Taking a break from vacation for this post, so I’ll be MIA again until at least Monday.

I previously mentioned that I believed the 2013 Eagles have perhaps the widest potential performance distribution in the entire NFL.  Between the roster turnover, the new coaching regime/scheme, and last year’s injuries and craziness, there are A LOT of uncertainties surrounding this team.  Today, let’s compare my prediction with that of the guys at Football Outsiders.  For those of you who don’t know, the 2013 Football Outsiders Almanac has been released, and is well worth the $12.50 price (you can buy it at that link).

In other Almanac news, the 2013 Eagles Almanac has been distributed to all Kickstarter backers and will be available for everyone else within the next day or two.  I haven’t gotten through the whole thing yet (91 pages), but it’s fantastic and is a must-read for any real Eagles fan.  Follow @EaglesAlmanac for more information. You can get the PDF now for $10 at EaglesAlmanac.com.

Within the Football Outsiders Almanac, there are projected performance odds for every team in the league.  The group assigns odds of achieving a number of wins within 4 categories; 0-4, 5-7, 8-10, 11+.  So how do the Eagles look?

It certainly looks like the Football Outsiders team/formula (I don’t know the methodology they use to determine those odds) agrees with the very wide expectation distribution.  According to FO, the Eagles have a 13% chance of winning 11 or more games, a very significant chance given the 4-win performance last season.

However, the team also has a 10% chance of winning 4 or fewer games.

Overall, the FO projection for the Eagles has a mean of 7.8 wins.  You’ll recall that my current projection is 8-9 wins (more likely 8 than 9, so lets call it 8.3); again, I’m more bullish on this team than most.

I think the odds above are underselling the actual potential for this team to have a “true” value of both 10-11 wins and 4-5 wins.  Remember that luck plays a very significant role in NFL teams’ final records.  So a “true 5-win” team will have a significant chance for finishing with 0-4 wins on account of the potential for bad luck.  Similarly, a true 10 win team will have strong odds for winning 11+ games by virtue of good luck.

I have no idea what the Eagles “true” value is right now, my guess is 8-9 wins.  However, it seems eminently possible for the true value to be both very high (if Chip’s system works as well) and very low (if the defense sucks again, Foles/Vick doesn’t work out, or Chip’s system fails).  If FO agreed with that, then I’d expect to see higher odds for both 0-4 wins and 11+ wins.

How do the Eagles compare?

In a vacuum, those odds don’t mean much.  We need to compare the Eagles with other teams to get a true sense of what FO expects.  Here is a chart showing the projections for the NFC East.

Overall, the Redskins are the heavy favorites.  The Giants and Eagles have remarkably similar projections, while the Cowboys lag.  There’s not a lot to disagree with here, but I do not have as high an opinion of the Giants as FO does.  That looks like a 6-7 win team to me, but FO probably knows exponentially more about the Giants than I do, so there’s that.

The Redskins definitely stand as the biggest threat in the division, but I’m skeptical RG3 can repeat his (outrageous) performance from last season.  Still, even if he takes a step back, he’s likely to be among the top QBs in the league, if healthy.  So there’s the target for the Eagles, making Game 1 about as important as any season opener can be.

What about the rest of the league?

In other words, do the Eagles actually have the widest distribution?

One way of looking at it (I’m going to avoid higher level statistical measures here) is to find the teams with the lowest “peak”.  For example, the Eagles “peak” is 42 (% chance for 8-10 wins).  Since all categories must add to 100%, a lower peak means a more even (probably wider) distribution.  Here are the teams with the lowest peak:

The difference between Detroit and Philadelphia (by this measure) is relatively small, just 4% difference in “peak” projection.

Another way to do this is to look for teams with the greatest odds of finishing in EITHER extreme (0-4 wins or 11+ wins).  These are the true “boom-or-bust” teams.  Here are the teams that, according to FO, have a 10%+ chance of finishing with both 0-4 wins and 11+ wins:

So there they are.  As should be expected, each of these teams is included in the previous table above.  Basically, these are the teams for which FO is MOST uncertain.  The Eagles are here, but do not feature as the MOST uncertain.  However, I do have to disagree with a few of the projections above:

– The Colts were very “lucky” last year, so it’s possible the team regresses greatly.  However, Andrew Luck is very good, and I believe he’ll be much better this year than he was last year.  Overall, I think the odds of the Colts finishing with 4 or fewer wins are basically the same as the odds of Andrew Luck getting injured and playing less than half the season.  I do not think the odds of an injury like that are anywhere near 12%.

– The NY Jets winning 11+ games seems laughable to me.  I know the team won 11 games as recently as 2010, but 11% odds seem very high to me.  That % is likely due to the potential for “good luck” to push the team several wins beyond its true ability, but that would require the Jets “true” win potential to be in the 8-9 range, which also seems at least a full win high to me.

