Testing the “3 Field Goal Theory”

Original Post: August 10, 2018by Eric Marturano

I’m not sure when it started, but it was definitely under Andy Reid.

The Eagles lost 16-17…or maybe it was 23-24. It probably wasn’t 9-10…but who knows, it could have been that too. Anyway, they lost and they kicked 3 field goals – that much I do know. I know this because I remember sarcastically lamenting to my Dad, “Hey, well at least we got down the field 3 whole times and have 9 to show for it!” during what was surely a losing effort. Since that undefined moment in time, “The 3 Field Goal Theory” was born.

Nowadays, my family and friends will text me when there is “3 Field Goal Game” in play. It feels like these games are (almost) always losses for the team with 3 Field Goals. Could there be something to this “3 Field Goal Theory?”

Before going any further, I should probably explain in more detail – “The 3 Field Goal Theory” can be described as follows:

“If you kick 3 field goals, you’re probably gonna lose”.

This theory rests on the following, semi-related premises:

1. Kicking field goals is often the result of stalled drives.
2. If you’ve kicked 3 field goals, you’ve probably stalled too many drives that were otherwise prime scoring opportunities – and in a 60 minute game where sustained drives can sometimes last up to 10 minutes, this can be the kiss of death.
3. If you converted all 3 of your field goal attempts (and thus have 9 points to show for it), you remain vulnerable to coming out down 1 point from that advantage in just two opposing scoring drives (TD + extra point + field goal = 10 points…which is 1 more than 9; the power of math, I know). Anybody who has ever settled for multiple field goals in a game of Madden (couldn’t be me!) knows this all too well.

So after years of having this goofy “3 Field Goal Theory” in my life, I wanted to know…does this theory, born out of the frustration that could only be induced by one Andy Reid, actually hold up against any sort of objective test?

As I quickly found out in my research, this is not an easy question to answer, at least with publicly available data. Not having the capital (or the trust, quite frankly) to pay for football data sets others may have compiled, I decided to take a few different routes in pursuit of some semblance of an answer. What follows is a journal of nerdy madness – please keep all hands and protractors inside the vehicle at all times as we proceed through the unhinged thought processes that occurred as I investigated this theory. If you black out halfway through, feel free to skip to the end; I won’t be entirely offended:

• First, I started with running a simple correlation between wins and field goal attempts per game from the 2015, 2016, and 2017 seasons (n=96; 3 seasons of 32 teams). I found it funny that in 2017, Andy Reid’s Kansas City Chiefs led the league in field goal attempts per game with nearly 3 (2.81 to be exact). Who better than Father Time himself to give me hope that I was onto something? (Data was pulled from our good friends over at ESPN.com)
• The correlation between wins and field goal attempts per game from these 3 years was a weak positive correlation (0.31), suggesting that 3 field goal attempts isn’t indicative in-and-of-itself towards losing a game. In fact, kicking three field goals seems to actually help, if only a little bit. This makes sense intuitively: more points is always better, and 3 points is better than the 0 points you didn’t have a moment ago. It should come as no surprise that more points generally means a higher likelihood of winning. To quote one of my high school defensive coordinators – “If they don’t score, they don’t win.”
• However, mere correlations don’t factor in the situation, or opportunity cost, of kicking a field goal – a key element to the “3 Field Goal Theory.” Touchdowns are worth more than twice as much as field goals (after accounting for the extra point), and there are limited chances to get them throughout a game. Through this lens, every field goal kicked potentially represents 4 (or 5) points left on the board. In other words, a gain of 3 points is nice…but a gain of 7 (or 8) is much nicer. Each possession not ending in a touchdown, thus, leaves the team that is failing to reach paydirt further and further exposed to their opponent as the clock marches towards 0:00.
• Brainstorming ways that I could begin to test this notion, I next attempted to manually construct a data set that would allow me to incrementally examine the potentially diminishing returns of kicking 1, 2, 3, 4, or 5+ field goals during the course of a game. I believe there must be a point of diminishing returns for attempting field goals, and I have a hunch that it’s around 3. After all, if an opponent plays its cards right, it can make up the 15 points from 5 made field goals in just two trips down the field. There is a reason teams don’t kick field goals until 4th down.
• Unfortunately, as I combed through and began to assemble various online data by-hand to answer this unorthodox question, I realized it would be a data set that would take multiple months to construct the right way. I’m impatient, so I elected to shift instead to general regression analysis regarding field goal attempts per game and their relationship with Wins.
• To build this dataset, I scraped two websites for 2015-2016 NFL regular season data: NFLSavant.com and ESPN.com. NFLSavant.com provided me with 2015 and 2016 season play-by-play data and ESPN.com was able to give me 2015 and 2016 final regular season standings, team offense, defense, and kicking data. This data was then copied, pasted, and formatted into columns in Microsoft Excel.
• Next, I further formatted the data that I had gathered from the web by using the pivot table feature in Microsoft Excel to more easily manipulate the data. My end result was an Excel database of two seasons worth of NFL play-by-play data that was ready for regression analysis.
• I used the correlation and regression analyses features in JMP Pro 13 (a very useful tool for those looking to dabble!) to quickly analyze my data. In total, 64 unique data points (32 teams x 2 years) were assessed.
• After loading my data into JMP, I ran multivariate correlations of each variable on others, looking for relevant correlations with wins.
  • One thing that shocked me was how little correlation any of these metrics had with Wins, let alone my metric of interest (FGA; 0.0634). It wasn’t like I skimped on metrics either – take a look at how expansive just this small section of my correlation table was. I checked everything from well known metrics to more detailed ones. The unique team dynamics of football are on full display here – no one aspect of the game is too heavily responsible for a win:

    
    

    The joys of JMP Pro 13

  • The measures that were most correlated with Wins were OFFPTS (Offensive Points…shocker, I know), XPM (Extra Points Made, which essentially serves as a proxy for touchdowns), and %4thIsRush (meaning the % of 4th down plays that are running plays). While these metrics were the most correlated with Wins, they only fell into the “weak positive” 0.25 to 0.37 range.
    • Another minor observation came from this analysis: when I compared tendencies of how playoff/non-playoff teams behave on a down-by-down basis, I found that they behave essentially identical, except for 4th down – where I found that teams that made the playoff teams were 5% more likely to run on 4th down than pass.
  • Finally, I was ready to explore the relationship between FGA and Wins using regression analyses. After much trial and error, I settled on the following 5 models, which collectively paint a similar picture:
    • Model 1 (Adj. R^2 = 0.22; FGA p=0.0545):
      Win = 14.149 + 0.125 FGA + 0.278 XPA – 0.004 OFFYDS
    • Model 2 (Adj. R^2 = 0.25; FGA p=0.0962):
      Win = 12.465 + 0.106 FGA + 0.258 XPA – 0.003 OFFYDS + 4.809 %4thIsRush
    • Model 3 (Adj. R^2 = 0.26; FGM p=0.0253):
      Win = 14.704 + 0.152 FGM + 0.275 XPM – 0.003 OFFYDS
    • Model 4 (Adj. R^2 = 0.29; FGM p=0.0380):
      Win = 13.019 + 0.138 FGM + 0.267 XPM – 0.004 OFFYDS + 4.866 %4thIsRush
    • Model 5 (Adj. R^2 = 0.21; FGA p=0.0676):
      Win = 13.940 + 1.89 FGA/G + 4.17 XPA/G – 0.05 OFFYDS/G
  • Not surprisingly, in the models above, Wins were better explained by FGM and XPM (made attempts) than FGA and XPA (attempts, regardless of make or miss). Again, having points is better than not having them.
  • It should also come as no surprise that each regression model also showed that an Extra-Point Attempt (XPA) is worth a little more than 2 FGAs (2.1), all things equal.
  • So what do those equations mean in English? I’ll use Model 5 as an example, which would translate to this finding:
    “We can reasonably expect each additional FGA per Game to result in an additional 1.89 Wins on the season.”
    • Note: Models 1-4 need to be interpreted at the season total level (i.e., for Model 3, each additional FGM results in 0.152 more wins on the season). It’s also important to remember regular season wins are capped at 16.
• Some more findings:
  • In most of my models, FGA hovered right around the 5% level, with Model 2 being the highest at p=0.0962 (i.e., significant at the 90% confidence interval) and Model 1 being the lowest at p=0.0545 (i.e., significant at about the 95% confidence interval). I took this to mean there was a weak impact of FGA on Wins, especially since my Adj. R^2 were fairly low for each model.
  • I found that including some form of OFFYDS helped control for a team’s ability to move the ball. Oddly enough, my coefficients for any iteration of this these were very, very small negative numbers. This further indicated to me that I should view OFFYDS as simply a way to remove or “hold out” a team’s ability to move the ball from the regression analysis.
    • Moreover, according to one of my “3 Field Goal Theory” premises, this finding provides some evidence that the disadvantageous point value of 9 (3 field goals) might carry more relative weight than the drawback of settling for a field goal on a stalled drive. While further study is needed, I found it to be an interesting finding even in a general analysis.
  • Another thing to note was the choice to include the %4thIsRush variable and its large coefficient of about 4.8 in Models 2 and 4. The interpretation here is that for every 1% increase in 4th down rushing tendencies, a team can expect 0.048 more wins. That means that about a 20% change in 4th down strategy should account for 1 extra win per season. I’m not sure this would exactly hold in reality, but it provides food for thought and future studies regarding run/pass tendencies in certain situations. Coaches who like to gamble on 4th down – like our very own Doug Pederson – would probably be pleased to know this sort of thing.
  • The overarching result of these regressions is that FGA has a fairly weak impact on a team’s likelihood to win.
    • Unfortunately, none of my models had an Adj. R^2 above 0.30 (which isn’t great to begin with). Given the right data set and the ability to bucket the data into my aforementioned categories of field goal attempt interest, perhaps I would have found something a bit more clear.
    • Regardless, the results of this general inquiry imply that the number of FGAs has little impact on if a team wins or not.

Are you still with me? Or did you black out from the joys of analysis? I hope you found that as fun as I did!

I’ll let my final word on “The 3 Field Goal Theory” be this: It was a theory that was born out of frustration with Andy Reid’s pace of play and is a theory that is a lot of fun to follow live, if only for the jokes when your friend’s favorite team attempts that 3rd field goal. The results of my various tests are inconclusive to me – there is some evidence both for and against this theory becoming a law. While this all began with Andy Reid, perhaps another Eagles coach – Doug Pederson – provided me with some even more compelling data to chew on: The Eagles won the Super Bowl on February 4th, 2018. Jake Elliot was 3/3 on Field Goals Attempts. Stephen Gostkowski? Well, he was only 2/3 that day. I guess when both teams have 3 Field Goal Attempts, the one that makes them wins. It also helps to have a quarterback that can catch – I’ll let you know if I find any more data on that topic some other time. Until then, enjoy the “The 3 Field Goal Theory” and feel free to argue with me on Twitter (@TheEMart) about it anytime a 3 Field Goal Game is in play. Go Birds.