Are NFL officials biased with their ball placement?

[Disclaimer: I’m British and trying to talk about the NFL, so it’s pretty likely I’m going to sound like either an idiot or an alien while trying to describe what’s going on here, my only request is that you send abuse using the anonymous field at the bottom which goes straight to my email instead of the comment box which everyone can see]

Imagine walking down the street and someone with a clipboard and a bored expression asks you the question “How many glasses of water did you have in the last week?”. You probably don’t really know the answer, and the person asking doesn’t really give too much of a crap. Maybe you could guess at any number between 30 and 40 glasses of water with an equal amount of belief, but you have to choose a number – are you just as likely to choose 32 as 35?

Maybe not, and in the NFL when the guy with the ball gets tackled or stopped at the end of a run and the officials only get a few seconds and a compromised view to decide where it stops, Will every yard line be treated equally?

What I’ve got:  A spreadsheet containing every single play run in the NFL from 2000-2014 (500,000 in all)

What I’m going to do with it: Show that the referees subconsciously change the outcome of a play based on where the painted lines are on a field, and subsequently show that it doesn’t matter.

OK let’s go, first off for the football illiterate, a walkthrough of all the words you won’t know that are important  in this post. (skip to next horizontal line if you don’t need me to explain what a play is)

American Football is based on a series of plays. A play is started by the offense taking the ball and either deciding to run with it or pass it to another player down towards the opponent’s endzone. The play finishes when the player holding the ball:

  1. Is tackled by the defence
  2. Runs off of the field
  3. Throws the ball to someone who doesn’t catch it
  4. Has their motion stopped by the defence.

For  1, 2 and 4 the next play then starts where the ball was when that event happened. However 1 and 4 often look like this:

Can you see the ball? You can take some time if you’d like. The situation above usually starts and ends within a second, and the officials (referees to those who follow soccer) need to get the ball and place it down on a yard line within a few seconds. This is the spot of the next play.

Also relevant to our discussion is the gridiron. This is a colloquial way to refer to the markings (required by regulations) on an official NFL field. It look like this:

so in a play you will start at yard x, and go yards – then on your next play you will start at the x+y yard line – in most cases you will start at a yard line such as 1,2,3,4,…,99 even though the only ones marked out by full lines are 0,5,10,15,..,100. The game of football is then essentially a slow crawl to the opponents end of the field.

Relevant later is the scoring. The two main ways to score are to walk into your opponents endzone (the darker green at the end of the gridiron) – that’s known as a touchdown and is worth 7 points. The second is to be able to kick the ball between the posts at the end of your drive, which is known as a field goal and is worth 3 points.

Okay, I can breathe now safe in the knowledge I haven’t alienated the vast majority of people who might read this. Let’s move on to the interesting part of this post.

The first thing I decided to do when I picked up the spreadsheet with these half a million plays was to ask the question where do plays start from?

So I took every single play in the 14 year dataset, took its starting position and plotted a bar graph. Here it is:


For those of you who realised that my explanation of football above was incomplete, or realise from this graph, an important point is that most of the collections of plays (known as drives) start from the 20 yard line, and the offense can lose the ball if they don’t move it upfield fast enough. This explains both the large peak at the 20 yard line and the smooth decline from 30 down to 100 (the opponents endzone) as the offense has to give the ball to the other team.

In fact, this graph is 90% completely inane and what you might expect. Drives start, some drives finish in midfield (30-60 yard line) and some drives make it all the way to the end (100) in which you have a tense goal line battle (see the peak at your opponents 1st (99th) yard line). What is less easy to explain though is the very sharp peaks which jut out above the smooth curve. I assumed these peaks were my fault and messed around for ages to get rid of them, but I just couldn’t shake them. Then I took this graph and compared it to the lines on a gridiron like so:


Every single one of those staccato sharp peaks occurs on a line which is drawn on the field. This isn’t a small effect, on the 40 yard line this deviation is around about 20%. And it isn’t due to a lack of data, the average deviation from the ‘true’ distribution for a dataset this large should be around 1%, so this is highly statistically significant.

So what could it be? The first thing that came to my mind was that perhaps football teams preferentially run plays which are based around the yard lines. Say instead of just running five yards forward, run to that next line across the field and I’ll chuck it to you. Or maybe there’s a conscious effort by a player to reach for a field line when they see one. Those two sound about reasonable until you consider that if someone was to receive the ball at the 30 yard line, they’re going to run in either direction until they get tackled, which means that a play that was based around the 30 yard line might end up at the 31 yard line, or the runner who is reaching for the 30 yard line might just miss and get the 29. The effect of this on that graph would be to spread out the peak across a few yards, but we instead see a perfectly sharp peak.

The only explanation that has stuck with me is that when a official thinks “oh damn this is a mess, there are seven separate six foot tall millionaires all piled up on top of the ball and I have 100 rules to try and remember, where did that ball stop?”  their subconscious makes them grab for the safety blanket of a line drawn and place it down on there.

This is known as Statistical Heaping and is a well known effect for respondents of surveys. It is the act of choosing a number you’re more comfortable with in the range of values you think it might be, is the number between 8 and 12? Just say its 10. For example take this graph of the birth weight of babies in Tanzania taken from this link:
You see that either you are to believe that the babies weights are being reported as round numbers to save time, or something is happening where you can only produce babies with a multiple of 500 grams.

So if it is true and we’re to believe that the referees are favouring putting the ball on the yard lines – what does it mean? We see that the peaks are far more pronounced by midfield, and when you get closer to the goal line they almost entirely disappear, this makes it seem like the referees are paying closer attention near the goal line because they know it’s more important.

Why is it more important, isn’t a one yard gain a one yard gain? Well to work this out I made a graph of the average amount of points scored based on where the team is on the field. This means that for every yard line I took all drives that had at least one play that started on that yard line, and then did an average over all their points. Shown below: (N.B. 7 points for a touchdown, 3 points for a field goal)


You can see that in the area where the peaks on the painted field lines are most pronounced (30-50 yards), the extra yard on average makes little difference to the outcome of the drive, however when you get close to the endzone between 80 and 90 the difference in one yard is quite significant – this is why the referees are being extra careful.

To sum up: are referees biased in where they place the ball? Yeah, probably. Does it make a difference to a football game? Not really. I feel like there might be something I’m missing as this hasn’t been brought up before to my knowledge, so if you know why this is wrong please hit me up below.

Further unbelievably complex reading on statistical heaping can be found at: Sex, lies and self-reported counts.