– Atlanta receiving a 12% chance of 0-4 wins also seems strange.  This is almost the mirror image of the Jets above.  The Falcons have won 13, 10, 13, 9, and 11 wins over the past 5 seasons.  The team still has Matt Ryan and Mike Smith.  Barring a big injury to Matt Ryan (very unlikely), how does this team win fewer than 6 games?  Just like with the Jets, we have to account for the potential for luck (bad luck this time).  However, even very bad luck will only account for a few wins, meaning the Falcons would have to be a “true” 7 win team for very bad luck to push them into the 0-4 win category.  FO has them at 7.6 wins, so that’s not far off, but I’d have them in the 8-9 win range.

That leaves the Eagles, San Diego, and Detroit as my “Most Uncertain” teams.  Detroit is a crazy team to follow statistically, and nothing that team does will surprise me (outside of a 16-0 season).  San Diego also seems permanently schizophrenic, so a wide distribution can be expected.

I think one of those teams will finish the season with a very good record (11+ wins)…

So yesterday (and the day before) I discussed game theory as it relates to 3rd down strategy, hilighting that it appears as though NFL teams should be running much more often on 3rd and 1 (and 3rd and 2 to a lesser extent).  I also believe teams are incentivized to run more often on 3rd and 3-5, but I’ll have to come back to that later.

Today we need to start looking at one of the potential reasons for the discrepancy we saw in the Call/Success rates for Run and Pass plays.  The overall “game” that we created assumes the goal is to get a 1st down.  On 3rd and 1, that’s obviously a very important goal, but it’s not the ONLY goal, complicating our game.

In the comments, I mentioned that a potential reason for the lack of efficiency is the fact that teams may not be valuing 1st downs as highly as I expect them to.  That raises an obvious question:

How valuable are 1st downs?

To get an idea, we are going to go back to the concept of “expected points”.  Some of you will remember that our 4th Down Strategy series (and the chart accessible off the main menu above) are built from this concept and largely derived from the work of Brian Burke at AdvancedNFLStats.com.  I’m not going to go through the explanation of expected points again, since most of you are already familiar with it.  If you aren’t, see this post, which is the initial post of the 4th Down Strategy Series.

Today we are looking at just one scenario: 3rd Down and 1 yard to Go.

Obviously, in this case, the FIRST yard is the most important one.  Put differently, we should expect the bulk of the value in any 3rd down and 1 yard play to result from gaining the initial yard.  Each gained yard after that also has value, but since you only need 1 yard for a first down, we should see diminished returns after getting the conversion.

That’s pretty logical, but now I want to quantify it.  To do that, I used the data from Advanced NFL Stats, found here.  At this site, you can actually download the Expected Points spreadsheet if you’re interested in exploring it yourself.

Methodology

From this spreadsheet, I put together a fairly simple analysis.  Remember this is only for 3rd and 1.

With every 3rd and 1 play, there are two major outcomes, a first down or a fourth down.  To gain the first down, you only need 1 yard.  So I compared the expected points value of a 1st down at each yard line with the expected value of a 4th down at each yard line.

I then offset them, to account for the gained yard and looked at the difference in expected points.  Here’s an example:

3rd and 1 at the 10 yard line:  A 1st down at the 9 yard line (so gaining 1 yard) is worth 4.83 expected points.  Conversely, failing to convert, resulting in a 4th down from the 10 yard line (original spot) is worth just 2.15 points.  Therefore, in that situation, the 1 yard gain is worth 2.68 points.

Simple enough?

From there, I looked at the marginal increase in value for each additional yard.  So gaining 1 yard in the above scenario gives us a 1st and goal at the 9 yard line, worth 4.83 expected points.  Gaining 2 yards gives us a 1st and goal at the 8 yard line, which is worth 4.94 points.  Consequently, the second yard gained in that scenario is worth 0.11 expected points.

I did the same thing for the third and fourth yard gained, then put them all in an area chart seen here:

As you can see, in a 3rd and 1, the first yard gained is worth A LOT more than each yard gained after it.  If we extrapolated further, it’d become clear that in any given 3rd and 1 scenario, there are TWO particular yards that are far more important than the others: the yard that get you the first down, and the yard that gets you the TD.  In fact, the yard that gets you the TD isn’t worth as much as you think, since being stopped just short would give you a 1st and goal at the 1 (itself worth nearly 6 points).

Pulling it Together

That’s a long way of saying that teams, in 3rd and 1 situations, should be valuing that one yard above all else.  I’ll do a more detailed analysis of this later, but choosing a less optimal play (lower odds of getting the first yard) in hopes of hitting a “big play” isn’t worth it, as least not in the offensive half of the field.

