Abstract
Starting quarterbacks in the National Football League command the largest contracts of any position group (Over The Cap, 2025). However, without clear frameworks for evaluating investment efficacy or projecting future performance, organizations risk wasting money on overpaid players and losing long-term competitive edge due to inflated resource allocation (Barnwell, 2024). Furthermore, with annual increases in the salary cap, the cost of mispricing a starting quarterback compounds over time (Over The Cap, 2025). This paper develops a publicly reproducible methodology for quantifying quarterback value in terms of wins above replacement, projecting future performance using deep learning, and estimating the financial value of players based on previous performance, projected performance, and market rates.
1. Introduction
Any football fan can tell you that the quarterback is the most impactful position on a roster, but the market reflects this reality as well (PFF, 2018). In 2024, quarterbacks collectively received $680,921,527 against their respective team’s cap – by far the most out of any position group in the NFL (Over The Cap). Unsurprisingly, that season’s officially selected Most Valuable Player, Josh Allen, received $30,356,281 for his efforts.
Well ahead of him in the list of most highly paid quarterbacks in the NFL for that season is Deshaun Watson, who received $63.77 million from the Cleveland Browns. Rather than winning the MVP, Watson delivered seven horrendous games before missing the rest of the season with a torn Achilles tendon (Barnwell, 2024). As demonstrated by Watson and Allen, one contract is the difference between being a respectable franchise with room to build a roster and being a walking punchline dragged down by years of cap inflexibility (Patuto, 2025). However, to make decisions about quarterbacks, many general managers rely on subjective scouting assessments, context-lacking box score statistics, and unverifiable data (Coller, 2023).
Through tracking over 900,000 plays from the nflfastR database across 19 seasons (2006-2024), I constructed a Wins Above Replacement (WAR) metric, trained a feed-forward neural network to predict annual performance changes, analyzed the efficiency of prominent player contracts, and then applied this analysis to project the performance and contract futures of four prominent rookie first-round quarterbacks from the 2024 NFL draft class. Upon evaluation, my neural net demonstrated a 10 percent relative improvement in projection accuracy over traditional forecasting, showing the ability of deep learning methods to capture non-linear career dynamics better than linear regressions or static assumptions.
2. Measuring Quarterback Value
2.1 The WAR Framework
In baseball, Wins Above Replacement (WAR) quantifies the number of additional wins that a player provides compared to a free agent at the same position signed at the league minimum salary. For this project, and much in line with statistical forefathers at Carnegie Mellon, I have created a personal version of WAR for quarterbacks (Yurko, et. al, 2018) .
WAR begins with Expected Points Added (EPA), a metric that measures the change in expected points on each play given down, distance, field position, and other contextual factors for evaluating quarterback production. EPA is sourced from nflfastR and calculated using expected points models trained on historical play outcomes. Plays with accepted penalties are excluded due to subjectivity and varying degrees of call quality, as well as attribution and the presence of missed penalties.
The replacement-level baseline is the 10th percentile of qualified quarterback seasons (-0.206 EPA/play) across the whole data set, which represents performance a team could obtain from a freely available backup. A quarterback’s EPA above this threshold constitutes his marginal contribution.
Converting EPA to WAR requires a season-specific factor (approximately 170-240 EPA per win) that reflects year-to-year variation in league-wide scoring. A quarterback share parameter (0.65) further adjusts for the proportion of offensive plays where quarterbacks directly influence outcomes. The full calculation: WAR = (QB_EPA – Replacement_EPA × Plays) / (EPA_per_Win × QB_Share).
2.2 WAR Results (Cumulative and Single Season)
| Player | Total WAR | Total Plays |
| Tom Brady | 30.74 | 10198 |
| Aaron Rodgers | 28.15 | 9888 |
| Drew Brees | 27.47 | 9213 |
| Phillip Rivers | 23.62 | 8855 |
| Matt Ryan | 23.44 | 9824 |
| Ben Roethlisberger | 20.72 | 8566 |
| Matthew Stafford | 18.02 | 8993 |
| Peyton Manning | 17.10 | 5247 |
| Russell Wilson | 16.77 | 7409 |
| Patrick Mahomes | 14.66 | 4648 |
Single-season leaders include four historic MVP campaigns at the very top: 2013 Peyton Manning, 2018 Patrick Mahomes, 2007 Tom Brady, and 2022 Patrick Mahomes.