Follow me at my shiny new ‘semi-pro’ twitter @JoeyMFaulkner

107 thoughts on “Are NFL officials biased with their ball placement?

  1. Matt Schnabel says:

    This is absolutely awesome man. As an avid football fan and a math junkie, this blew my mind. Imagine how many small plays throughout history have been affected by this heaping… tons of yards could have been lost, or gained in the nonsense. Great study though man, I would love to see this get the attention of an analytic company like PFF or something, that would be awesome

  2. adarshsekharp says:

    The 30 yard mark is the only without a proper cut back into (+1). I wonder why…

    (no seriously, I have no idea why)

    • dbgoff says:

      I think the lack of a peak at the 30 is due to one of the game mechanics the author didn’t mention: the first down line.

      The offense is given four plays (downs) to move the ball forward ten yards. If they succeed, they get another set of four plays to advance ten more yards from the current ball location.

      Since many drives start at the 20, the first line to gain is the 30. Because of that, I would venture that plays that ends close to the 30 get extra scrutiny.

      • Eeefree says:

        Agree on the 30 yard line getting extra “scrutiny” but would like to clarify.

        Since the 30 yard line is often the first down line I would suggest that the refs would tend to avoid putting the ball exactly on the 30 yard line in these cases. The reason being that putting it there would mean that it would be debatable whether it was a first down or not causing the refs themselves to receive extra “scrutiny”.

      • annonuesr says:

        This is the first thing that came to mind here as well. Following on the question of why an official would be more accurate here, that first drive is critical to momentum for a team and the game as a whole. While it doesn’t immediately lead to points, it’s a similar time for officials to pay extremely close attention to where the play ends.

      • Hey EeeFree, NFL footballs are 11 inches long (0.28 m) so they’re quite long. To achieve a 1st down, any part of the ball needs to be at or beyond the 30 yard line, making it quite easy to judge.

      • Doc says:

        Also, a player running the ball or on a pass route will focus his efforts on getting to the 30 yard line to ensure that he gets the first down. But he won’t be aiming exactly for the 30. He will be aiming to cross the 30. This will also be the case if he is running toward or down the sideline. He will try to stay in bounds until he crosses the 30.

        In each case, he will put in the extra effort to get that last yard or two to get the first down. In turn, the defense will be trying extra hard to stop him before he reaches that line. Since so many plays start on exactly on the 20, many plays will likely end just before or just past the 30 rather than right on it. This would help explain why the spike around the 30 is rounded over two or three yard markers.

    • Jeremy says:

      I’m pretty sure it’s because so many drives start at the 20 which means a lot of drives need to reach the 30 for a first down. I think it’s similar to what happens near the goal line. Referees are more careful when you’re near the first down marker and the 30 is a very common marker so it makes the heaping far less pronounced on that particular yard line.

      • Justin M says:

        I think that’s an incredible observation. For every play that was run from the 20 that started a drive, that many times the 30-yard line was the point of the initial first down. It does appear that the line judge is extra careful and meticulous not to falsely award the drive’s initial first down.

        Another point I wonder is that since there is such a high number of plays run where the 30 is the first down mark, chances are the line judge is closer to the end result of those plays and doesn’t have to “catch up” to a play when marking the spot. It could be a physical proximity + higher frequency of opportunity seen at the 30 than other places on the field.

    • chris says:

      I’ll add that it is because from the 20, most sets of plays don’t go exactly 10 yards. After that, the arbitrary starting position causes heaping, but because of the set start line, the randomness of plays causes the lack of it at the 30 yard line.

    • steve alexander says:

      because so many plays start at the 20, and achieving the 30 gets you your first “first-down”, the referees are, again, more diligent? (or more samples smooth out the effects).

  3. John says:

    Came here from reddit.

    Like adarshekharp, I noticed that the 30 is flat. I think this might be due to the lack of penalties that will actually move the offense forward 10 yards. Almost all are 5 or 15 in that direction.

    Are you able add to the data whether the play was run following a penalty or not? As different colors in the bar? It seems unlikely that penalties would propagate all the way down the field like the data would suggest when hypothesizing penalties are the cause, but would be interesting to see.

    I had also been thinking that anything between a line +/- 1 yard would be more likely to round to the line as a mark, but then why no spike at 30?

    • Yes I’ve had quite a lot of questions about the effects of penalties, I’ll have to do a followup blog in a few weeks to address some of the problems/improve some of the analysis. My gut instinct is that penalties will have some effect but not a huge one, just because the deviations (around 20% at maximum) would mean there would have to be a tremendous amount of penalties at the 20 yard line, and the effect still happens near the 70, which would need around 50 yards tacked on. But this is gut and not based on anything deeper than that.

      Thanks for your feedback!

      • Midwest_Product says:

        One thing to bear in mind when looking at penalties is the fact that there are no 10-yard defensive penalties in the game. At least one reason for the lack of a peak at the 30-yard mark, because it would require two consecutive penalties of very specific types to get from a play at the 20 to one at the 30.

        Why it’s so persistent on the other half of the field seems like it has the greater need for explanation.

      • jan says:

        Penalties must be a significant factor for the size of all of the peaks within 15 yards of the 20 yard line. This is because most penalties are awarded from the start of the play, and more plays start from the 20 yard line than any other. Also kickoffs that go out of bounds are often fielded at the 35 yard line by the receiving team. I definitely look forward to any updates from you.

    • klo says:

      Came hear from Reddit also and immediately thought about penalties. Particularly with the assumption that Refs pay more attention to yardage at the goal line. This could definitely be affected by the change in how penalties are assessed so close to the goal line (half the distance to the goal vs. 5/10/15 yards).

  4. Chuckie23 says:

    Cool article, penalties could help explain some of this trend (they are most often awarded in 5/10/15 yd increments) but certainly this effect would diminish the farther out you go from the 20 yd line, so the conclusion is reasonable.

    • Carter says:

      Regardless of how bug the penalty is, they still should only add the exact amount it is. Penalties don’t affect this data at all.

  5. tt612 says:

    Really interesting study of ball spotting. I’m gonna be paying attention to that more next weekend. And just because it’s bugging me, Touchdowns are actually 6 points with the possibility of adding 1 through kicking or 2 through a goal line play. Since you never know when someone new to football would see this, best not to misinform.

  6. dbgoff says:

    Came here from Reddit, too. This is great stuff.

    The offense has four plays (downs) in order to advance the ball ten yards. As the offense moves downfield, the ten-yard mark moves accordingly based on the location of the ball.

