, but I intercept when FG range is reached. This means that prior to the early FG zone, both models should look the same. ```{r Early-FG policy simulation} simulate_drive_early_fg <- function(start_yl100, range_min_yl100 = fg_range_min_yd100, max_plays = 100) { down <- 1L togo_bin <- binner(10, togo_cuts) yl_bin <- pmin(20L, pmax(0L, floor((100 - start_yl100)/5))) for (i in 1:max_plays) { # Check range *before* calling next play (we kick as soon as we're in range) yl100_now <- ylbin_to_yardline100(yl_bin) if (yl100_now <= range_min_yl100) { kd <- yl100_now + 17 make <- rbinom(1, 1, p_make_fg(kd)) return(ifelse(make == 1, 3, 0)) # simplified: offense points only } res <- sample_next(down, togo_bin, yl_bin) if (res$type == "ABSORB") return(0) if (res$type == "CONTINUE") { down <- as.integer(res$state$down_next) togo_bin <- as.integer(res$state$togo_bin_next) yl_bin <- as.integer(res$state$yl_bin_next) next } if (res$type == "TD") return(7) # simple TD+XP if (res$type == "FG_ATT") { # Traditional behavior would attempt; Early-FG would've tried earlier if in range, # but if we haven't been in range yet and a historical FG_ATT appears (rare), simulate it. kd <- ylbin_to_yardline100(yl_bin) + 17 make <- rbinom(1, 1, p_make_fg(kd)) return(ifelse(make == 1, 3, 0)) } # Other terminals => 0 return(0) } 0 } ``` Finally, I ran head to head simulations calculating the expected points per drive ("EPD") from a set of starting yard lines for both the Traditional Model and the Early FG Model. Simulations for each model were repeated 10,000 times and the results were compared. ## Model Outputs Much of the comparisons between the Early FG model and the Traditional Model are dependent on the minimum FG make probability. The chart below shows the model and the actual historical FG make probability vs field position. For example, if you set a 50% make probability, then you need to kick from the Opponent's 40 yard line of closer. ```{r chart make prob vs field position} # Grid of thresholds fg_thresholds <- seq(0, 1, by = 0.05) # Possible LOS yardline_100 values for kicks yl_grid <- 1:80 kick_grid <- yl_grid + 17 # Model probabilities for each possible kick prob_df <- data.frame( yardline_100 = yl_grid, kick_dist = kick_grid, make_prob = p_make_fg(kick_grid) ) # Map threshold → farthest yardline_100 and kick distance range_map <- lapply(fg_thresholds, function(thresh) { in_range <- prob_df %>% filter(make_prob >= thresh) if (nrow(in_range) == 0) { tibble(fg_thresh = thresh, yardline_100 = NA, kick_dist = NA) } else { tibble( fg_thresh = thresh, yardline_100 = max(in_range$yardline_100, na.rm = TRUE), kick_dist = max(in_range$kick_dist, na.rm = TRUE) ) } }) %>% bind_rows() # Empirical FG data by yardline_100 empirical_df <- clean_pbp %>% filter(play_type == "field_goal", !is.na(field_goal_result), !is.na(yardline_100)) %>% mutate( make = as.integer(field_goal_result == "made"), kick_dist = yardline_100 + 17 ) %>% group_by(kick_dist, yardline_100) %>% summarise(make_rate = mean(make), .groups = "drop") # Bar chart for yardline_100 ggplot(range_map, aes(x = fg_thresh, y = yardline_100)) + geom_col(fill = "skyblue", alpha = 0.7) + geom_point(data = empirical_df, aes(x = make_rate, y = yardline_100), inherit.aes = FALSE, color = "red", size = 2, alpha = 0.7) + scale_x_continuous(labels = scales::percent_format(accuracy = 1)) + scale_y_reverse() + theme_minimal() + theme( panel.grid.minor.x = element_blank(), plot.title = element_text(size = 20, face = "bold"), plot.subtitle = element_text(size = 12), plot.caption = element_text(colour = "grey60"), plot.title.position = "plot" ) + labs( title = "FG Make Probability Threshold vs Field Position", subtitle = "Bars = model range frontier, Points = empirical FG yardline_100 & make rate", caption = "jstoetz.com", x = "FG Make Probability Threshold", y = "Yards from Opponent End Zone (yardline_100)" ) ``` The second chart relates the make probability to the kick distance rather than field positon. Recall that since 17 yards are added for the holder and end zone to the line of scrimmage, a 50% probability of a make equates to a kick distance of 57 yards. ```{r chart make prob vs kick distance} # Bar chart for kick distance ggplot(range_map, aes(x = fg_thresh, y = kick_dist)) + geom_col(fill = "lightgreen", alpha = 0.7) + geom_point(data = empirical_df, aes(x = make_rate, y = kick_dist), inherit.aes = FALSE, color = "blue", size = 2, alpha = 0.7) + scale_x_continuous(labels = scales::percent_format(accuracy = 1)) + labs( title = "FG Make Probability Threshold vs Kick Distance", subtitle = "Bars = model range frontier, Points = empirical FG distance & make rate", caption = "jstoetz.com", x = "FG Make Probability Threshold", y = "Kick Distance (yards)" ) + theme_minimal() + theme( panel.grid.minor.x = element_blank(), plot.title = element_text(size = 20, face = "bold"), plot.subtitle = element_text(size = 12), plot.caption = element_text(colour = "grey60"), plot.title.position = "plot" ) ``` ### 85% FG Percentage Threshhold At `fg_thresh` = 0.85, the range starts around the opponent's 22 yard line. From those distances, the Traditional Model drives still have a solid chance to convert first downs and push for a TD. This simulation compared kicking a FG immediately once the ball was within range vs the Traditional Model. ```{r 85 head to head experiments} fg_thresh <- 0.85 simulate_head_to_head <- function(starts = c(85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25), # yardline_100 n_sims = 2000) { map_dfr(starts, function(yl100) { trad <- replicate(n_sims, simulate_drive_traditional(yl100)) early <- replicate(n_sims, simulate_drive_early_fg(yl100)) tibble( yardline_100 = yl100, EP_traditional = mean(trad), EP_earlyFG = mean(early), EP_diff = EP_earlyFG - EP_traditional, pr_3plus_trad = mean(trad >= 3), pr_3plus_early = mean(early >= 3) ) }) } results_85 <- simulate_head_to_head() knitr::kable(results_85, align = "c", caption = "85% FG Percentage Threshhold") %>% kableExtra::kable_classic(full_width = FALSE) ``` The table output columns are defined as follows: - **yardline_100** Starting field position (yards from opponent's end zone). Lower numbers = better starting position. - **EP_traditional** Expected points per drive using historical 4th-down behavior (drive until stopped or choose FG). - **EP_earlyFG** Expected points if you kick as soon as you're within range for an **\~85% make rate**. - **EP_diff** `EP_earlyFG` − `EP_traditional`. Negative means the early FG strategy is worse. - **pr_3plus_trad** Probability the drive ends with ≥ 3 points under Traditional Model. - **pr_3plus_early** Same probability under Early FG Model strategy. ```{r chart 85 make vs field position} results_85 %>% pivot_longer(cols = c(EP_traditional, EP_earlyFG), names_to = "policy", values_to = "EP") %>% ggplot(aes(x = 100 - yardline_100, y = EP, linetype = policy)) + geom_line(size = 1) + labs(x = "Yards from Opponent End Zone (smaller = closer)", y = "Expected Points per Drive", title = "Traditional vs Early-FG: Expected Points by Field Position", subtitle = paste0( "Model make prob ≥ ", fg_thresh*100, "%" ), caption = "jstoetz.com") + theme_minimal() + theme( panel.grid.minor.x = element_blank(), plot.title = element_text(size = 20, face = "bold"), plot.subtitle = element_text(size = 12), plot.caption = element_text(colour = "grey60"), plot.title.position = "plot" ) ``` ```{r chart 85 FG make prob vs model} plot_fg_make_prob <- function(clean_pbp, fg_mod, fg_thresh = 0.85) { library(dplyr) library(ggplot2) # Empirical make rates by yardline_100 fg_emp <- clean_pbp %>% filter(play_type == "field_goal", !is.na(field_goal_result), !is.na(yardline_100)) %>% mutate(make = as.integer(field_goal_result == "made")) %>% group_by(yardline_100) %>% summarise( attempts = n(), makes = sum(make), make_rate = makes / attempts, .groups = "drop" ) # Model predictions for every yardline_100 pred_df <- data.frame(yardline_100 = seq(min(fg_emp$yardline_100), max(fg_emp$yardline_100), by = 1)) pred_df$kick_dist <- pred_df$yardline_100 + 17 pred_df$pred_prob <- predict(fg_mod, newdata = pred_df, type = "response") # Determine shaded "in range" zone based on model in_range_df <- pred_df %>% filter(pred_prob >= fg_thresh) if (nrow(in_range_df) > 0) { range_min <- min(in_range_df$yardline_100) # closest range_max <- max(in_range_df$yardline_100) # farthest still in range } else { range_min <- NA range_max <- NA } ggplot() + # Shaded zone for in-range yardlines { if (!is.na(range_min) && !is.na(range_max)) geom_rect(aes(xmin = range_min, xmax = range_max, ymin = 0, ymax = 1), fill = "green", alpha = 0.15) } + # Empirical points geom_point(data = fg_emp, aes(x = yardline_100, y = make_rate), color = "blue", alpha = 0.6, size = 2) + # Model line geom_line(data = pred_df, aes(x = yardline_100, y = pred_prob), color = "red", size = 1) + scale_x_reverse() + # so closer to goal is on the right labs( x = "Yards from Opponent End Zone (yardline_100)", y = "Probability of Made FG", title = "FG Make Probability vs. Field Position", subtitle = paste0( "Shaded = model make prob ≥ ", fg_thresh*100, "%" ), caption = "jstoetz.com" ) + theme_minimal() + theme( panel.grid.minor.x = element_blank(), plot.title = element_text(size = 20, face = "bold"), plot.subtitle = element_text(size = 12), plot.caption = element_text(colour = "grey60"), plot.title.position = "plot" ) } plot_fg_make_prob(clean_pbp, fg_mod, fg_thresh = 0.85) ``` ### 75% FG Percentage Threshhold ```{r 75 head to head experiments} fg_thresh <- 0.75 simulate_head_to_head <- function(starts = c(85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25), # yardline_100 n_sims = 2000) { map_dfr(starts, function(yl100) { trad <- replicate(n_sims, simulate_drive_traditional(yl100)) early <- replicate(n_sims, simulate_drive_early_fg(yl100)) tibble( yardline_100 = yl100, EP_traditional = mean(trad), EP_earlyFG = mean(early), EP_diff = EP_earlyFG - EP_traditional, pr_3plus_trad = mean(trad >= 3), pr_3plus_early = mean(early >= 3) ) }) } results_75 <- simulate_head_to_head() knitr::kable(results_75, align = "c", caption = "75% FG Percentage Threshhold") %>% kableExtra::kable_classic(full_width = FALSE) ``` ```{r chart 75 make vs field