| Season | Player | Total Plays | Total WAR |
| 2013 | Peyton Manning | 687 | 3.17 |
| 2018 | Patrick Mahomes | 655 | 2.84 |
| 2007 | Tom Brady | 623 | 2.83 |
| 2022 | Patrick Mahomes | 730 | 2.81 |
| 2011 | Drew Brees | 699 | 2.81 |
| 2011 | Aaron Rodgers | 585 | 2.80 |
| 2011 | Tom Brady | 676 | 2.72 |
| 2016 | Matt Ryan | 601 | 2.62 |
| 2012 | Tom Brady | 679 | 2.59 |
| 2013 | Drew Brees | 702 | 2.51 |
Although these numbers may intuitively seem low for quarterbacks involved, even 1.5 WAR across a whole season is proportionally massive in the context of football always having twenty two players on the field in each play. Across the projected time span of a whole regular season (700 snaps) and all else held equal, a player who produces two cumulative wins above replacement via statistical production can roughly add a calculated 8.82 percent to their team’s probability of winning each game.
EDITOR’S NOTE: The 700 number is based on a rounding up from the real number of plays per season, which ranges from the mid-to-late 600s. The “win probability added” calculation here is related to WAR divided by 17, which is the typical number of games played in the regular season. These are admittedly more ‘napkin math’ estimates than precise, but the specific empirical values don’t change the findings much.
2.3 Market Validation
To see if WAR reflects market value, I validated its output against market outcomes across that same period of time. Within 118 quarterbacks with 500 or more career plays, career WAR has a strong correlation (r=0.935) with career earnings and explains 87 percent of the variance in quarterback compensation.
| Player | Total WAR (2006-2024) | Total Earnings (2006-2024) |
| Tom Brady | 30.7 | $250.3M |
| Aaron Rodgers | 28.1 | $373.4M |
| Drew Brees | 27.5 | $236.6M |
| Phillip Rivers | 23.6 | $231.7M |
| Matt Ryan | 23.4 | $259.9M |
As Watson’s contract with the Browns demonstrates, franchises are not always perfect with decision making, but for the most part, teams are paying largely for what WAR measures, even before adjusting for cap inflation across our data set. Yet while this strong correlation validates WAR as a meaningful measure of quarterback value, the market still prices quarterbacks based on past production, reputation, leverage, and largely linear assumptions (Venkatesh, 2024).
The real opportunity for teams lies in combining WAR with predictive modeling. In other words, WAR might accurately assess performance relative to the market, but the key for any general manager is to identify quarterbacks likely to overperform or underperform their expected contract at market rate, and make a proactive decision accordingly.
3. Projecting Future Performance
3.1 Why Prediction is Hard
Predicting future performance of athletes is notoriously difficult in team sports (Aoki, 2017). In addition to injuries, coaching changes, personnel changes, and supporting cast performance, variables like the strength of opponents, the weather, and luck can shape career trajectories (Riske, 2021).
3.2 Marcel the Monkey
Developed by baseball sabermetrician Tom Tango, the Marcel method is infamous in sports analytics circles for being both extremely simple, yet remarkably effective at outperforming more complex forecasting models. The Marcel method takes a weighted average of the past three seasons for a given player (5, 4, and 3, from the most recent to the oldest), and then regresses the total value to the mean for a following year. On my held-out test set (2021-2024 seasons), Marcel explained nearly 23% of variance in the next year’s following WAR of a given player.
3.3 Neural Network Model
Rather than looking at absolute WAR of the following year, I trained a feed-forward neural network to predict changes in WAR. By framing the problem this way, it forced the model to learn the most pressing factors behind improvement or decline. Predicting changes in WAR rather than absolute WAR also prevents the model from gaming the evaluation metric by simply predicting “good quarterbacks stay good.”
The final model uses two hidden layers (16 and 8 neurons), ReLU activation functions, and L2 regularization (alpha = 0.5) to minimize the likelihood of overfitting. It is trained on all qualifying quarterback seasons from 2006-2020 and tested against 2021-2024, the four most recently completed seasons. Instead of manually selecting inputs, I used Lasso regularization to identify the most predictive variables.
| Feature | Importance |
| Current WAR | 36% |
| WAR Trend | 29% |
| Career WAR | 9% |
| Career Avg WAR | 8% |
| First Round Pick | 3% |
| Years Before Peak | 2% |
The lack of age-related features suggests that regression to the mean and recent performance has more impact on future quarterback performance. This parallels recent trends of quarterbacks playing longer than they ever did before, reflected by returns to relevance for Baker Mayfield, Sam Darnold, and Geno Smith.