Not all yards are created equal.  Any yardage that gets you a First Down should be the absolute priority on 3rd down.  This will require another post, but I’ll leave you with another example.

Given 3rd and 1 and the 20 yard line, a 1 yard run is worth 2.39 expected points.  A 5 yard gain (presumably from a pass) is worth 2.65 expected points.

Let’s just assume for a second the odds of success for each are equal to the Run/Pass odds we saw yesterday (I know that isn’t right, but its instructive). That means the expected payout for each is:

Run: 2.39 expected points * 70.7% success = 1.69 Expected Points

Pass: 2.65 expected points * 54.6% success = 1.45 Expected Points

For that to be correct, that expected yardage for a run on 3rd and 1 would have to be 1 yard and the expected yardage for a pass would have to be 5 yards, neither of which is likely the case.  However, as you can see, the difference in expected yardage gained would have to be very big to account for the difference in success rates.

Administrative Note: I may or may not be going on vacation next week.  I have no idea if I will be able to post or not, so apologies in advance if I don’t get much up.

Today I’m following up on yesterday’s post.  I encourage anyone who hasn’t done so to read that before moving to this post.

Now, onto the important stuff.

I discussed how we can apply Game Theory to NFL 3rd Down Strategy, highlighting what appeared to be a large inefficiency in 3rd down play-calling.  Basically, we should expect the Run/Pass play call breakdown to reach a point at which both options are equally likely to succeed.

This is the point of equilibrium.

I did some more digging into the numbers, the result of which is better resolution and more actionable intelligence.  Yesterday we looked at all plays run on 3rd down with between 1 and 5 yards to go.

Given what we know about the NFL, this is a very wide range for yardage; teams should run more often on 3rd and 1 than on 3rd and 5.  Below, I’ve broken the data down into smaller parts.  The results are encouraging.  Here is the complete table.  Note that I’ve put this together under the assumption that the original ranges are inclusive of each smaller range (3rd and 1-5 INCLUDES the 3rd and 1 stats), if that’s not the case, then this data is useless.

See why I find it encouraging?

Starting with the bottom row (3-5 yards), we see that the NFL has, in fact, reached the expected equilibrium (close enough).  In a 3rd down situation with between 3 and 5 yards to gain, run and pass plays are both equally likely to succeed.

Remember the Tecmo Bowl Model, though.  As we can see, the equilibrium point occurs at a Run/Pass split that his HEAVILY tilted towards the Pass (18%/82%).  This is expected.  The important part is that play-callers appear to be operating efficiently, that is, calling runs and passes with the theoretically correct frequency.

This could be a coincidence, but given that we made the prediction beforehand and its the logical extension of yesterday’s theory, that seems unlikely.

Now the important part:

While the league looks to have hit its Nash Equilibrium in 3rd and 3-5 yard situations, it DOES NOT look to be operating efficiently in 3rd and 1 and 3rd and 2 situations.

Again, our theory is that at the league level (a very important point), the call rate on 3rd downs should naturally evolve to a point at which the average success of both run and pass are close to equal.

Given the information above, teams should be running a lot more often on 3rd and 1.  Even though they are already calling a run roughly 75% of the time, the success rate of such plays is still significantly higher than for pass plays.

So….teams should run more, which will cause defenses to adjust by “expecting” the run more (Tecmo Bowl), which will presumably lead to Pass plays being “less expected” and therefore succeeding a higher percentage of the time.  Over time, the success rates for both run and pass should converge until they reach equilibrium.

Looking at the 3rd and 2 situations, we can still see some inefficiency, though it’s not as severe as in the 3rd and 1 situations.  Again, the process should be the same.  Offenses should run more, defenses should then commit to the run more often, and pass success rates should increase (while rush success decreases) until both Run and Pass have an equal chance of success.

It’s very important to note that this is League-level data.  Therefore, applying it to any individual team is tricky.  We can NOT say, for example, that the Eagles should definitely run more than 75% of the time in 3rd and 1 situations.  All we can say is that the LEAGUE should run more than 75% of the time in these situations.  It’s certainly a logical step to then take it to the team level; but know that it becomes more difficult at that point, since you have to weigh individual strengths and weaknesses as well as the relative strength of the opponent.

Conclusion:

– NFL offenses are not running enough in 3rd and 1 and 3rd and 2 situations.

– This is a short-term opportunity to exploit an inefficiency in the game.  Once offenses adjust, defenses will too, with the end result of equal success rates and no advantage.

– While I didn’t discuss it here, teams should likely ALSO be running more often in 3rd and 3-5 yards situations, though for a different reason.  I haven’t run the numbers yet, but my guess is that once we incorporate 4th down opportunities into the equation (especially 4th and 1), running will still carry the higher overall success rate (and therefore need to be used more until the defense adjusts).