position} results_75 %>% pivot_longer(cols = c(EP_traditional, EP_earlyFG), names_to = "policy", values_to = "EP") %>% ggplot(aes(x = 100 - yardline_100, y = EP, linetype = policy)) + geom_line(size = 1) + labs(x = "Yards from Opponent End Zone (smaller = closer)", y = "Expected Points per Drive", title = "Traditional vs Early-FG: Expected Points by Field Position", subtitle = paste0( "Model make prob ≥ ", fg_thresh*100, "%" ), caption = "jstoetz.com") + theme_minimal() + theme( panel.grid.minor.x = element_blank(), plot.title = element_text(size = 20, face = "bold"), plot.subtitle = element_text(size = 12), plot.caption = element_text(colour = "grey60"), plot.title.position = "plot" ) ``` ```{r chart 75 FG make prob vs model} plot_fg_make_prob(clean_pbp, fg_mod, fg_thresh = 0.75) ``` ### 65% FG Percentage Threshhold ```{r 65 head to head experiments} fg_thresh <- 0.65 simulate_head_to_head <- function(starts = c(85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25), # yardline_100 n_sims = 2000) { map_dfr(starts, function(yl100) { trad <- replicate(n_sims, simulate_drive_traditional(yl100)) early <- replicate(n_sims, simulate_drive_early_fg(yl100)) tibble( yardline_100 = yl100, EP_traditional = mean(trad), EP_earlyFG = mean(early), EP_diff = EP_earlyFG - EP_traditional, pr_3plus_trad = mean(trad >= 3), pr_3plus_early = mean(early >= 3) ) }) } results_65 <- simulate_head_to_head() knitr::kable(results_65, align = "c", caption = "65% FG Percentage Threshhold") %>% kableExtra::kable_classic(full_width = FALSE) ``` ```{r chart 65 make vs field position} results_65 %>% pivot_longer(cols = c(EP_traditional, EP_earlyFG), names_to = "policy", values_to = "EP") %>% ggplot(aes(x = 100 - yardline_100, y = EP, linetype = policy)) + geom_line(size = 1) + labs(x = "Yards from Opponent End Zone (smaller = closer)", y = "Expected Points per Drive", title = "Traditional vs Early-FG: Expected Points by Field Position", subtitle = paste0( "Model make prob ≥ ", fg_thresh*100, "%" ), caption = "jstoetz.com") + theme_minimal() + theme( panel.grid.minor.x = element_blank(), plot.title = element_text(size = 20, face = "bold"), plot.subtitle = element_text(size = 12), plot.caption = element_text(colour = "grey60"), plot.title.position = "plot" ) ``` ```{r chart 65 FG make prob vs model} plot_fg_make_prob(clean_pbp, fg_mod, fg_thresh = 0.65) ``` ### 50% FG Percentage Threshhold ```{r 50 head to head experiments} fg_thresh <- 0.50 simulate_head_to_head <- function(starts = c(85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25), # yardline_100 n_sims = 2000) { map_dfr(starts, function(yl100) { trad <- replicate(n_sims, simulate_drive_traditional(yl100)) early <- replicate(n_sims, simulate_drive_early_fg(yl100)) tibble( yardline_100 = yl100, EP_traditional = mean(trad), EP_earlyFG = mean(early), EP_diff = EP_earlyFG - EP_traditional, pr_3plus_trad = mean(trad >= 3), pr_3plus_early = mean(early >= 3) ) }) } results_50 <- simulate_head_to_head() knitr::kable(results_50, align = "c", caption = "50% FG Percentage Threshhold") %>% kableExtra::kable_classic(full_width = FALSE) ``` ```{r chart 50 make vs field position} results_50 %>% pivot_longer(cols = c(EP_traditional, EP_earlyFG), names_to = "policy", values_to = "EP") %>% ggplot(aes(x = 100 - yardline_100, y = EP, linetype = policy)) + geom_line(size = 1) + labs(x = "Yards from Opponent End Zone (smaller = closer)", y = "Expected