3.4 NN vs. Marcel
On the held-out test set, the neural network achieved an R-Squared of 0.251, outperforming the Marcel method (0.227). This is because of one key disadvantage that the Marcel method has, which is its assumption that all players follow the same structure for projected future performance. In contrast, the neural network learns non-linear patterns that exist within the data rather than ‘cheating’ by always predicting a regression to a static mean.
3.5 Sample Predictions
Here are predictions for several quarterbacks from the test set, starting with the five most accurate:
| Seasons & Player | Prev_WAR | Pred_Next | Actual_Next | Approx_Error |
| 2023-2024 Jalen Hurts | 1.44 | 1.38 | 1.38 | 0.00 |
| 2021-2022 Lamar.Jackson | 0.87 | 1.10 | 1.10 | 0.00 |
| 2021-2022 Kirk Cousins | 1.17 | 1.34 | 1.33 | +0.01 |
| 2023-2024 Bryce Young | -0.07 | 0.51 | 0.55 | +0.04 |
| 2023-2024 Daniel Jones | -0.08 | 0.51 | 0.47 | +0.04 |
The model nailed Jalen Hurts’ performance in between two years with similar supporting casts. Another interesting takeaway here was how the model correctly predicted both an improvement for Lamar Jackson in between 2021 and 2022, despite him missing five games in each respective season. The model’s accuracy in light of injuries not being directly factored in would suggest that it still accounts for this risk indirectly through its emphasis on total volume, which is impacted by availability precedent.
| Seasons & Player | First Season WAR | Next Season Predicted WAR | Actual Next Season WAR | Approximate Error |
| 2021-2022 M.Stafford | 1.58 | 1.46 | 0.32 | +1.15 |
| 2022-2023 D.Jones | 1.40 | 1.04 | -0.08 | +1.13 |
| 2021-2022 P.Mahomes | 1.86 | 1.81 | 2.81 | -1.00 |
| 2021-2022 J.Goff | 0.40 | 0.76 | 1.73 | -0.97 |
| 2023-2024 B.Mayfield | 1.19 | 0.88 | 1.77 | -0.89 |
Conversely, the model’s least accurate predictions largely came in evaluating players that had drastic shifts in supporting casts or changes in health. Both the two highest ‘misses’ came from players whose predicted declines in WAR were more drastic than the model’s predictions due to injury issues in the following season. In the case of Mahomes, his historic 2022 MVP season, in spite of predicted regression and the loss of his former star receiver Tyreek Hill, illustrates his status as a true statistical outlier among even the greatest quarterbacks.
In total, the model’s mean absolute error was 0.45 WAR. Though it sounds high, this model is contextually robust given that it doesn’t account for supporting cast (due to time constraints), injury risk, or other extraneous variables that go into quarterback performance. When all else is held ‘equal,’ as demonstrated by its successful predictions, the model performs better than traditional forecasting under the same restraints.
4. Contract Analysis
4.1 Fair Value, Market Value, and the Scarcity Premium
When determining quarterback value in terms of dollars spent, fair value and market value represent two distinct concepts. Fair value reflects what a team should pay for a given level of production based on its correlation with wins above replacement. Meanwhile, market value reflects what teams actually pay. To establish a defensible benchmark, I calculated the league-wide market rate across all qualified QB-seasons from 2006-2024 with available cap data. The median rate is 6.7% of cap per 1.0 WAR. By this standard, a 2.0 WAR quarterback, true MVP-caliber production, should cost approximately 13.4% of the cap. Furthermore, the distribution of quarterback WAR reveals why the position commands a premium above actual performance.
Out of 759 qualified quarterback-seasons from 2006-2024, only 146 (19.2%) produced elite value (1.5+ WAR). The median season (0.77 WAR) represents roughly league-average starter production, but the distribution is heavily right-skewed. In a typical season, only eight to ten quarterbacks produce elite WAR, and only 16 to 18 exceed the above-average threshold of 1.0 WAR. As a result, there exists a small middle class of quarterbacks above replacement level; predicting how they will perform is crucial for successful roster-building.
