Extra Points
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Why Is 16 Better Than 21?

Fun article from Jon Bois at SB Nation. Did you know that more points doesn't always mean a better chance to win? In the history of the NFL, it turns out the graph of points scored and how often teams won that particular game is far from a straight line. This is true even if you only use more common scores like combinations of 3 and 7. Why do teams with 16 points win more often than teams with 17 or 21 points? It looks like scores that require multiple field goals win more often than scores that don't. It's fascinating since we know that its better to score a touchdown than a field goal. It seems to have to do with turnovers more often leading to field goals. Interesting stuff here. Discuss.

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23 comments, Last at 17 Dec 2020, 4:07pm

17 I guess if the game is so…

I guess if the game is so low scoring - the team that manages to get a safety generally has the better defense.

That doesn't have to do much with field goals. I wonder how many teams won with 5 points though. Can't be many.

3 What is implication here?…

What is implication here? Clearly its not better to be conservative and kick the field goals as a general principle. However, it does suggest that if you are a very turnover prone team, you probably are better off kicking a field goal than going for it. Or to state it more bluntly, if you are turnover prone, you should be less aggressive overall in approach deep in your opponent's territory.


There are still issues of sampling bias that I am curious if they accounted for. Once you start slicing and dicing data down, you may end up oversaturated by a certain types of teams. There's also the issue of time trends biasing the data.


Still, interesting read. 

4 Chase Stuart wrote an…

Chase Stuart wrote an article on this a few years ago;  teams with 6 points have a better record than 7, 9 better than 10, 13 better than 14, 16 better than 17, 20 better than 21, 23 better than 24, 27 better than 28, and so on;  it's weird that it holds up consistently, but there must be some utility to more scoring drives, even if it results in fewer points (and yeah, it holds up even for bigger gaps in points like 16 to 21).  here's the article:  https://www.footballperspective.com/two-field-goals-are-better-than-one-touchdown-despite-math/

5 If you have two field goal…

If you have two field goal drives, your opponent takes a kickoff (unlikely a strong field position) both times; whereas after one touchdown drive and one punt, maybe the opponent ends up with better field position and is more likely to score a tying touchdown. (I would think this is built into DVOA - two good drives where you fail in the red zone are a better indicator of team quality than one good drive with a TD and a three and out).

7 I suspect what's going on is…

I suspect what's going on is that an increase in the number of scoring drives for you weakly implies a decrease in the things going right for the other team's offense and special teams.  You might be getting the additional scoring drives from turnovers, or from better field position and special teams, or by chewing up clock and decreasing the number of total drives in the game, but any of those situations make your odds of winning better.  I expect that if you chart stats like average field position or time of possession versus score in the same way that the article charts turnover margin, you'll get similar results.

It would be an interesting follow up project for somebody to try to figure out if there is a decent formula for winning percentage given just the types and numbers of one team's scores (so the inputs would be num touchdowns score, num field goals scored , num extra points scored, and num safeties scored, and the output would be a winning percentage estimate).

6 I'd be fascinated to see…

I'd be fascinated to see whether this also held up in pro Rugby - another sport with almost identical scoring increments. That might tell us something about what is going on here.

I.e. is this something unique to do with the game of football, or is it a wider game-theory type issue? 

You can easily argue that a greater proportion of points scored in field goals (or penalties in Rugby) by one of the teams team could imply that a) offensive conditions are difficult, and/or b) the game is close. In which case the other team is likely to behave more conservatively and also have their points total driven down. 

8 Last paragraph

I suspect that both (a) and (b) are true. [In my post, I assume that BJR also is implying a game where both defenses are better than the offenses, not just weather conditions.] When (a) is true, both teams are more likely to have a "take the points if you can get them" mindset--so a FG attempt of <45 is a good outcome. Even in today's more analytically inclined NFL, the offense probably wouldn't go for it unless it was 4th and <1.5.

When (b) is true, coaches tend to become more risk-averse, knowing that one big play could tie the game or give them the lead. If your defense has been dominating, why give their offense a 35-40 yard head start (net field position after a punt)? Plus the "momentum" of a 4th down stop for the other team, while not really measurable, may lead their play-caller to attempt a higher variance play (flea-flicker, reverse, halfback pass, etc.) that he might not attempt while inside his own 25 or worse. 

I also suspect that the "more scoring drives=better team quality" factor applies here too.

