Adjusting Field Goal Percentage for Perceived Kick Difficulty
By: Jeremy Rosenbaum – jrosenba@syr.edu
Introduction & Background
Although often overlooked, kickers and field goals are an extremely important aspect of football. Unlike most plays from scrimmage, there are few moving parts in field goal attempts, which makes it easier to isolate specific potential factors that led to the outcome of any given field goal attempt.
Statistics that reflect kicker production on free public statistical databases, such as Pro Football Reference, have remained underdeveloped and simple since their inception, despite the implementation of more advanced statistics for other positions on the field. On Pro-Football Reference specifically, while they provide a field goal distance breakdown, which is good for giving a quick, at a glance summary of any given kicker’s performance, the distances are binned arbitrarily, which can be misleading when trying to fully understand how well a kicker has performed.
Additionally, while well-known benchmarks for performance exist in other sports (such as hitting .300 in baseball, or scoring 20 PPG in an NBA season), the drastic improvement of NFL level kicking in recent years has made achieving an outstanding field goal percentage a moving target (LeDoux, 2016). Because FG% is so widely used to evaluate a kicker’s performance, creating a statistic where league average is 0 (much like ERA+/OPS+ in baseball is centered around a league average of 100) is key for comparing kickers through eras.
It is also extremely important when evaluating a kicker’s performance based on field goal percentage to consider variables out of the kicker’s control, namely kick selection. Over the course of a kicker’s career, we would expect the sample of FGAs would be big enough that there would be fairly low variance between different kickers’ average kick distances. However, over the course of one season, where the sample tends to be in the ballpark of thirty FGAs, a team’s kick selection can heavily impact a kicker’s field goal percentage, potentially hindering their FG% through no fault of their own.
Although an extreme and bizarre hypothetical, suppose Kicker A were asked over the course of a season to attempt 20 field goals from fifty yards. In the same season, Kicker B was asked to attempt 20 field goals from thirty yards. If both Kicker A and Kicker B ended the season with a field goal percentage of 80, using solely FG% to evaluate performance, we would think these kickers performed equally over the course of the season. However, because the disparity of kick distances between the two is so dramatic, it’s fair to say Kicker A had the more impressive season (see Figure 1), despite the fact that it’s not reflected through their respective field goal percentages.
While the strong juxtaposition of these situations makes it easy to assess each kicker’s relative performance, it’s much harder to do so in more realistic scenarios in which both FG% and FGA distances differ between kickers. A simple example of the complications that arise when comparing FG% between different kickers can be demonstrated through the staggering of FG%, while keeping kick selection the same in the previously established scenario. Suppose Kicker A has a FG% of 60 while Kicker B records a FG% of 80. In this situation, it’s much more complex to answer the question ‘Which kicker had the better season?’ simply by looking at a player’s field goal percentage.
The idea behind the adjusted field goal stat is to answer just that question by asking: “How much better did a player kick than a league average
kicker in his position would have kicked?” After doing these calculations, we can much more accurately assess how well kickers performed in relation to league average, and therefore in relation to one another, and through different eras, all while accounting for the estimated difficulty of their FGAs.
Data:
In order to answer this question, I utilized the NFL Field Goal Index provided by pro-footballreference.com to manually pull individual field goal attempt statistics from every season in the Super Bowl Era (dating back to 1966). Listed below are the variables and metrics considered in my analysis.
Kicker Name
While not used in the calculation of xFG%, recording kicker names was necessary to create the AxFG% statistic that compared kickers to league average. Using kicker names, we can distinguish between different players’ performance over the course of a season.
Kick Result
Kick result was recorded as a binary result (Y/N). This statistic was used as the primary method for calculating xFG%.
Kick Distance
Kick distance was used in conjunction with kick result and was used to bin kick distances during the calculation of xFG%. This enabled the ability to separate the ‘expected level of difficulty,’ or expected kick percentage at each distance.
Kick Date
NFL Season was extracted from the kick date and used to construct eras by which to judge players’ performance.
Enter Figure 2 Google Chart code for Figure 2: NFL Season vs. Number of Kicks Attempted…Methods:
In total, my method of analysis included utilizing publicly available data on Pro-Football References’ kick index and utilizing RStudio to analyze the raw data. The initial retrieval included a manual scrape of the kick index, and the data was subsequently organized by kicker and season. The data was then cleaned and filtered in order to provide the most accurate analysis possible.