– This, along with 4th down strategy that we previously discussed (see tab on menu bar), is an area ripe for a “forward-thinking” coach to take advantage of.

Unfortunately, I haven’t yet found the necessary data to complete the type of 3rd down examination I’m aiming for.  Yesterday, I mentioned that many commentators are overlooking the fact that you have to be a very good offense in order to run a lot of plays (you need to gain a lot of first downs).  That might sound obvious, but it’s important to consider when thinking about Chip Kelly’s stated preference for “pace”.  Just wanting to push the pace won’t mean much if the team can’t gain first downs.

Obviously, that train of thought needs more research.  For today, though, I figured I’d highlight something I stumbled across while searching for data.  See this site:

http://football.10flow.com

I have no idea where it came from, but I’ve downloaded the data its supposedly based on and it seems legit.  It’s useful for illustrating an area of the game that I believe is potentially the largest untapped resource of analytical advantage: Run/Pass play selection.

At a very basic level, we can look at play selection through what I will call the Tecmo Bowl Model (or Tecmo Super Bowl if you prefer the upgrade).

What’s the Tecmo Bowl Model?

I’m making this up as I type, but in my head, it’s an incredibly simple construct for visualizing the importance of Game Theory in play selection.  For those who don’t know the game (I’d be very surprised if any readers don’t, but just in case), Tecmo Bowl was a groundbreaking football game for the original Nintendo system.  I won’t go into any more detail than they that, but if you haven’t played it, you should go find an emulator and change that.  The important part is the play selection screen, shown here:

Basically, for both offense and defense, a selection of 4 plays are shown.  The player picks one of these plays by pressing the corresponding button combination (shown below each play).  Here is the key part:

If the Defensive player picks the same play as the Offensive player, then as soon as the ball is hiked, pretty much every offensive lineman is pancaked, resulting in a likely sack or a throw from the QB that’s no more than a jump-ball.

Without getting into any higher-order strategy, the defense has a 25% chance of “picking” the offenses play.

Despite its relative simplicity, I believe this game has a LOT to tell us about modern (and real) football.  In essence, the defense is continuously trying to “pick” the offense’s play.  The results aren’t as dramatic as in the game above, but the fundamentals are the same.

Is the offense going to run or pass? Short or deep? Maybe play-action?

These are all questions defensive play-callers have to ask themselves.  Each subsequent decision is largely determined by both the defense’s overall strategy/strengths AND the subject down/distance/score/time scenario.  

Just as in the video game, if the defense successfully “picks” the offense’s play, the result SHOULD be a “win” for the defense.

So what?

This has obvious reprecussions for offensive strategy.  It is not enough to just pick a good play; you also need to account for what the defense will be expecting.  Correlating to the statement above: if the offense picks a play that the defense is NOT expecting, it has a distinct advantage and will be more likely to “win” that down.

Let’s take a look at an example.  From the site I referenced at the top:

The Scenario:  3rd Down, 1-5 yards to go, All Scores, Any Time.

The Results:

For this scenario, “success” is defined as a 1st down or a touchdown.  What can we infer from the data above?

The output makes it very easy to see the relevant discrepancies.  In this situation, Run plays were 14% MORE successful than Pass plays.

Despite this, Pass plays were called nearly TWICE as often.

There are two leading explanations for this difference:

– It’s a true inefficiency.

– It’s simply the result of the type of Game Theory I described in the Tecmo Bowl example above.  Basically, Run plays are more successful BECAUSE they are called less often.  Pass plays are called 67% of the time, meaning the defense is most likely EXPECTING PASS, leaving them more susceptible to a RUN.

The big question is, has this game (long-term play selection) reach its Nash Equilibrium?

The Nash Equilibrium (very basic explanation) is the point at which both sides know the other’s strategy, but neither side is incentivized to change its own in response to that knowledge.

This situation is slightly different, since we’re talking about individual occurences within a long term game, but I believe the overall point holds.  More importantly, I do NOT think the NFL has reached the point of equilibrium (within this particular scenario at least).

Here’s where I need some help.  It seems to me that the point of equilibrium would naturally occur around the Run/Pass split that equates to a roughly equal chance of success for each.  Note that because of the Tecmo Bowl Model explanation above, this does NOT necessarily equal a 50/50 split in play calling.  Regardless, I might be mistaken in my reasoning here.  If you have any other predictions/analysis, please let me know.

Also, lest we fall victim to a small sample, here is the output when we include every season from 2002-2012:

The numbers are almost identical, which means I’m either missing something in my prediction/analysis (very possible), or NFL play-callers are operating at a very inefficient clip.

Obviously, if it’s the latter, it has HUGE implications for in-game strategy.