9 I agree with these posts…

In reply to by Joseph

I agree with these posts that more field goals likely implies a close defensive game whereas if you have scored lots of TD's you don't care about allowing a late TD additionally teams trailing by a lot will bypass a FG attempt to try to score a TD

10 The close defensive game…

The close defensive game argument doesn't match the data; if that was the primary driver the effect should go away when comparing scoring 27 points to scoring 28 points (since at that point you aren't playing a close defensive game) and it doesn't.

11 Simply sample size

only take away I get from it. 

That and it's like passing yards. You get a lot because you're behind but can still fall short as opposed to having a 16-0 lead and you being content with running the clock out. 

Otherwise idk what else to do with this info. On a large scale it does show scoring more is better, instead of two arbitrary numbers picked out. 

Another good example is (I bet, I have no evidence of this specific example) the average pick #21 is better than #16 in drafts. Doesn't mean you should trade em straight up to move back. And over the whole scale a random 1st rounder>any other pick. Just one of those things you probably should read too much into.

13 This is an interesting…

This is an interesting theory that could very well be right.  You could try to measure this by throwing out all games that had a margin of more than 10 points, or two scores, or something.  Because you're right - a team down 42-14 in the third quarter isn't going to kick two field goals, they'll probably keep going for touchdowns.

12 I wonder if it has to do…

I wonder if it has to do with the other team.  If a coach is playing against the 2007 Patriots or 2019 Chiefs, he is probably going to play more aggressively...going for it on 4th more rather than settling for FG's.  And that will lead to more points (and higher occurrence of TD only scores rather than lots of FG scores).  However, because he's playing such a good team, he's going to lose more.  Whereas a coach that is willing to settle for 6 FGs may be so willing because he's playing the Jets.

In other words, scoring fewer FGs instead of TDs doesn't make you more likely to win, but rather, when you're more likely to win (because you're playing a bad team) you're more likely to settle for FGs.


15 1) Scoring drives seldom…

1) Scoring drives seldom give your opponent good field position. So 2 field goals may in fact be more valuable than one touchdown drive and a short drive followed by a punt.

2) More sustained drives usually mean fewer drives overall, for both teams. So your opponent has fewer chances to score.

3) Scoring drives do not end in turnovers. Other drives might. It’s another reason scoring, even a field goal, confers better field position than an average non-scoring drive.

4) Near the end of a game, teams usually settle for a field goal only if it improves their chance of winning. So the presence of a late field goal biases the sample towards games where a field goal has a chance to be decisive. In a sense, winning causes late field goals. It’s a little like running to win.

5) There may be an era thing going on here. The field goal to TD ratio has changed (I think). So 20 points, for example, may be a winning score more often than 21 because it happened more back in the days when 20 points was a good score.

This is all speculative. But it’s interesting to theorize about.


19 Yeah, I think game…

Yeah, I think game stituation, like #4 may be a strong factor.  I wonder if this sort of analysis holds up if you look at points scored by halftime, or at the end of third quarter.

16 In case you were wondering,…

In case you were wondering, that bar that shows up at 3 that means someone won by scoring only 3 points.

Steelers vs Dolphins, 2007. Mud Bowl. The punt stuck in the swamp game.

There could be other games, where a team won by scoring only a FG, but it won't be many.

18 My theory...

My theory would be that a team is much more likely to decide to kick three field goals to get to 16 points in a situation where 16 points is a winning score. Otherwise, they're probably going to go for it on 4th down a time or two. So the fact that scores reflecting multiple field goals would be more likely to win is because of the game flow situations that lead to the decisions to kick multiple field goals, not anything about the fact of the multiple field goals themselves.

22 Some scores are too easy to hit

My theory is that the common scores are too easy to hit.  A team can score 21 points without making any decisions, so their opponents might have scored anything from 0 to 60+.  A team that has scored 16 points has probably kicked 3 field goals, which means they decided to kick 3 field goals, which means making 3 field goals kept them in the game.  If the opponent is in the process of scoring 40 points you probably won't have the opportunity to attempt 3 field goals.

I would want to look at the standard deviation of the opponents score for each possible score.

23 PFR's blog had a post about…

PFR's blog had a post about this back in 2006. I'll repeat the same basic point I made then: teams don't win because they kick field goals instead of going for touchdowns. They kick field goals because they are extending a lead, instead of going for touchdowns to catch up.

That's why teams that score 16 points (1 TD + 2 FGs) win more than teams that score 17 points (2 TDs + 1 FG). It's the same reason winning teams have more rushing plays, higher time of possession, more kneeldowns, etc.