    For example, if the offense starts on the 20, their first line to gain is the 30 yard line. If they complete a play that ends at the 33, then their next line to gain is ten yards from that spot (the 43), and so on down the field.

    As for why you don’t have the same peak at the 30 that you see at the other lines, I think there’s a simple explanation: since so many drives begin at the 20, the first line to gain is the 30, and plays that end close to that line will get extra scrutiny.

  7. sean says:

    This is really cool!

    On a kickoff, if the ball is kicked out of bounds, the recieving team gets the ball at their own 40. Maybe that accounts for some of the associated peak there (which seems larger than the others). It’s not exactly a common occurence, so it wouldn’t totally explain it, but maybe it’s a significant contribution…who knows

    • This is exactly what I was going to comment. I think that’s also why there is such a spike at the 40. The penalty doesn’t refer to only the opening and halftime kickoffs but also kickoffs after any points are scored whether it be a safety, field goal, or a TD (In case the writer wants to know).

  8. JT says:

    This is great, i always had a suspicion that the refs were more lenient away from the end-zone. I like being able to see it documented over such a long period.

    I have a theory about the peak between the 20 yard line and the 40 yard line. I think it is the placement of the first drive after a punt return. Most drives start at the 20 yard line but that is after a kickoff. However i think the average starting point after a punt is what moves the starting point closer to end zone. I’d be curious to see the average starting point after a punt.

    • John says:

      There was a recent rules change that has discouraged kickoff returns. Be interesting to see how that moves the peak over time.

  9. Hismikeness says:

    It could be extra scrutiny but more likely it is the positions of the officials near the goal line that would increase their accuracy of spots. In the middle of the field, the back judges are sometimes 20-30 yards apart from their counterparts down line- the side judge- and plays that end in those voids are guesses by stripes at best. Near the goal line, the positioning of the officials is such that all areas of the “shortened” field have multiple eyeballs on it.

    Great stuff here. That was a fun read.

    • Tim says:

      Exactly. The ‘increased scrutiny’ effect isn’t referree indifference. It is caused by the fact that there are more eyes closer to the play when it starts further downfield.

      If you look at the numbers for plays with many yards gained, I’ll bet you’ll see the same level of heaping from upfield. Even more so for interceptions with lots of yards.

    • Tim says:

      That is to say It has more to do with where the refs are at the beginning of the play than where the players are at the end of the play.

  10. jmitchell3 says:

    Great analysis! and kuddos for tackling an explanation of american football as a brit. I doubt I could do as well when describing “soccer”. Also, pun intended. I’ll have to think about your analysis a bit more before I can really digest it. But yeah, good work!

    One more thing: I decided to be “that guy”. Please forgive me.

    Touchdowns, technically, are worth 6 points. Then there is either a 1 or a 2 pt “conversion” based on a single play immediately following a touchdown to either a) kick the ball through the uprights (1pt conversion) or b) score by passing or running the ball into the endzone (2pt conversion).

    • jmitchell3 says:

      Also, those 1 and 2 pt conversions start at the 2 yard line (or 98 yard line)…until this year…1 pt conversions were moved from the 2 yrd line to the 15 yard line.

  11. Chad English says:

    Statistical heaping is an interesting hypothesis, but if that were the case you’d expect the peak to be symmetric about the peak, rounding upward as much as rounding downward, as with the case of the baby weights. Since these peaks are overlaid on a slope, it’s harder to do visually, but it does appear that there is a pretty regular pattern than the slope is undervalued just prior to a 5-yard line, sharp peak at the line, and then the bias tapers off in steps on the high side.

    This implies that it is rounded up more than rounded down, and potentially that 1 yard above the line is still above the natural curve, i.e., 76 yards (no drawn line) appears to be above the curve as well. This may be an optical illusion simply because 74 yards is below the natural line. But there is clearly a high-side taper and not the low side taper is going in the wrong direction.

    Does this not imply the refs are biasing high, not just biasing to the nearest line?

    • Peter says:

      Chad, I also noticed the highside taper, but justified it through normal game play. It is common to see players extend a hand, or cut out of bounds with the goal of making it just past the first down line. If plays disproportionally start from a multiple of ten, so will the first down markers. The high side taper may be the 1 extra yard that players know they need for a first down.

  12. CoolHanMatt says:

    I agree with the above posters who mentioned the variable that you are leaving out is perhaps the penalty. In football penalties are typically nice round numbers 5-10-15 yards. While (as one poster above mentioned) you wouldn’t expect to see them propagate all the way down the field. You actually would but to a lesser and lesser degree of significance. Which is actually what I think this graph visually implies. The lines at the 30 maybe 2-3 standard deviations off when the difference at the 60-70 yard markers is only .5 sigma off.

    i am not sure what kind of information you have access to in your data set but you can test and prove (or disprove this theory) with a bit more testing. You could test to see if plays that were the result of a penalty are statistically significant at those yard markers and compare those to the significance of the plays from the other yard markers.

    Another variable that I think you may want to consider is not actually ref bias but player bias. Since (as another poster mentioned) 1st downs are always 10 yards the players are actively struggling against the opposition to hit that mark. This happens often on a play like 3rd and 1 or 3rd and 2 when the offense runs a play specifically designed to get that exact amount of yardage. The defense also calls a play to prohibit that exact amount of yardage. The result is a normally distributed data set around that marker. In essence you get smaller normal curves centered around 10 yard increments.

    One last thing (variable) we are neglecting is that the refs can place the ball at any point between the yard markers. However the recording of the start of the play its not possible (or at least I don’t think its ever been done) that plays start from the incremental yard lines. So there is error inherent in the recording of the data and the yard lines are always rounded up or down. They never record plays as starting from the 26.2 yard line…they record the 26 yard line instead…even thought that is slightly inaccurate.

    All these variables combined I think will show the result you are finding in this graph.

    Just FYI I have an undergraduate degree in mathematics and work as a six sigma black belt so stats analysis is what I do .

  13. jmitchell3 says:

    Ok, so my first substantive reaction is that, because “first downs” are achieved by progressing 10 yards downfield, and because penalties are 5,10, and 15 yard increments, this may explain these “mini” clusters around each 5-yard interval? Players would have incentive to travel *at least* to the next 10-yard or first-down marker more than other yardages?

    • Tim says:

      After a team reaches a new 1st down, they have to go another 10 yards from that spot for the next 1st down, so if their first play from the 20 gets to the 33, the next 1st down is at the 43.