Eras were then constructed using a five-year period preceding the season of any given kick. The five-year period is meant to encapsulate the kicking ability of players in the time period in which a kicker played in and contextualize his performance in relation to his peers. The period, however, was created in a desultory manner, and can be easily revised if need be. The results section will be discussing trends found with this particular five year “era.” The five-year period includes on average a sample of 4,410 field goal attempts, although the sample size is not extremely consistent throughout varying time periods (see Figure 2). Although the rules of field goal kicking have not made kicking easier, the gap in performance between today’s kickers and kickers in past decades (see Figure 3) calls for an adjustment based on era to accurately assess a kicker’s performance.
Table 1: Summary of Average FG% By Distance
| Distance | 1975 | 1985 | 1995 | 2005 | 2015 |
|---|---|---|---|---|---|
| 20 | 87.14% | 96.55% | 96.39% | 98.83% | 99.06% |
| 25 | 79.71% | 89.33% | 92.56% | 95.10% | 98.25% |
| 30 | 72.49% | 80.90% | 86.73% | 91.09% | 94.59% |
| 35 | 70.10% | 71.77% | 81.00% | 85.89% | 88.70% |
| 40 | 54.81% | 58.07% | 72.22% | 79.70% | 86.57% |
| 45 | 37.00% | 54.62% | 54.44% | 65.32% | 78.09% |
| 50 | 27.27% | 39.06% | 49.76% | 60.64% | 71.55% |
and FGA Distance as a time series while grouped by era
Once all kicks not attempted within the parameters of the era are removed from the dataset, xFG% is calculated for each distance a kick was attempted from within that era by calculating average performance from each distance in that era. (see Table 1). From there, a kicker’s actual FG% is compared to their xFG% (what we estimate an average kicker would have done given their kick selection), and the difference is collected under the AxFG% statistic.
Enter the Google Chart code for Figure 3: Kick Distance vs. Field Goal Percentage by Year….Analysis & Results:
Although AxFG% is highly correlated with FG% (see Figure 4), we can see some adjustment for distance take place through varying AxFG% results in seasons in which identical FG% was recorded. We can also observe a clustering of early seasons towards the left end of the x-axis, further highlighting the improvement in quality of NFL kickers over time. This additionally shows how much of an impact creating the eras had, as kickers who played more recently tend to have lower AxFG% stats attached to identical FG%.
Table 2: Summary of FG% and Year for AxFG% Leaders by Era.
1966-1983
| Rank | Year | Name | FG% | AxFG% |
|---|---|---|---|---|
| 1 | 1966 | S.Baker | 72.00% | +23.89 |
| 2 | 1979 | T.Fritsch | 86.67% | +23.03 |
| 3 | 1983 | R.Allegre | 85.71% | +22.14 |
| 4 | 1980 | R.Wersching | 78.95% | +20.81 |
| 5 | 1981 | J.Stenerud | 91.67% | +20.57 |
| 6 | 1978 | G.Yepremian | 79.17% | +19.82 |
| 7 | 1979 | M.Moseley | 75.76% | +19.64 |
| 8 | 1971 | T.Dempsey | 70.59% | +19.34 |
| 9 | 1980 | F.Steinfort | 76.47% | +18.99 |
| 10 | 1979 | T.Franklin | 74.29% | +18.14 |
1984-2002
| Year | Name | FG% | AxFG% |
|---|---|---|---|
| 1989 | E.Murray | 95.24% | +25.32 |
| 1991 | T.Zendejas | 100.0% | +23.51 |
| 1985 | M.Andersen | 88.57% | +21.45 |
| 1985 | N.Lowery | 88.89% | +21.02 |
| 1993 | N.Johnson | 96.30% | +20.05 |
| 1984 | J.Stenerud | 86.96% | +18.43 |
| 1998 | D.Brien | 90.91% | +17.64 |
| 2000 | J.Wilkins | 100.0% | +17.26 |
| 1988 | E.Murray | 95.24% | +16.86 |
| 1998 | G.Anderson | 97.50% | +16.74 |
2003-2019
| Year | Name | FG% | AxFG% |
|---|---|---|---|
| 2008 | J.Hanson | 95.46% | +23.01 |
| 2009 | S.Janikowski | 89.66% | +19.64 |
| 2003 | J.Hanson | 95.65% | +19.37 |
| 2005 | N.Rackers | 95.24% | +16.79 |
| 2003 | M.Vanderjagt | 100.0% | +16.75 |
| 2016 | J.Tucker | 97.44% | +16.56 |
| 2005 | J.Nedey | 92.86% | +14.44 |
| 2018 | M.Bryant | 95.24% | +13.88 |
| 2011 | S.Janikowski | 88.57% | +13.13 |
| 2011 | R.Bironas | 90.632 | +12.93 |
Note: Values are recorded using single-season performances and adjusted based on the kicks of the previous 5 NFL Seasons
As we can see in Table 2, as time has passed, the bar to record a relatively high AxFG% has continually been raised. We can see in 1966 Sam Baker recorded an AxFG% of 23.89 with a FG% of 72.00%. A comparable AxFG% was later recorded in 2008 by Detroit kicker Jason Hanson. However, in order to reach his AxFG% mark of 23.01, he recorded a much higher FG% of 95.46%. Barring any dramatic rules changes, it is expected this trend will continue into the future.