Points per Drive", title = "Traditional vs Early-FG: Expected Points by Field Position", subtitle = paste0( "Model make prob ≥ ", fg_thresh*100, "%" ), caption = "jstoetz.com") + theme_minimal() + theme( panel.grid.minor.x = element_blank(), plot.title = element_text(size = 20, face = "bold"), plot.subtitle = element_text(size = 12), plot.caption = element_text(colour = "grey60"), plot.title.position = "plot" ) ``` ```{r chart 50 FG make prob vs model} plot_fg_make_prob(clean_pbp, fg_mod, fg_thresh = 0.5) ``` ## Minimum FG Make Probability Having struck out defining specific `fg_thresh` values, I decided to expand my view to see if the Early FG model ever had higher EP than a Traditional Model. The steps were as below: - Pick a grid of `fg_thresh` values (0.50 → 0.95). - Pick a set of starting `yardline_100` values which is the Team starting field position (30 → 75) - Run both the Traditional Model and Early FG strategies for each combination. - Find the cross-over point (where `EP_diff` is positive). - Plot the curves an tables so you can visually see where the Early FG starts to make sense. ```{r min FG charts} # Function to run one sweep value of fg_thresh simulate_sweep <- function(fg_thresh, starts, n_sims = 1000) { # Set the global fg_range_min_yd100 for this threshold yd100_grid <- 1:80 mk <- p_make_fg(yd100_grid + 17) fg_range_min_yd100 <- max(yd100_grid[mk >= fg_thresh], na.rm = TRUE) map_dfr(starts, function(yl100) { trad <- replicate(n_sims, simulate_drive_traditional(yl100)) early <- replicate(n_sims, simulate_drive_early_fg(yl100, range_min_yl100 = fg_range_min_yd100)) tibble( fg_thresh = fg_thresh, yardline_100 = yl100, EP_traditional = mean(trad), EP_earlyFG = mean(early), EP_diff = mean(early) - mean(trad) ) }) } # Sweep parameters fg_thresholds <- seq(0.50, 0.95, by = 0.05) start_positions <- seq(30, 75, by = 5) # from opp 30 to own 25 # Run the sweep sweep_results <- map_dfr(fg_thresholds, simulate_sweep, starts = start_positions) # Identify crossover points (where EP_diff >= 0) crossover_points <- sweep_results %>% group_by(yardline_100) %>% summarise( min_thresh_break_even = min(fg_thresh[EP_diff >= 0], na.rm = TRUE), .groups = "drop" ) # Plot EP_diff curves for each start position ggplot(sweep_results, aes(x = fg_thresh, y = EP_diff, color = factor(yardline_100))) + geom_hline(yintercept = 0, linetype = "dashed") + geom_line(size = 1) + labs( title = "EP Difference (Early FG - Traditional) Across FG Thresholds", x = "FG Make Probability Threshold", y = "EP Difference", caption = "jstoetz.com", color = "Start Yardline_100" ) + theme_minimal() + theme( panel.grid.minor.x = element_blank(), plot.title = element_text(size = 20, face = "bold"), plot.subtitle = element_text(size = 12), plot.caption = element_text(colour = "grey60"), plot.title.position = "plot" ) ggplot(sweep_results, aes(x = fg_thresh, y = yardline_100, fill = EP_diff)) + geom_tile() + geom_text( size = 3, fontface = "bold", aes( label = EP_diff, colour = "white" ) ) + scale_colour_identity() + # Use the specified colors without a legend scale_fill_viridis_c(option = "H", guide = FALSE) + scale_x_continuous(breaks = seq(0.50, 0.95, by = 0.05)) + scale_y_continuous(breaks = seq(30, 75, by = 5)) + labs( x = "\nMinimum FG Percentage Threshhold", y = "Yards from Opponent End Zone (yardline_100)", title = "EP Difference - Field Position vs FG Pct Threshhold", subtitle = "Expected Points per drive difference (Early FG minus Trad Model) based on minimum field goal percentage and yards from opponents endzone", caption = "jstoetz.com" ) + #theme_bw() + theme( plot.title = element_text(size = 20, face = "bold", colour = "black"), plot.subtitle = element_text(size = 12, colour = "black"), plot.caption = element_text(colour = "grey60"), plot.title.position = "plot", axis.title.x = element_text(size = 10, colour = "black"), axis.text.x = element_text(size = 10, colour = "black"), axis.text.y = element_text(size = 10, colour = "black"), panel.border = element_blank(), panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank() ) ``` ## Break-Even Calculation for Early FG Model To this point, I failed to find a situation where the Early FG model beat the Traditional Model when comparing points per drive. My initial explanation was that NFL kickers aren't making a high engough percentage of field goals from far enough away. Which brings me to the last question: **what make percentage would be required for the Early FG model to break even versus the TM model from a given start, if we commit to kicking at a particular field position?** How good would a kicker have to be to make the MoneyballFB Model *better* than the existing NFL approach? Turns out there is no real limit. The plot below is showing that for every tested starting field position and kick distance, the **minimum make percentage required for “Early FG” ≥ “Traditional EP” is 100%.** That means: - Even if a kicker could make every single attempt from those distances, the Early FG strategy just barely ties the traditional strategy at best. - At any real-world FG% (<100%), Early FG is always worse in terms of expected points. - The reason is that a traditional drive has upside beyond 3 points (touchdowns, closer FGs, penalties in your favor), while Early FG caps you at 3 points and adds the risk of a miss. Thus, **there is no distance (under current NFL kicking skill levels and rules) where “kick immediately” outperforms the traditional strategy.** ```{r frontier kickers} # ---- Probability of ever reaching a frontier (yl100) from a start ---- reach_prob <- function(start_yl100, frontier_yl100, n_sims = 1000, max_plays = 200) { reached <- logical(n_sims) for (i in seq_len(n_sims)) { down <- 1L togo_bin <- binner(10, togo_cuts) yl_bin <- pmin(20L, pmax(0L, floor((100 - start_yl100)/5))) hit <- FALSE for (j in seq_len(max_plays)) { yl100_now <- ylbin_to_yardline100(yl_bin) if (yl100_now <= frontier_yl100) { hit <- TRUE; break } res <- sample_next(down, togo_bin, yl_bin) if (res$type != "CONTINUE") break down <- as.integer(res$state$down_next) togo_bin <- as.integer(res$state$togo_bin_next) yl_bin <- as.integer(res$state$yl_bin_next) } reached[i] <- hit } mean(reached) } # ---- Break-even p* for (start, kick_dist) pairs; also compares to your model p_make_fg ---- break_even_grid <- function(starts, kick_dists, n_sims_ep = 30, n_sims_reach = 30) { starts <- as.integer(starts) kick_dists <- as.integer(kick_dists) # Cache Traditional EP by start to avoid re-simulating needlessly ep_trad_map <- tibble(start_yl100 = unique(starts)) %>% mutate(EP_traditional = map_dbl(start_yl100, ~ mean(replicate(n_sims_ep, simulate_drive_traditional(.x))) )) expand_grid(start_yl100 = unique(starts), kick_dist = unique(kick_dists)) %>% mutate(frontier_yl100 = pmax(1L, round(kick_dist - 