      The only way for first downs to make consistent peaks at the 40, 50, 60, 70 yard lines would be if you have a lot of games where teams get exactly 10 yards over and over… all it takes is one first-down-earning-play that goes 1+ yards past it and the rest will stop lining up on the 10’s.The only time you are actively targeting the 1st down line and not past it is if it’s 4th and inches and a player is trying to dive just over the line – otherwise the player will usually get at least another yard or two (the defense is trying to stop them BEFORE the line, so if he made it to the line he already broke past the first defender and has an opening for more yards).

      The theory that the refs are being biased with the ball placement seems more likely than teams marching down the field exactly10 yards at a time.

  14. Reese says:

    An alternative explaination to the increased heaping near midfield, or perhaps an additional factor. In the NFL plays are overseen by 7 officials, 1 behind the line of scrimmage, 2 on it, 1 a short distance downfield, and three deep. On a play from the 50 yard line, the four officials who are downfield must be prepared for a pass play that ends anywhere in that half of the field and to do this must watch up to 5 eligible receivers spread over that area. This makes it more likely that a tackle is made without an official nearby, and the official may be more likely to place the ball on a line. Once a team approaches the end zone, these 7 officials have an increasingly small area to cover and it becomes more likely that a given play ends with an official right on top of it who can confidently spot the ball at 19 and a half yards out. I suspect both this and the importance factor you propsed play a role here.

  15. Nick says:

    While I agree that referees probably subconsciously place balls on the yardage lines, the other factor to consider is that ten yards is the distance that many (if not a majority) of plays are designed to go. If you’re facing a 3rd and 10 from the 40, you’re not going to run a play to get to the 47, you’re going to have your receiver run to the 50, then turn back for the ball. He then often gets tackled right there. Or how often do you see a running back dive out of bounds right at the yardage marker? With most plays originating at the 20, it makes sense that you would see spikes in plays at ten yard increments for a bit, then taper off with more variation in plays called further down the field.

  16. Awesome analysis. One thing that I think could add depth is examining how many yards remained until a first down at each turnover (if this data is available). In other words, I think it should be possible to figure out how many drives have actually been unduly ended (or extended) by this heaping by figuring out how many yards the team needed and how many they got.

  17. James says:

    “…some drives make it all the way to the end (100) in which you have a tense goal line battle (see the peak at your opponents 1st (99th) yard line).”

    Can’t remember where I heard this, but I’m pretty sure the NFL defines the yard line a team is “on” by rounding in the direction of the end zone the offense is trying to reach (so if they’re at the opponents 30 and run a play that goes 2.4 yards, the next play is recorded as starting at the opponents 27, even if the ball is technically a few inches closer to the 28). But plays that start inside the opponents 1 are an exception, since they’re still recorded as being “on” the 1 yard line. That means a play starting on the 1 could really be anywhere inside the 2, an area almost twice as large as the area covered by any other single yard line on the field.

    I think that explains at least some of the spike at the 1 yard line. Anyway, this is really cool, thanks for writing/posting it!

    • James says:

      Come to think of it, that may also explain (again, at least in part) the lack of a spike at a team’s own 30. A team that starts on the 20 and gets a first down is going to be beyond the 30, unless they happened to gain exactly (or reasonably close to) 10 yards. And if they don’t get a first down, they probably didn’t get past the 29.

      Of course, in that scenario a team could still be “on” the 30 if they get within a yard of a first down, but my hunch is that the record-keeping conventions are more like loose guidelines, and that even if the ball is just inches short of the 30, if a drive started on the 20 and the offense hasn’t gained a first down the person generating the play-by-play data is more likely to record the yard line as the 29.

    • Charlie says:

      You also have defensive penalties in the end zone, like pass interference, where the ball is placed at the 1.

  18. hangnail says:

    This is a brilliant analysis. Thanks! As a lifelong fan of American Football (and a US resident) the ball spot is often a point of contention but I have always understood (since playing peewee) that the ref closest to the ball decides on the spot, and in critical situations (to make 1st down, etc) the coaches are allowed to challenge the spot (except in a few specific instances). It is definitely a judgement call, and the refs need to keep the flow of the game going, so it is usually more of a guideline than precision call. Thanks again!

  19. NPGenerical says:

    I wonder if some of the reason for a lack of a peak at the 30 is time. Since drives typically start at the 20 and since drives are also typically preceded by a tv timeout, this is the one first down goal in a normal drive that refs have significant time to ‘plan’ for. They all know inherently the line to gain and can set up to watch for it specifically.

    It would be interesting to see if this same bias occurs at the same frequency on plays following team or injury timeouts or other stoppages of play.

  20. Denny says:

    Also here from Reddit.

    While you considered game play and the refs as factors in your analysis, you did not consider the game statisticians themselves.

    I believe the game statisticians are a much better explanatory factor than either the refs or game play.

    Game play and the refs are both messy and imprecise, yielding the ball often sitting in the middle of green space not adjacent to the “grid”. Yet the statistics are always reported in whole yard increments. Even in cases when it should explicitly not be so (half the distance to the goal penalties from odd numbered yard marks).

    I think it is much more likely that the statistician, sitting in a box seat far above the field and guessing about ball placement from that distance, is more likely to be influenced by the ball’s appearance of proximity to a big white line and report the 39.2 yard line ball as 40 rather than 39.

    Otherwise a neat analysis of this weird game we Americans call football.

    • Scott says:

      Yes, I think this is a very plausible explanation of the anomaly in the data! Not a result of real ball placement, but a result of recording it.

  21. dbgoff says:

    I’m wondering how well this would scale to NCAA D-1A college football, where you have ~4 times the number of teams, and officiating crews from multiple conferences, all of whom presumably follow and enforce the same NCAA rules but likely don’t all do so exactly the same way.

  22. Mike says:

    Really interesting analysis. I agree that it looks like you’ve found evidence of statistical heaping; however, I would challenge your conclusion that it must be the referees whom are necessarily guilty of this. I would think that it is just as likely, if not more so, that the bookkeeper recording the plays of the game (and thus your data) might more casually observe where the ball is placed further from the endzone.

  23. nitpicky says:

    Great analysis, but there is one major complication: the data are “rounded” to the nearest yard line. In American football, the official will spot (place) the ball wherever he judges the appropriate spot to be at the end of the play, so the ball can and often is spotted between yard lines. For record keeping, but not for play, the spot is recorded at the nearest yard line.