Yesterday I looked at defensive plays per game, trying to get a sense of whether teams created more fumbles purely because they had more opportunities to do so.  They do not, but that’s because the difference in # of plays defensed is so small, on average.

More interesting, though, is this chart.  You’ll recognize it from yesterday, though I’ve re-labeled it “Offensive”.

As mentioned, this clearly illustrates an uptrend in the # of plays run per game by NFL offenses over the past 10 seasons.  The overall magnitude is small (see the Y-Axis labels), but the direction is unmistakable.  Last season, teams ran about 1.5 more plays per game than they did in 2003.

The difference is small enough that it could easily be the result of chance.   However, if is was purely a result of natural variability, we’d be very unlikely to see such a smooth trend in the chart above.  Aside from 2008, a distinct outlier, the annual increase in plays run per game has been both smooth and accelerating.

What’s going on?

Let’s take a look at the data in more detail, drilling down to the team level.  As usual, I’ll start with the Eagles.  Here is the same chart, with the Eagles annual plays per game illustrated.

The Eagles annual variability is expected, since the league average will always be more smooth than the individual team measures.  However, notice that the Eagles individual trend is also unmistakable.  Here is the raw data for the team:

Last season, the Eagles ran more than 7 more offensive plays per game than they did during the 2003 season.  Again, the increase hasn’t been smooth (the team ran just 60.6 plays per game in 2009), but it’s real.

Looking at the Eagles line in the chart above versus the League line also tells us that the team has a disproportionate influence on the league-wide uptrend.  The Eagles began the subject time-period well below the league average and finished well above it.

There are a number of potential explanations for this, but before we get to that, let’s look put the Eagles into context.  Here is a table showing the average plays per game run by each team from 2003-2012.

There are a few obvious results (Patriots and Saints at the top, Buffalo and Cleveland at the bottom), but some surprises as well.  St. Louis ranks 7th, for instance, which I certainly would not have guessed.  However, the 10-year average isn’t really what we’re interested in, is it?

We want to look at the relative increase.  Here is another table, this one showing each team’s average over two time periods, ’03-’05 and ’10-’12.  In other words, the first and last 3 seasons of the 10 year period.  Also, I’ve included the change for each team (+/-) and ordered by that measure, so teams that saw the biggest increase in average plays run are at the top.

This confirms what I asserted earlier, that the Eagles have had a disproportionate effect on the overall league trend. Just 5 teams have seen larger increases between the two time periods.

So what?

I probably shouldn’t have taken this long to get to Chip Kelly, but better late than never.  As we can see, the Eagles have already been towards the front of the league in terms of running higher numbers of plays.  Whether this was an emphasis or not, it means that Chip Kelly’s overall effect on the # of plays run may be more muted than is expected.

Given the finite amount of time in each game, the minimum required time for each play to be called and set up, and the fact that the other team get’s a roughly equal number of possessions, there is only so much that Chip can do to ensure the Eagles run more plays.

Notice that New England, a team that clearly emphasizes speed of play, averaged just 2.43 more plays per game than the Eagles did over the past 3 seasons.  Last season, the Patriots ran 74.3 plays per game, which I believe is the all-time record.  Still, that was just 7 more per game than the Eagles.

Overall, a difference of 7 plays per game is HUGE.  However, from a practical standpoint and from a fan’s viewpoint, it’s not going to LOOK much different.  When one considers that the Eagles are very unlikely to be able to run as many plays as the Patriots did last year, that means the team will likely be running no more than 4-5 more plays per game than it did last year (and that’s if things go according to plan.)

Why should we care about # of plays run?

As explained in this article over at Philly Inferno, positive play differential is correlated with winning.  Looking purely at offensive plays run per game, I get a correlation value of .30 (off. plays run – Wins).

SImply put, more plays —-> more yards —-> more points.

However, I want to emphasize something that isn’t getting a lot of attention.  Emphasizing offensive pace is not enough to ensure you will run more plays.

In order to run more plays, you need to keep the ball.  In order to keep the ball, you need to convert on 3rd down.

If the Eagles can’t convert 3rd down’s at a high rate, it doesn’t matter how fast Chip wants to play.  Want to see the data?  I thought so.  Here is a chart of offensive plays per game against 3rd down conversion %.

Given that I’ve probably lost a lot of readers by now, I’m going to come back to this point in another post.  For now, though, let’s leave it at this:

Last season, the Eagles converted 37.4% of 3rd downs.  If the team can’t improve on that measure (significantly), it won’t matter how badly Chip wants to run more plays.  

After last week’s fumble posts, I realized that no team-level analysis would be complete without equalizing for number of plays.  We saw that the distribution in forced fumbles (team totals) over the past ten years does not appear to be random and is certainly not normally distributed.