Implications:
While AxFG% accurately provides some much-needed context to FG%, it is not a perfect measure of a kicker’s performance. Firstly, AxFG% may potentially occasionally suffer from small sample size, and xFG% from longer distances may as a result be flawed as a result. For example, if only one kick was taken from 55 yards away within a five-year period and that kick was successful, AxFG% would not reward the kicker for making the kick, as the calculated xFG% from 55 yards would be 100%. While this flaw does occasionally occur, it does not occur consistently and only occurs on extremely long and rarely taken kicks, as the sample is large enough to negate any other discrepancies.
Enter Google Chart code for Figure 4: Field Goal Percentage vs. AxFG%…The next potential flaw is that AxFG% only adjusts for distance. That means it does not account for other factors that potentially influence the outcome of a kick, such as time in game, precipitation, temperature, and score margin. Although elementary analysis of the relationship between score margin and FG% did not find any consistent relationship between the two, temperature is known to influence FG% (Pasteur & Cunningham-Rhoads, 2014). While these factors may affect the success of a kicker, accounting for every variable may fall victim to the creation of unreasonably small sample sizes by which xFG% is calculated, especially when comparing performance across eras.
Enter Google Chart code for Figure 5: Career Kick Distribution by Kick Distance…A third potential flaw is that as kickers continue to improve at the rate they have up to this season (see Fig 3), players may in the future become so good from close range that a team’s kick selection may hurt a kicker’s ability to efficiently produce AxFG%, thereby falling victim to the same thing we’re trying to negate. If this is the case, comparisons between players in the same era will still be fair and accurate but using AxFG% to compare production through eras may lack complete and total accuracy.
Lastly, while this stat is able to be applied to approximate a kicker’s talents over the course of his career, this may be a fruitless endeavor. As seen in Figure 5, the distribution of FGA distances tends to normalize over the course of a kicker’s career, especially in the case of kickers who have longer lasting careers. Additionally, a kicker may be penalized if they play past their prime and their talents deteriorate, although this potential regression will also be reflected in that respective player’s FG% as well. Another idea to measure a kicker’s career is measure how consistently good they were at the peak of their career, and while isolating the best 3-5 years of a kicker’s playing career may give us a good idea of how good a kicker’s prime was, it may not fairly and accurately encapsulate the longevity of a kicker’s performance, and may therefore inadvertently reward a kicker who had an equally impressive, yet shorter prime of their career.
Acknowledgements
I would like to thank Stefan Walzer-Goldfeld (swalzergoldfeld23@amherst.edu) for his assistance and feedback throughout this project.
References
Pasteur, R. D., & Cunningham-Rhoads, K. (2014). An expectation-based metric for NFL field goal kickers. Journal of Quantitative Analysis in Sports, 10(1). doi:10.1515/jqas-2013-0039
LeDoux, J. (2016). Extra Point Under Review: Machine Learning And The NFL Field Goal. Elements, 12(2).doi:10.6017/eurj.v12i2.9448