    It’s not clear to me who actually records these spots for record keeping. If it is not one of the field officials, it is possible that the officials have no bias in spotting the ball, but that whoever is keeping the records is biased towards round numbers (in this case, multiples of five). Even if the field officials are doing the record keeping, their actual spotting could be accurate but their bias is their record keeping instead.

    • nitpicky says:

      Thinking about this a bit more, if the difference is between “true” spotting and rounded record keeping, then we would expect the bias to be roughly of the same magnitude at every five yard line. Since we don’t, some of the bias must be due to poor spotting.

  24. This is a great study, well done. I would also theorize (after watching way too much football than I’d like to admit), punts that go out of bounds might be the best example of this rounding effect. Often times, on a change of possession, a sideline referee will have to approximate where a ball that is 5-20 yards up in the air goes out of bounds and spot the ball. The ref usually isn’t standing underneath the ball when it travels out of bounds, so I would theorize they approximate. I see it all the time where a ref who was standing 20 yards down from where a ball was punted out of bounds, runs to spot the ball, and stops on one of the 5-yard increments.

    If you were able to filter to just possessions that started on a punt that went out of bounds, these spikes would be even more drastic I think.

  25. I entered a comment in the “Why this analysis is wrong” field, I didn’t scroll down to find the comment box, sorry.

    I believe that the heaping you are noticing in this data is not due to the referee’s spot, but to the statistician who is logging this information for each game. In football, the referee spots the ball at the (theoretically) exact location where the ball is downed. This means that more often than not, the ball is spotted at the 31.5 or 31.75 or 31.8234 yard “line”. Also, the ball is sometimes spotted up to several yards (laterally) away from the hash-marks. It is then the job of the statistician (correct term?) to log the whole-number yard line where the ball was spotted.

    If the ball is between the 31 and 32 yard lines, it is probably a toss-up as to which the statistician chooses for the logged spot. However, when the ball is between the 30 and 31 yard lines, I would venture a guess that the statistician is more likely to use the white line that crosses the field.

  26. Travis says:

    My background: I’m a statistician that enjoys building predictive sports models as a hobby.

    My take: What you’ve shown in this graphic is interesting. However, there are 4 key factors at play here, the 3 strongest of which, you have overlooked. They are as follows:

    1) Penalties assessed before or after kick-offs will place the ball within 5, 10, or 15 yards of the 20-yard line with MUCH higher frequency than a smoothed out trend line would imply. I would argue that this is hands down the biggest contributor to the trends we are seeing. It is also why the spike at 30 yards is much less pronounced than the others since moving the offense forward 10 yards requires a parlay of penalties (2 5-yard penalties or a 15 yarder and a -5, etc). It is also why we see the spikes decreasing in size as teams move up the field, because these penalty spots are dependent variables which are parlayed as you move up the field. So if penalties were the root cause, this is PRECISELY what we would expect to see.

    2) The next key factor is in the reporting of ball placements. If the ball is at the 33.5 yard line, the spot of the ball is probably almost as likely to be called on the 33 as it is on the 34 (remember, there’s no option to record the ball as being on the 33.5 yard line. That’s just for TV announcers). The actual play-by-play data spots them on integer values only. This is important because when the ball is on the 39.5 yard line, guess what’s going to change? It will overwhelmingly be reported as being at the 40, and not the 39.

    3) The 3rd key factor is that teams design plays to reach the first down markers. This is likley less of a factor than the two above, but if you plot the distribution of yards per play for any down with 10 yards to go, you’ll notice that it does not follow a poisson distribution, but rather that 10 yard plays are over represented. This is due to the players “aiming” for that 10 yard marker, and designing plays to target it.

    That said, interesting analysis, and thanks for sharing. I do believe that there is likely a bit of an eyeball bias by the officials as you’ve pointed out, but it’s certainly not responsible for the spikes we see in your graphic. It is only a minor contributor to the trend.

  27. David says:

    I also left a comment in” the Why is this wrong box”. I don’t believe it is heaping, rather the affects of penalties. Penalties are generally assessed in 5, 10 and 15 yr increments. When combined with the number of plays that start on the 20, will inevitably result in more frequent ball placement on a 5 yrd hashmark.

  28. Chris says:

    Don’t forget the importance of instant replay. When the ball is closer to the goal line and more scrutiny is expected, so will scrutiny from the head coaches who may want to challenge a spot. Also, in the last few years, every turn over is now reviewed. So, during the review they actually look at where to spot the ball correctly. I’d like to see a graph of the starting field position of every play run AFTER a turnover. I’ll bet the starting position isn’t grouped around the 5 yard lines.

  29. Eric says:

    Ok, the first thing that stands out to me is that it is perhaps not an anomaly of ball placement, but rather one of ball position reporting. How was the data entered into the spreadsheet? If the referees have little incentive to accurately place the ball, then the persons reporting the position at the start of the play have much less. It would be interesting to analyze the accuracy of ball position reporting versus something like the game film. As the ball can be anywhere on or between the lines, perhaps the tendency to assign a lined yardage is a fault of rounding as much as anything else.

  30. The goal of each set of downs is to get 10 yards and a new set of downs. That leads to the results we see in the graph – over the thousands of plays run there are naturally more spotted 10 yards beyond where the set of downs started. Since the 20 yard line is the most common starting point due to touchbacks it would make sense to see spikes at each line. Also would make sense that the spikes flatten the further along a drive goes.

  31. This effect is due to the bias towards sets of plays which advance the ball just past the first down. Since the 20 is a highly likely starting point, and penalties have 5 yard increments, this makes the statistical outlier of the 20 “echo” on all the yard lines that are multiples of 10 and 5 away. This is very strongly supported by the fact that the effect becomes muted the further away from the 20 yard line you are, as the initial condition effects start to die out.

  32. dawgstripes says:

    I am currently a football official in the high school ranks in America and one of the things that makes our job easier after a change of possession is “starting on a line” if we are close. For example there is a punt that is down on the 29 or 31 yard line, we will put it on the 30 because this helps with the first down marker. If the offense gets to the 40 yard line we know we have a first down without even looking really. Your observation is right on about the spots on the offense’s side of the 50, they really don’t matter if its the start of a series. This is very interesting that it carries all the way up to the NFL.

    • matskralc says:

      As a former high school football official, I concur. If we were in between the 20s and we could start a series on a big line, we would. It made setting the chains and quickly determining first downs a lot easier. There were plenty of fields where the big lines were the only lines we had. Once in the red zone, and especially in goal-to-go, exactness of spots (obviously) became much more important than the flow of the game.