It’s also worth noting the importance of a successful quarterback for general managers in terms of structural incentive. With typically short career spans and high pressure to deliver results, general managers face short-term pressure to find a long-term plan at quarterback; even successful leaders, like Howie Roseman of the Philadelphia Eagles, are quickly put under fire when quarterback situations go wrong (Silver, 2025). Signing a potential franchise quarterback or extending a rookie quarterback, even at the risk of overpaying someone underqualified for the role, showcases organizational stability and buys time.
4.2 Surplus of WAR vs. Cap
To evaluate contract efficiency, I analyzed ten manually picked long-term and high-profile quarterback contracts in the league as of right before the 2025 regular season. For each contract-year, I compared the player’s actual WAR production against their cap hit as a percentage of that season’s salary cap – essentially asking “how well had this player performed in their most recent contract at the time of right before the current season?” Note: due to Josh Allen’s contract extension starting in 2025, he has technically been excluded from this table, though he will appear in subsequent ones for this section.
| Player | Avg Cap % | Avg WAR/year | Surplus |
| Jared Goff | 10.7% | 1.97 | +18.9% |
| Patrick Mahomes | 11.0% | 2.02 | +18.4% |
| Jalen Hurts | 4.0% | 1.41 | +12.9% |
| Lamar Jackson | 11.3% | 1.72 | +12.6% |
| Justin Herbert | 5.7% | 1.13 | +7.0% |
| Joe Burrow | 10.1% | 1.21 | +6.7% |
| Jordan Love | 8.1% | 1.09 | +4.9% |
| Trevor Lawrence | 5.9% | 0.50 | -2.1% |
| Dak Prescott | 17.5% | 0.35 | -14.9% |
In his second long-term stint as a starter, Goff delivered phenomenal production at a moderate cap hit. Mahomes has practically funded Kansas City’s championship window while also performing excellently as a player in the early part of his extension. Prescott, however, has not performed up to expectations for his contract, with the surplus between his performance across his contract and ‘suggested’ performance by contract being extremely large.
The following table shows average cap percentage across each contract’s full duration. This reveals which deals are truly team-friendly over their full duration versus those that choose to kick the can down the road.
4.3 Contract Structure Importance
| Player | Signed (year) | Length (years) | Range of Cap% Across Contract | Avg Cap % |
| Jalen Hurts | 2023 | 5 | [2.7%, 13.5%] | 8.0% |
| Trevor Lawrence | 2024 | 5 | [5.9%, 14.4%] | 9.1% |
| Jordan Love | 2024 | 4 | [8.1%, 14.2%] | 11.3% |
| Justin Herbert | 2023 | 5 | [3.8%, 18.8%] | 11.8% |
| Joe Burrow | 2023 | 5 | [8.7%, 16.7%] | 13.9% |
| Patrick Mahomes | 2020 | 10 | [2.7%, 26.5%] | 14.3% |
| Jared Goff | 2024 | 4 | [10.7%, 23.6%] | 15.9% |
| Josh Allen | 2025 | 5 | [13.0%, 19.1%] | 16.8% |
| Lamar Jackson | 2023 | 5 | [9.9%, 25.2%] | 17.5% |
| Dak Prescott | 2024 | 4 | [17.5%, 25.1%] | 20.7% |
Hurts’ deal is by far the most team-friendly, which stands out given his Super Bowl MVP performance two seasons into his contract. The wide distribution of the Mahomes contracts shows both his value to the Kansas City Chiefs, as well as how their front-loaded team-friendly years have come at a cost of significant cap pressure during the middle of the contract. On the other hand, Prescott’s deal stands out here as a heavily inflated deal, and, surprisingly, Jackson’s hints at a potential issue lurking in the future for the Baltimore Ravens.
I was surprised by the last finding given that Jackson is fresh off an MVP runner-up season and, before that, an MVP season. With that said, the structure of his contract in terms of percentage of cap and his age hint at two conclusions: the Ravens have little margin for error in Jackson’s future performances and they had little leverage to work with after Jackson declined the team’s fifth-year option to play his way into a bigger contract (Schefter, 2022). The key problem here was that Jackson properly realized his value before the team did.