However, it’s possible that the teams forcing the most fumbles (Chicago) simply had more opportunities.  Basically, is there a “natural” fumble rate?  If so, then the difference in forced fumbles could be largely dependent on the number of defensive plays run.

In compiling the data for this problem, I noticed something interesting, which I’ve touched on previously (very lightly).  Specifically:

There is a surprising lack of variability in # of plays run from team to team.

In my post about potential injuries and Chip Kelly’s offense, the main takeaway was that even the “fastest-pace” offenses do not, on average, run a lot more plays than “slow-paced” offenses.  Today we are looking at # of defensive plays, but since every defensive play is also an offensive play (for the other team), the higher level distribution should be the similar.

Here are the average defensive plays run per game over the past 10 years (for each team, ordered highest to lowest):

The Eagles rank 10th, with an average of 63.51 defensive plays per game.  However, the key is to look at the Max and Min of the table above.  Cleveland has faced the most plays, just under 65 per game.  Pittsburgh has faced the least, just under 60 per game.

So the long-term difference comes out to an average of just 5 plays per game.

Put differently, over the past 10 years, the defense that ran the MOST plays faced just 50 more plays than the defense that faced the fewest.  Note that this is an approximation since there are presumably rounding differences due to the use of averages rather than # of plays (only data available).

Going back to last week, it means that the variability in the number of forced fumbles for each team is likely NOT a function of # of plays (I say likely because the # of plays data does not include Special Teams, which could potentially skew the numbers, though I think that’s extremely unlikely.)  The correlation between average plays against and forced fumbles is -.03; so no connection.

While that’s not a huge surprise, the overall lack of variability in the # of plays data is.  Given how many different factors there are in every football game that affect the number of plays run, I expected to see a somewhat random but certainly WIDER distribution.

Perhaps it’s simply a result of the sample used (a big one, 10 years).  Over that length of time, teams are likely to cycle between “good” and “bad”, which may help the overall numbers even out.

Also, defenses have much less control over the number of plays they face than offenses have over the number of plays they run.  We can assume that “good” defenses will tend to face fewer plays than “bad” defenses, but that’s about as far as we can go.

Let’s look at individual season numbers.

Perhaps most importantly, the entire NFL is trending upward in terms of number of plays per game.  Here is a chart showing defensive plays per game over the past 10 years.  Remember that this is equivalent to offensive plays per game.

If you look at the Y-Axis, you can see that the overall difference isn’t huge (the increase from 2003 to 2012 is just 1.57 plays per game.) However, the trend is unmistakable, with the past 4 seasons showing the most severe increases.

To this end, Chip Kelly’s offense (presumed to emphasize # of plays) is not revolutionary; it’s EVOLUTIONARY.  Tomorrow, I’ll take a detailed look at offensive plays run (same overall data, but different team data and we can draw more from it due to the “control” of the offense).  The key point here, though, is that Chip Kelly’s offense appears to be a natural extension of what we are already seeing in the league.  We have not, of course, actually seen what Kelly’s offense will look like; but it’s safe to say his “plan” fits firmly within the long-term NFL offensive progression.

Let’s take a quick look at some individual defensive play stats.

Over the past ten years:

– The 2010 Titans faced the most offensive plays, with an average of 71.2 per game.

– The 2004 Pittsburgh Steelers faced the fewest plays per game, with 55.6.

– The long-term, league-wide average is 62.9 defensive plays per game.

– The 2006 Eagles faced 65.8 plays per game, the most for the team over the past ten years.  The 2007 Eagles faced the fewest; 61.2.

– There is, not surprisingly, a positive correlation between defensive plays per game and points against, with a value of .28.

As I said above, tomorrow I’ll do a deep dive into OFFENSIVE plays per game, which should give us some idea of what we can expect from Chip Kelly.   I looked at defensive plays today since I had to address the # of Plays effect on forced fumbles (no effect).

NOTE: This post got away from me a bit.  It’s a long one (1200+ words).  If you’re short on time, read the first section covering the 2012 Eagles, then skip to the very end to see the conclusions for today.

So yesterday I showed that Total Fumble Recovery Rates are both random and Normally distributed.  The takeaway was that there is a 97.5% chance that the Eagles will recover fumbles next season at a higher rate than they did this season.

That’s important, since it will almost definitely be a push in the positive direction for the team.  However, it’s far from the whole story.

There are a couple more aspects to cover.  I told you yesterday that we would take a look at recovery rates broken down by giveaways and takeaways, so I’ll do that first.  Then I’ll take a look at the more interesting question: Is Forcing Fumbles the result of luck or skill?  Feel free to skip to the end if that holds more interest for you.