  33. David R. says:

    This is great, did you break out by down? For example I think an official is far more worried about placement on 4th and 3rd down then he might be on second and first…

  34. SOJ says:

    The only thing I would add is that the spike at the 40 yd line probably has to do with the fact that if you kick the ball out of bounds on the kickoff it is spotted on the 40 yd line, which may add to the data spike

  35. Stephen Flavall says:

    All the explanations about bias (recording bias, official bias) are missing that they would require equivalent drops in plays starting at the X-1 and X+1 to make up for all the extra plays starting at the X. I’m guessing it’s mostly penalties incrementing in fives and teams running plays which attempt to reach the first down marker.

  36. “that’s known as a touchdown and is worth 7 points” It’s worth 6, but you get the chance to add 1 (a kick) or 2 (a rush) afterwards. Usually they go for the 1 (the 2 is harder) and usually they get it.

  37. Stephen Flavall says:

    Second comment to say (after reading more comments on this) that a HUGE number of people seem to be making a lazy assumption that refs are the only humans who could be influenced by the large lines on the field. There are 22 players on the field every play who can also be influenced by them and the actions of those players (reaching further, squaring for a tackle earlier, cutting for a reception) can also change where the ball ends up.

    • I don’t think that’s even the problem. This has nothing to do with “round number” bias on anybody’s part. It has to do with the fact that football has 5’s and 10’s all over the place in the rules, and thus isn’t not even remotely surprising that you see ball placement that is a multiple of 5 and 10 from the biggest initial condition: the 20. If you had touchbacks start at the 22, you’d see spikes at 32, 37, 42, etc. If you had first downs require 13 years, you’d have spikes at 33, etc. As somebody else pointed out, if there was a bias towards round numbers, you’d see that in a drop at the numbers from which the rounding is occuring. Nice that one can get such phenomenal attention from a completely lazy and incorrect hypothesis.

  38. Has anyone mentioned yet that when you “walk” the ball across the goal line for a touchdown you don’t get 7 points for doing it? Any and all touchdowns are valued at 6 points no matter how the ball crossed the line. Probably a minor point in the greater statistical analysis but valid if this data is ever used to show a correlation in scoring.

  39. Ian Anderson says:

    This is something that I’ve been legitimately thinking about recently too, which has led me to also think about the wishy-washy clock management in the middle of the quarter, but when it gets within 4-ish minutes the clock must be precisely adjusted regularly. This lack of precision in the middle of the games is why I prefer baseball.

  40. I think this is great analysis but I am not entirely convinced. From the comments above the debate seems to be whether the spikes are caused by referee bias as you suggest, or through the propagation of the spike at the 20 yard line either through penalties or strategic offensive play. However there seems to be an easy way to test this: Draw the graph again removing all drives which started at the 20 yard line, if you are right the spikes should remain.

    Two other quick points:
    1) If you are right then one would expect there to be fewer plays from the X9 and X1 yard lines than expected from a smooth distribution, whereas strategic offensive play would probably increase these. You could look at the deviations from a 10 yard moving average.

    2) If you are right and the effect remains excluding drives starting at the 20 yard line, then there is a potential explanation of lack of peak at 30 in the ‘bizarre rule’ discussed in this article: Namely due to the large number of plays starting at the 20 yard line, 30 yard line is disproportionately a first down marker, and when this is the case a ball at 29.5 yards is coded as 29 yards in your data, but would have been coded as 30 yards had the 30 yard line not been required for a first down.

    Fellow British NFL fan and stats geek.

  41. Rob says:

    I think this is more influenced by statisticians sitting way up in the booth. The referees do not advertise the yardage line. It is interpreted by people sitting way up in the box. It is likely they subconsciously round toward the white yard marker whenever the ball is close. When in between yard markers, they likely indiscriminately round up or down. i’ve noticed this when attending games in person. often there may be a disagreement on where exactly the ball is, unless you were really close to the yard marker.

  42. Rob says:

    Also, having played the sport, players will reach toward the big white lines every 5 yards. For example, if I need to get to the 39 yard line for a first down, players will actually pick out the 40 yard line as a target because it is easier to see. You do not want to run the risk of interpreting the 39 yard line differently than the referee.

  43. droopy78 says:

    I’m an avid football fan, and I really think you are showing the result of penalties, not statistical heaping. Most drives start at the 20 yards line (or 40 yard line if kickoff is kicked out of bounce, which I would guess happens 10% of the time). From there, you may have multiple 5, 10, or 15 yard penalties back to back (happens a lot of).

    Until you can add the actual % of penalties in to your study, I am unconvinced of the statistical heaping or ref bias theories,

  44. Cyrus says:

    I believe a cause of bias could be whoever takes the statistics, not necessarily the referee. Because of the width of the ball, it would be tempting to round 39 up to 40 if the ball is indeed at 39.5.

  45. You missed the effect of penalties.

    Touchback – you start at your own 20
    Kickoff out of bounds – you start at your own 40

    Penalties can be +/- 5, 10, or 15 yards.

    That leads to clumping at 5, 10, 25, 30, 35, 45, 50, …

    At the end of the game, when you’re behind, you might start at your own 20 yard line, throw 4 incomplete passes, and turn it over on downs. Now the other team has a spike at their 20.

  46. Erik Olson says:

    The reason the spots appear to be heaped together is simply that they are deliberately moving the ball to the line when it’s close. Officials at all tiers of the game are instructed that in general, if the play ends near the white lines, spot the ball on the line. The exception is if there’s a very short distance needed for a 1st down — then they’ll make sure to spot the ball exactly where they declared it down.

    You’ll see this as well when they’re spotting at the hash marks — the rows of short lines between the 5/10 yard lines. You spot the ball where it went down, except if it’s outside the two middle hashmarks, you spot it at the hashmark. When they do that, they’ll almost always spot the ball exactly on the hashmark. Again the exception is unless it’s less than a yard to go for a first down, then they measure exactly where it was spotted when downed, using the 10 yard chain, and use that mark to place the ball exactly.

    You are completely right that there is a lot of guessing to exactly where the ball was downed, and thus, to be spotted. It’s significant enough that the coaches can actually officially challenge the spot if they feel it’s too far from where the ball was downed. Obviously, they only do so when they think it’ll help them.

  47. Jay Feldman says:

    It also wouldn’t affect the plays too much because there isn’t a bias in either direction, i.e. teams are just as likely to gain a yard as to lose one. In the end, even if a yard in a direction mattered a lot, on average this wouldn’t affect the score.