4.4 Break-Even Analysis: The Bar for Remaining Years
Using the league-wide market rate of 6.7% cap per 1.0 WAR, I calculated what each quarterback must deliver in remaining years to justify their cost. “Break-Even WAR” represents the production needed each remaining year to justify that year’s cap hit at market rate.
| Player | Banked Surplus So Far | Break Even WAR/year | Break + WAR/year |
| Dak Prescott | -15.1% | 3.25 | 4.00 |
| Lamar Jackson | +0.4% | 3.23 | 3.20 |
| Joe Burrow | -4.0% | 2.46 | 2.66 |
| Josh Allen | 0.0% | 2.51 | 2.51 |
| Jared Goff | +2.5% | 2.63 | 2.50 |
| Patrick Mahomes | +12.5% | 2.74 | 2.27 |
| Justin Herbert | +3.7% | 2.38 | 2.20 |
| Jordan Love | -0.9% | 1.84 | 1.89 |
| Trevor Lawrence | -2.5% | 1.49 | 1.57 |
| Jalen Hurts | +10.9% | 1.60 | 1.06 |
Prescott essentially needs to perform at the rate of the greatest WAR season in recorded history (2013 Peyton Manning) for multiple seasons merely to break even in cumulative performance. In contrast, Hurts only needs to perform like an above-average starter to match his estimated contract value.
4.5 Forward-Looking Contract Assessments
Finally, I used the neural network from Section 3 to project each quarterback’s WAR for their remaining contract years. Following that, I compared these projections against the break-even thresholds calculated above.
| Player | Years Remaining | Projected – Desired WAR Difference | Relative Performance & Contract ZScore |
| Jalen Hurts | 3 | +0.12 | 1.59 |
| Trevor Lawrence | 4 | -0.70 | 0.64 |
| Patrick Mahomes | 4 | -0.82 | 0.51 |
| Jordan Love | 3 | -0.84 | 0.48 |
| Justin Herbert | 3 | -1.12 | 0.16 |
| Josh Allen | 4 | -1.21 | 0.06 |
| Joe Burrow | 3 | -1.33 | -0.08 |
| Jared Goff | 3 | -1.58 | -0.37 |
| Lamar Jackson | 3 | -1.96 | -0.80 |
| Dak Prescott | 3 | -3.16 | -2.18 |
Hurts is the only quarterback outright projected to exceed his break-even threshold and end his tenure with a positively graded contract. But relatively speaking, Lawrence, Mahomes, and Love each have strong deals and likelihoods of performing up to par. In Lawrence’s case, his contract structure sets a reasonable bar, while Mahomes’ performance from previous seasons has earned him grace; Love, whose league-leading EPA/play in 2025 has not been factored into this, lands somewhere in the middle, yet still positive.
However, the model’s output suggests more pessimism about Burrow, Goff, Jackson, and Prescott’s ability to play up to their respective contracts through the rest of their tenures – importantly, as of the end of the 2024 regular season. As of when I’m writing this, all four quarterbacks are in danger of missing the playoffs thanks to dealing with injury problems, as well as regressions in their actual performance for Goff, Jackson, and Burrow.
5. Implications
5.1 Team Takeaways
These findings suggest an opportunity for general managers to take a risk with younger quarterbacks. Rather than riding out their entire rookie contract and milking the surplus in resources for the short-term, it may be contextually beneficial for general managers to secure high performing quarterbacks to long-term extensions early to avoid a potentially higher and less team-friendly payday down the line, as the Ravens learned the hard way with Jackson.
Cases like these demonstrate when it comes to managing franchise quarterbacks, NFL teams are put in a paradox. They have to both realize a quarterback’s long-term value faster than the player, but also delay paying him long enough to retain roster flexibility and contract leverage.
5.2 Limitations and Future Directions
Any user of this current model should understand that despite its superior performance to traditional forecasting, it remains very limited in current application due to only explaining a quarter of variance. Because my version of WAR is built from EPA, an industry standard for quantifying quarterback production, it inherently ignores the difference between quarterbacks with elite supporting casts and quarterbacks without them. The most immediate recommendation would be to add other positions to the WAR model and, for each one, use their WAR values as predictors for future quarterback performance before finding a way to calculate an adjusted WAR score.
It is also possible that there remain proprietary or publicly unavailable models that teams or sports bettors use to account for this factor, along with other ones like roster turnover, injuries, and randomness. Therefore, the benchmarks I have compared my neural network to may not be the ones used in practice by key stakeholders in quarterback performance.