Giveaway/Takeaway Recovery %

Not all fumbles are created equal.  For starters, see this article.  In general, it shows that recovery rates differ by TYPE of fumble.  For example, an offense is much more likely to recover a dropped snap than fumble by a receiver.  I won’t go into that much detail here; the linked article is worth a read for anyone interested.  Let’s take a look at the higher level stats though (Source: Teamrankings.com).

The long term NFL average recovery rate for “giveaway” fumbles is 52.31%.  That means that an offense, on average, recovers 52.31% of the fumbles it commits.

Conversely, a defense recovers, on average, 47.48% of the fumbles the OPPOSING offense commits.

Note that those two numbers do not add to exactly 100%, which I assume is due to fumbles that go out of bounds and are therefore recovered by neither team.

So what happened to the 2012 Eagles?

The Eagles, last season, recovered just 40.5% of the fumbles they committed.  That is roughly 12% below the expected recovery rate.  That’s bad.  However, it’s hardly a large enough deviation from the average to explain the overall performance. So…

The Eagles, last season, recovered just 25% of the fumbles the other team committed.  That is more than 22% below the expected recovery rate, a huge deviation.  In fact, over the past 10 years, only 4 teams have recovered opposing fumbles at a lower rate.  Previously, I highlighted that the Eagles only “gained” 5 turnovers on fumbles last season, FAR below the long-term league average of 11.  However, the team (according to ESPN) forced 17 fumbles, almost equal to the NFL long-term average of 17.15.

So the 2012 Eagles actually forced fumbles at a league average rate, but recovered them an extremely low percentage of the time (which is luck).  That is also extremely unlikely to happen again next year.

Is Forcing Fumbles Luck or Skill?

Now we’re getting to the more interesting stuff.  Recovering fumbles appears to be ENTIRELY luck.  However, if forcing fumbles is the result of skill, then teams have some control over the Fumble Differential equation.  So how do we know?

Similar to yesterday, we can’t know for sure without an extremely in-depth study and a lot more computing power than I have.  However, let’s look at a few different areas to get a good idea of what’s happening.

First up is team persistence.  If forcing fumbles is the result of skill, then we can expect teams that are “good” at it to continue being good at it year after year.  If it is a skill, then it is repeatable.

Here is the chart for forced fumbles, the axes are Year X and Year X+1.

Doesn’t look like much.  The correlation value is .083, which is very small (obviously).

Just in case a year-to-year look was too susceptible to short-term variability, I also looked at the correlation between the 2-yr average and the following seasons total for each team.  Again, a value of .087, still very weak.

That’s certainly a strike against skill, but we’re not finished.

What about individual players?

We all remember watching Charles Tillman last year (he forced 10 fumbles).  Based on just last season, it seems like it’s safe to say he is actually “good” at forcing fumbles.  If he is “good”, than it’s a small logical step to say that others must be good as well.

If forcing fumbles is a skill, then we should see the “best” fumble forcers towards the top of the leaderboard each year.  Here is every player that forced 4 fumbles or more in a single season over the past 5 years.  Click to enlarge.  I’ve highlighted the players who appear on more than one list.

It appears as though there are some players who consistently force a high number of fumbles (relative to the rest of the league).  However, notice the degree of variability in both the number of fumbles forced and the number of players who appear just once.   Some of you will have already noted, though, that what we should really be looking for is RATE.  Next week, I’ll try to equalize for that (thought of it too late for today’s post).

For now, I think it’s best to say that at an individual level, certain players appear to force fumbles more often than others, meaning it may be the result of skill.  However, given how many people are on the field at once, the relative impact of that player contribution may be small enough that it’s relatively insignificant to the overall game.  Not there yet, I’ll try to detail this more next week.

What about teams?

Certain teams appear to be better at forcing fumbles than others (the Bears are the obvious example).  The Bears look as though they’ve made forcing fumbles a large point of emphasis.  Looking at the overall totals from the last ten years bears this out.

The Eagles are close the middle of the pack, having forced 164 fumbles over the past ten seasons.  The NFL Average is 166.9.

Does this mean the Bears are “better” at forcing fumbles than other teams?  Maybe.

As I showed above, there is really no persistence in the year-to-year forced fumble data.  However, the team totals data is Non-Normal and skewed negatively (meaning the distribution is thicker at the high-end than the low), as are the single season totals.  Despite the persistence values, it appears as though, at the margins, some teams/players do create fumbles at a relatively high rate (have to confirm though).

Similar to yesterday, I have now provided more questions than answers.  I will attempt to answer some of those next week.  Allow me though, to sum up in as clear an explanation as possible:

“Creating” fumble turnovers is the result of two discrete factors.

– Forcing the fumble.

– Recovering the fumble.

How do the relative correlations of these two factors compare?  In other words, to what degree is “fumbles gained” explained by each of these?

Here is Forcing Fumbles to Fumbles Gained:

The correlation value is .676, very strong.