  48. Michael Schou says:

    Interesting the cut back in the average points scored in the 60-70 yard range, I’m guessing because it’s around the edge of FG range. Would this imply that teams should take fewer FG attempts from that range/go for it more often on 4th down?

    • Neal says:

      There’s two things to consider when deciding whether to attempt a field goal: the *expected* number of points earned and the *variance*. Choosing to attempt a FG from this range might earn fewer points on average, but it’s a safer play. Choosing to make a play is high risk, high reward. If the difference in expected points earned from attempting a FG versus not attempting is small, it could make more sense to go for the safe play rather take a big risk for maybe a few more points; a bird in the hand is worth two in the bush.

  49. I’d think part of the deviation, particularly close to the 20-yd line, is due to fouls. These are enforced by means of a yardage penalty, usually in multiples of 5 yards. So, for example, a kickoff which results in a touchback, but where someone in the kicking team commits a personal foul (15-yd penalty), would have the receiving team starting from 35.

  50. Stinky says:

    I am a football official and I can explain. You are correct about the bias. You are correct that it has little affect on the outcome of the game. However, you are incorrect to assume that the ball is placed on yard lines subconsciously. It is done intentionally.

    The reason for this is because of the first down markers. The offense must gain 10 yards within 4 downs to keep the drive going and maintain possession of the ball. Markers connected by a chain 10 yards long are used to designate the yardage the offense must gain to obtain the first down. If the offense is close to the first down, officials use the chains to determine whether they made it or not. Sometimes this involves bringing the chains on the field and actually measuring.

    I’m here to tell you, the officials hate having to measure for first downs. It disrupts the game, is extra work for them and takes up their time. So whenever the ball is close enough and they can get away with it, officials will place the ball on a yard line. This ensures that the 10 yard marker needed for a first down will be on a yard line and make the officials’ jobs easier.

    This also explains why the bias disappears when the ball is near the goal line. Once the ball is within ten yards of the goal line, the offense cannot obtain a first down. Therefore, the chains are not needed. Because of this, the officials receive no benefit from fudging the spot of the ball.

    Hope this helps you.

    Stinky Whistleteeth

  51. Two corrections in relation to people’s views on the officials. Firstly it’s not the rules that govern where balls get placed, it’s the mechanics. This is the officials bible on where to be and what to look at for each officiating position on the field. In terms of ball placement there are three positions in relation to each yard line. Nose of the ball on the line, tail on the previous line and half way between (as has been discussed at length, the people who record the stats don’t have that granularity!). If the play ends close to the line to gain then the exact position of the ball is used and the chains are moved to the ball to ensure accurate measurement. Secondly the people who are assessing the location on the end of the play are generally the officials known as the wings (Head Linesman and Line Judge (there are some exceptions by distance and type of play)), depending on how far the play went their view on the angle won’t be exact as they will be trailing the play slightly. Again there are exceptions in the mechanics such as plays on the goal line and plays where a close first down call is likely to be needed, when they will get to the line first and come back to the end of the play if necessary. If it’s a longer play then the fact that it ended up 12 or 13 yards past the line to gain isn’t that important as you are still then trying to gain 10 yards on another 4 attempts. Also in terms of initial placing to start each set of 4 downs, beginning on a yard line (not a 5 or 10) makes it relatively easy to judge if a new set of downs has been gained and aids the flow of the game (rather than using the exact spot which then makes it more likely the chains would be used/needed).

  52. beni says:

    I think a lot of it has to do with penalties. If you have the greatest number of plays on the 20 from the kickoff, many times there will be a penalty from this place, which most of the time is going to either add or subtract 5 10 or 15 yards. This is also why you see spikes on the 10 and 15 yard lines – a lot of offenses immediately will false start or get a holding penalty, pushing them back. On the other side, a defensive offside or unsportmanlike penalty is 5 or 15 yards, but there aren’t a ton of 10 yard defensive penalties. So that’s why you’re seeing a bigger peak at 25 and 35 compared to the 30. And the 40 yard line is where the ball starts if the kickoff goes out of bounds. So that’s what I am seeing here, but you could also be right.

    • Aaron says:

      Also, pass interference in the end zone will result in the ball being placed on the one yard line (or 99 as the article says) explaining why there is a spike there.

      • Lou says:

        The one yard line is also the most scrutinized spot on the field. When a player is given an extra yard on the official spot when really being down at the one (and thus awared a touchdown) it is often overturned on replay and placed back at the one. A player given an extra yard from the two to the one (or anywhere else on the field) is never corrected unless it is the difference between getting a first down or not. Also, the one yard line is quite wide, since anything behind the one but close (potentially back to the 1.5 yard line) is still reported as being at the one yard line.

  53. Anecdotally, I don’t buy the ball placement bias from the officials. I can’t recall a single time I’ve been watching a game and thought “wow, they biffed that spot by over a yard”. If that were the case, we’d expect frequencies at, for example, 49 and 51 to not only be lower than at 50 (true) but also lower than at 48 and 52 (not true) because those placements are being rounded off to 50.

    The giant spike at 20 is clearly due to touchbacks. Big spikes at 10, 15, 25 and 30 are impacted by penalties (ex: touchback followed by false start, offsides, holding, … ) . The likelihood of penalties adding up and keeping plays on the x0 and x5 yard lines going down the field falls rapidly. I believe the big spike at 99 is not due to defensive penalties, but rather playcalling. Anecdotally, teams on the 99 will frequently run it and fail to score, thus getting another play from the 99. In other words, once a team is on the 99, they often run subsequent plays from the 99. This gives us a hint: perhaps it’s the playcalling choice. Maybe teams are more likely to throw the ball when on a multiple-of-5 yard line. Throws fail about 35% of the time, thus about that often there will be a next play from the same yard line. The spikes are not remotely this big, so even a partial bias towards throwing in these scenarios would accomplish the spikes. Runs, gain exactly zero yards far less frequently.

    I think the lone play where placement is really somewhat arbitrary and prone to placement bias is out-of-bounds punts. I’ve noticed those are always placed on an exact yard line, perhaps a multiple of 5 is chosen more often. Such punts account for a few plays (out of ~150?) per game, so they could impact the stats, but not to the degree we see.

    To confirm (or deny) my theory, the same dataset should be analyzed for frequency of called run vs pass as a function of ball placement, or the dataset should be filtered only for plays where placement is at the discretion of the official: remove touchbacks and plays following incomplete passes or penalties. That would be the real test of how officials spot the ball.