17L))) %>% left_join(ep_trad_map, by = "start_yl100") %>% mutate( pi_reach = map2_dbl(start_yl100, frontier_yl100, ~ reach_prob(.x, .y, n_sims = n_sims_reach)), p_required = if_else(pi_reach > 0, EP_traditional / (3 * pi_reach), NA_real_), p_required = pmin(pmax(p_required, 0), 1), p_model = p_make_fg(kick_dist), early_fg_EP_positive = p_model >= p_required, EP_early_model = 3 * p_model * pi_reach, EP_diff_model = EP_early_model - EP_traditional ) %>% arrange(start_yl100, kick_dist) } # ---- Example: specify your starts & kick distances ---- starts_test <- c(95, 85, 75, 65, 55, 45) # yardline_100 starts dists_test <- c(45, 50, 55, 60, 65, 70, 75, 85, 95, 100) # kick distances in yards be_tbl <- break_even_grid(starts_test, dists_test, n_sims_ep = 30, n_sims_reach = 30) # Nicely formatted view be_tbl %>% transmute( start_yl100, kick_dist, frontier_yl100, EP_traditional = round(EP_traditional, 3), pi_reach = round(pi_reach, 3), p_required_pct = scales::percent(p_required, accuracy = 0.1), p_model_pct = scales::percent(p_model, accuracy = 0.1), EP_diff_model = round(EP_diff_model, 3), EP_positive = if_else(early_fg_EP_positive, "YES", "NO") ) %>% arrange(desc(EP_diff_model)) %>% knitr::kable(align = "c",caption = "Break-even make% for Early-FG to exceed Traditional EP (by start & distance)") %>% kableExtra::kable_classic(full_width = FALSE) # Heatmap of required make% (p_required) ggplot(be_tbl, aes(x = kick_dist, y = start_yl100, fill = p_required)) + geom_tile(color = "white") + scale_fill_viridis_c( option = "plasma", limits = c(0,1), labels = scales::percent, name = "Min FG% Required" ) + geom_text( aes(label = scales::percent(round(p_required, 2))), color = "black", size = 3 ) + scale_x_continuous("Kick Distance (yards)", breaks = seq(40, 100, 5)) + scale_y_reverse("Starting Yardline_100 (yards to goal)", breaks = seq(40,95,5)) + theme_minimal(base_size = 13) + ggtitle("Break-even FG Make% by Start Position & Kick Distance", subtitle = "Each cell = minimum FG% needed for Early-FG ≥ Traditional EP") ``` ## Notes & Research - american football - Could an immediate field goal be advantageous in NFL? - Sports Stack Exchange - [Link](https://sports.stackexchange.com/questions/25216/could-an-immediate-field-goal-be-advantageous-in-nfl) - [DB](https://www.dropbox.com/scl/fi/wad9a2vkpz0wjpluyyy70/2025-Aug-13-american-football-Could-an-immediate-field-goal-be-advantageous-in-NFL-Sports-Stack-Exchange.pdf?rlkey=nsvol2z5rkbwo4xlchb27z1s7&dl=0) - Field Goal Success Probabilities by Direction \| NFL Football Operations - [Link](https://operations.nfl.com/gameday/analytics/stats-articles/field-goal-success-probabilities-by-direction/#) - [DB](https://www.dropbox.com/scl/fi/f6652swvr7e5nwl0pnytr/2025-Aug-13-Field-Goal-Success-Probabilities-by-Direction-NFL-Football-Operations.pdf?rlkey=lhreuyxam640w1chywv2izcu4&dl=0) - Visualizing NFL Kicker Accuracy Trends (1999-2024) // Conor McLaughlin - [Link](https://conormclaughlin.net/2025/01/visualizing-nfl-kicker-accuracy-trends-1999-2024/) - [DB](https://www.dropbox.com/scl/fi/iygvgvs87depttl50jx6e/2025-Aug-13-Visualizing-NFL-Kicker-Accuracy-Trends-1999-2024-Conor-McLaughlin.pdf?rlkey=g8350l7zh2x9ivbbfb7zoxjgf&dl=0) - Using Ridgeline Plots to Visualize the NFL's Shift Towards Longer Field Goal Attempts // Conor McLaughlin - [Link](https://conormclaughlin.net/2025/01/using-ridgeline-plots-to-visualize-the-nfls-shift-towards-longer-field-goal-attempts/) - [DB](https://www.dropbox.com/scl/fi/p4n3ktlvza2e1d3w8dxhy/2025-Aug-13-Using-Ridgeline-Plots-to-Visualize-the-NFL-s-Shift-Towards-Longer-Field-Goal-Attempts-Conor-McLaughlin.pdf?rlkey=tv2h2672eyugqdjfrlfc9vmjk&dl=0) - Field goal - Wikipedia - [Link](https://en.m.wikipedia.org/wiki/Field_goal) - [DB](https://www.dropbox.com/scl/fi/p6xqryi0hfsgadanqppnn/2025-Aug-13-Field-goal-Wikipedia.pdf?rlkey=ylikcm9ccbx71fbimjg3dryne&dl=0) - Mathematically If a Team Invests in a kicker, could they kick it every drive? : r/NFLNoobs - [Link](https://www.reddit.com/r/NFLNoobs/comments/1hyo8n9/mathematically_if_a_team_invests_in_a_kicker/) - [DB](https://www.dropbox.com/scl/fi/vbee6vyj0evgoq4ml0hfv/2025-Aug-13-Mathematically-If-a-Team-Invests-in-a-kicker-could-they-kick-it-every-drive-r-NFLNoobs-1.pdf?rlkey=ztbkep1oo7wuagndcl0co35fo&dl=0) - What are Expected Points Added (EPA) in the NFL \| nfelo - [Link](https://www.nfeloapp.com/analysis/expected-points-added-epa-nfl/) - [DB](https://www.dropbox.com/scl/fi/ice1nxnx87s36648bdjp7/2025-Aug-13-What-are-Expected-Points-Added-EPA-in-the-NFL-nfelo.pdf?rlkey=5km88cl1aiaxualfk1io0recv&dl=0) - Operations research on Football - [Link](https://pubsonline.informs.org/doi/pdf/10.1287/opre.19.2.541) - [DB](https://www.dropbox.com/scl/fi/qznt34g0o73rjxmd1wgdw/2025-Aug-13.pdf?rlkey=6lco6qkfx8nwlcdvllaae5oo1&dl=0) - College Football Expected Points Model Fundamentals - Part I • cfbfastR - [Link](https://cfbfastr.sportsdataverse.org/articles/college-football-expected-points-model-fundamentals-part-i.html) - [DB](https://www.dropbox.com/scl/fi/08ee3lnx4wdj2jr1uvt1c/2025-Aug-13-College-Football-Expected-Points-Model-Fundamentals-Part-I-cfbfastR.pdf?rlkey=9ve0r3jnkjsee5okopllcrmfu&dl=0) - College Football Expected Points Model Fundamentals - Part II • cfbfastR - [Link](https://cfbfastr.sportsdataverse.org/articles/college-football-expected-points-model-fundamentals-part-ii.html) - [DB](https://www.dropbox.com/scl/fi/o7ukdsfjv9yayi7yrc0zb/2025-Aug-13-College-Football-Expected-Points-Model-Fundamentals-Part-II-cfbfastR.pdf?rlkey=bdvnps835sj2c2leptnp1rr4x&dl=0) - College Football Expected Points Model Fundamentals - Part III • cfbfastR - [Link](https://cfbfastr.sportsdataverse.org/articles/college-football-expected-points-model-fundamentals-part-iii.html) - [DB](https://www.dropbox.com/scl/fi/yzqhyyg0u5isv8jm5j35c/2025-Aug-13-College-Football-Expected-Points-Model-Fundamentals-Part-III-cfbfastR.pdf?rlkey=ce2okse6efq8e6oibzgqbjv4b&dl=0) - What is the Predicted Probability of a Field Goal Given Yards - [Link](https://ckchiruka.github.io/projects/fieldgoals.pdf) - [DB](https://www.dropbox.com/scl/fi/4loxbd4zcov5zg9cg6lk8/2025-Aug-13-1.pdf?rlkey=2aeio31jdje1hvxsfh14wollp&dl=0) - Advanced Football Analytics (formerly Advanced NFL Stats): Expected Point Values - [Link](https://www.advancedfootballanalytics.com/2009/12/expected-point-values.html) - [DB](https://www.dropbox.com/scl/fi/fqjr8x4g81o7f6figh35x/2025-Aug-14-Advanced-Football-Analytics-formerly-Advanced-NFL-Stats-Expected-Point-Values.pdf?rlkey=p9uh6rozrrarz16lwcs1pyn1y&dl=0) - An R package to quickly obtain clean and tidy NFL play by play data • nflfastR - [Link](https://www.nflfastr.com/) - [DB](https://www.dropbox.com/scl/fi/m93u3le88txml0wpp9x8g/2025-Aug-14-An-R-package-to-quickly-obtain-clean-and-tidy-NFL-play-by-play-data-nflfastR.pdf?rlkey=qtpgaq80vjpyvjai0xf3d5plr&dl=0)