When it comes to assessing contracts, this current research uses cap percentage per year as a general cost metric. However, guarantees, performance incentives, bonuses, and distribution across years also affect team flexibility and player security. I used cap hit and percentage of cap as a good enough proxy for the purpose of this assignment. A future extension of this project would incorporate those other variables for determining contract value.
The last and largest limitation is the small data set. While it covers 19 seasons and many quarterbacks, the model struggles to predict outcomes for rookie quarterbacks due to their limited data. A natural evolution of this project would appropriately set ‘defaults’ for specific types of prospects depending on where they are in the draft or other biographical factors for low-data players via preliminary clustering methods.
6. Conclusion
Franchise quarterbacks are the most valuable and most expensive assets in professional football. This paper showcases a transparent framework for quantifying that value, projecting future performance, and evaluating contract efficiency. Although my analysis may not directly change how general managers evaluate quarterbacks or plan for contract extensions, I believe it demonstrates the power of publicly available data and accessible machine learning tools to generate insights about player valuation and roster management.
7. References & Readings
- Aoki, R., Assuncao, R., & Vaz de Melo, P. (2017). Luck is hard to beat: The difficulty of sports prediction. arXiv preprint. https://arxiv.org/abs/1710.01624
- Baldwin, B. (2025). nflfastR: Functions to efficiently access NFL play by play data [R package]. GitHub. https://github.com/nflverse/nflfastR
- Barnwell, B. (2012). The NFL’s most valuable person. Grantland. https://grantland.com/features/jim-harbaugh-continues-biggest-bargain-football/
- Beaton, A. (2025). Where the NFL’s Broken Quarterbacks Go to Get Fixed. Wall Street Journal. https://www.wsj.com/sports/football/daniel-jones-colts-vikings-anthony-richardson-7a3484a8
- Coller, M. (2023). Football is a numbers game: Pro Football Focus and how a data-driven approach shook up the sport. Triumph Books.
- Drinen, D. (2008). Approximate value: Methodology. Pro Football Reference. https://www.sports-reference.com/blog/approximate-value-methodology/
- Fitzgerald, J. (2021). Positional value in the NFL. Over The Cap. https://overthecap.com/positional-value-in-the-nfl
- MLB.com. (2004). Marcel the Monkey forecasting system. https://www.mlb.com/glossary/projection-systems/marcel-the-monkey-forecasting-system
- Over The Cap. (2024). NFL salary cap and contract data. https://overthecap.com
- Palakurthi, A. (2025). Untangling the NFL Pt. 4: Wins above replacement (QBs). Big Nokh. https://bignokh.com/2025/11/14/untangling-the-nfl-pt-4-wins-above-replacement-qbs/
- Patuto, G. (2025). Cleveland Browns QB contract named among worst in league history. Sports Illustrated. https://www.si.com/nfl/browns/news/cleveland-browns-qb-contract-named-among-worst-in-league-history
- Pro Football Focus. (2018). PFF WAR methodology. https://www.pff.com/war
- Riske, T. (2021). Investigating positional aging curves with PFF WAR. Pro Football Focus. https://www.pff.com/news/nfl-investigating-positional-aging-curves-with-pff-war
- Schefter, A. (2022). Lamar Jackson turned down Baltimore Ravens’ contract offer believed to be worth about $250 million, sources say. ESPN. https://www.espn.com/nfl/story/_/id/34566275/sources-believe-lamar-jackson-turned-baltimore-ravens-contract-offer-worth-250-million
- Silver, M. (2025). How Eagles GM Howie Roseman has gone from firing chants to Philly royalty. https://www.nytimes.com/athletic/6113552/2025/02/05/philadelphia-eagles-howie-roseman-super-bowl/
- Venkatesh, A. (2024). PAVing the way for the future: A model that determines player value and evaluates trades in the NFL. Dartmouth Sports Analytics. https://sites.dartmouth.edu/sportsanalytics/2024/02/13/paving-the-way-for-the-future-a-model-that-determines-player-value-and-evaluates-trades-in-the-nfl/
- Yurko, R., Ventura, S., & Horowitz, M. (2018). nflWAR: A reproducible method for offensive player evaluation in football. Journal of Quantitative Analysis in Sports, 15(3), 163–183.
Tools Used
- Anthropic. (2025). Claude Opus 4.5 [LLM]. Used for coding assistance.