  54. The mechanics for deciding on the spot where a punt goes out of bounds use correlation between the view of the referee (white hat) to get ball trajectory and the intersection of the out of bounds line as held by the wing official. The wing moves down the line and looks for the referee to indicate, stopping when the WH signals. As discussed this may not be precise but is unlikely to favour the main lines as the WH would be far enough away not to see them clearly and the wing isn’t choosing the line. The placement on an exact yard line goes more to the ease of assessment of the line to gain if starting from a line that’s clear to see, doesn’t matter if it’s A line or a 5/10 yard line.

    • Right, I don’t get the sense that the ball actually ends up on a x5 or x0 yard line more often after an oob punt. I just wanted to call it out as the one place where officials could reasonably be more than a yard off from the reality, and thus perhaps subjected to placement bias. But even so, there’s not enough volume of oob punts to account for what we see. My money’s absolutely on playcall bias 🙂

  55. Phil says:

    I think that’s a really interesting finding

    I think you explanation sounds generally correct,

    I have an idea that you might want to check that might test your hypothesis further

    if the theory is that they pay more attention when they closer to the goal line, the effect is probably similar when they’re spotting the ball close to a first down (rather than a relatively low impact down like a 2nd 7)

    you could run the data for just plays where the next play is a 2&1, 3&1, 4&1, 1 &10 where is 10 or 11 yards from the previous 1 & 10 (implying that they just made the first down), or a turnover on downs 9 or 10 yards form the other teams previous 1&10 (implying that they just missed a first down)

    if you check for the spots on high impact downs and in fact the effect smooths out

    it would seem like that would support the idea that they’re just putting on the big lines out of carelessness


    antedoctally, it does seem like there is more questionable spotting on low impact downs that aren’t right around a 1st down (that’s entirely antedoctal though

    anyway, really interesting post

  56. Once you have filtered the data to include only plays in which the referee actually spots the ball (i.e. no plays following a touchback, penalty, or incomplete pass), we still cannot be sure that the bias is in the placement of the ball: it may be in the reporting of the field position. The officials on the field are able to spot it at fractional yard positions, but the data entry person responsible for this dataset is only returning whole number field position. So, for example, when the ball is spotted at the 19.5 yard line by the official, there is a person watching the game (likely via TV broadcast) entering this position as either 19 or 20. I find it more plausible for this person to be influenced by the painted lines on the field than the referees.

  57. Donald Lacopo says:

    Hi Joey and thanks for the interesting data.
    I had to look twice before I realized what was going on. I read through the comments to make sure no one else has submitted the same explanation. I am pretty sure I have the answer (or at least part of the answer), and I will explain below.
    1. I am sure everyone agrees that the 20-yard line spike is due to touch backs, which is when the ball goes into the end zone on a punt, kick-off, or short field goal.
    2. The 99-yard line is due to the fact it is more difficult to advance the ball from that point, so you see teams run multiple successive plays from that point on the field than in other positions on the field. This is also explained by some of the other comments.
    3. All of the other spikes on the painted lines 5 yards apart, I believe can be explained also. First off, I want to comment on the referee’s comment. I have watched NFL football for over 40 years religiously, and I wasn’t aware of officials bias on the painted lines. I doubt very much that NFL officials are biased when spotting the ball. Maybe a very small amount of bias could be used in order to avoid measuring for first down. I guess in high school and youth leagues, this may be more present. But in the NFL, I doubt that it really exists. Those guys are trying their best to get that ball within a few inches of where it belongs, and if they are biased to use those lines, that bias (I am fairly certain) is not enough to cause the spikes you are seeing.
    The thing you are missing is that once the ball is spotted and move to the center of the field, someone somewhere has to record where the previous play ended and thus where the next one starts. I believe someone is manually entering a number into a computer. I don’t know if this person is part of the official NFL crew, or is like a clock keeper you would see at high school games. My guess is that the NFL has an assigned statistician for every game.
    His job is to record each and every play to a specified amount of detail (incomplete pass, or complete pass from QB x to another player y for a gain of so many yards, or a run by player x for so many yards, etc.) and record what yard line each play was started from and where it ended. They do not record yards gained with real numbers. They use integers. So the guy doing this rounds the nearest yard line to the end of the play, which will also be used for the start of the next play.
    Therefore it is the bias of the statistician that is the reason for the spikes. For example, if the ball is placed halfway (or close to halfway) between the 31 and the 32, the statistician will choose either the 31 or the 32. So let’s say half the time he chooses the 31 and the other half he chooses the 32. This causes no spikes on either yard line. Same thing happens between the 32 and 33. Same thing happens between the 33 and 34.
    But between the 34 and 35 and also between the 35 and 36, he usually will show some bias and pick the 35 more often than not. The reason for this is probably exactly the same reason you had surmised for the referee’s bias. He sees the line. It is very close to the line, it is easy for him to record the 35 in both cases. I can see that this type of bias would definitely create a spike on the 35.
    However, it seems it would also create a little dip on the 34 and the 36, and I am not sure your data shows that. It appears there are a few dips in some of the yard lines next to a painted lines, but not enough to verify this theory. Maybe there are other biases involved also?
    But an important point to realize is that the bias of the statistician has not bearing on the game whereas a referee’s bias would affect the game in either a small or possibly a large way. But statisticians are only tracking statistics. And statistics are used for game planning, fantasy football, etc., but they do not affect the game being played in any way at all.

  58. Gregg says:

    I think you’re on to something. Penalties do account for some of the reason for the painted line bias, but not all of it, I’d bet. Something else to consider is that offensive coordinators may call plays they designed to get just far enough for the first down. So if you start at the 20 and end up with a 3rd and 4 from the 26, you may call a pass play that has a receiver running right to the 30 but no further because that would be unnecessary risk. And then you start the next 3 downs from the 30 and need to get to the 40. The likelihood that these exact 10 yard increments would be possible as you matriculate the ball all the way down the field is unlikely and that could be why the spikes get smaller and smaller as you get towards the right of the graph.

    Great post.

  59. Paul Ostwick says:

    I think an important point was missed here. Since teams very frequently start on the 20 yard line and penalties are 5, 10, or 15 yards, this would explain much of the results for those yard lines. You should remove any spots that are due to a penalty from the chart and see how it looks.

    Also, you are making an improper connection between where the officials spot the ball and where the RECORDS show the ball was. I’ve watched enough football to know that the ball is rarely spotted directly on any line (except for the 20). However, when recording it on paper they don’t write down “20 yard and 2 inch line” they just write down “20 yard line.”

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