Here is Recovery rate to Fumbles gained:

The correlation here is .59, also quite strong.

The difference in correlation strength is big enough to notice (.086), but relatively small.

Here’s the key part:

– The two factors (recovery rate and # forced) appear to be relatively equal in importance.

– Recovery rate is completely random.

– # of fumbles forced appears to be largely random (though skill is involved).  This needs more work, but putting those two factors together means:

While there may be some individual skill involved in forcing fumbles, when incorporated into the whole “fumble equation”, that contribution is small, and certainly less of a factor than random chance (luck).

Congratulations if you’ve read this far.  As is often the case, I ended up pretty far from where I intended to.

Today, let’s go back to talking about fumbles and luck.  It occurred to me (or was pointed out), that there are two sides to the equation, and I’ve only really looked at one.  To refresh, I previously explained that “fumble problem” is largely overblown.

For individual players, there is some year-to-year persistence in fumble rate (fumbles/rushes), but it’s small.  Overall, there is a large amount of luck and natural variation in any particular player’s rate of fumbling.  Here is the post.

Additionally, I explained that while not all fumbles are equal, over the long-term we should expect every team to recover approximately 50%.  The counterpoint to this argument is that it’s about “hustle” and “heart”.  As you can imagine, I have little patience/regard for that side of things (in this specific scenario, not necessarily in everything).  However, I do not believe I actually took a look at the team-level statistics to back that assertion up.

Let’s look at that now.

First up, we’ll tackle the OVERALL team fumble recovery percentages.  Then I’ll break it into recovery percentages for giveaways and takeaways (much different situations which carry different expected recovery rates).  NOTE: I’ve decided to push the breakdowns until tomorrow, after reaching nearly 1000 words on the first section.

Team Fumble Recovery Percentage

This statistic (data taken from Teamrankings.com) covers the percentage of ALL fumbles that a team recovers.  This is very important for Eagles fans.

Last year, the team lost a historic amount of fumbles (22) and gained just 5 (NFL long-term average is 11).  Not coincidentally, the Eagles recovered just 35% of all fumbles last year, 4th worst in the league (Buffalo was worst with a rate of just 30.6%).

If Fumble Recovery % is truly random, then the Eagles can be expected to regress to the mean next year (50%), which would result in a better TO differential (which is highly correlated with Wins/Losses).

To get a look at the randomness, I’m going to look for year-to-year persistence.  This is where it gets tricky.  Due to the amount of players on NFL rosters and the constant turnover in personnel, just looking at a team’s year-to-year persistence isn’t enough to conclusively prove anything about fumble recovery %.  As usual, we will have to settle for a strong indication, since equalizing the data for every player and every play is far beyond the scope of anything I can (or want) to do.  Just know that this is an issue inherent in almost every NFL analytic breakdown or long-term analysis.

Before we look at the whole league, here are the Eagles’ yearly total fumble recovery percentages from 2003-2012:

As expected, the annual totals seem to fluctuate relatively narrowly around the 50% mark.  Also of note is just how much worse last year was when compared to the previous 9 seasons.  This is a major reason why I expect improvement next year.  It’s not just that the Eagles were below the expected recovery %, it’s that they were FAR below it; it’s difficult (though far from impossible) to get much worse.

Now let’s look at the entire league.  Here is a graph showing the One Year persistence of Fumble Recovery Percentage for the entire league over the last 10 seasons.

As you can see, there is no correlation (officially its -.06).

Due to the factors I cited above (roster changes, personnel differences, etc…), we can’t say definitively that fumble recovery % is all luck.  However, we can absolutely say that a team’s % for one year doesn’t tell us anything about it’s expected % next year.  In other words, the Eagles 35% recovery rate in 2012 doesn’t tell us anything about the 2013 season.

Mean Regression

The flip side of what I just said is that just because the Eagles were below the expected mark last year in no way means the team will be at or above the mark next year.  That’d be a bit like playing roulette and expecting the next roll to be black because the last 3 were red.  The overall idea is that each season’s recovery percentage is entirely independent.

So why do I expect the Eagles to recover?

Looking at the overall data, the standard deviation of all team recovery percentages over the last 10 years is 7.46%.  That means, if the data is random and Normally distributed, we should see approximately 68% of all individual team rates fall between 42.5% and 57.46% (1 standard deviation above and below the mean).

In our data, 220 teams fall within that range.

220 divided by 320 (our sample size) = .6875 or 68.75%

Additionally, we should expect 95% of all team rates fall within the range of +/- 2 standard deviations (35.07% – 64.927%).

In our data, we have 306 teams that fall within that range.

306 divided by 320 = .956 or 95.6%

Lastly, we should see 99.7% of teams to fall within 3 standard deviations of the mean.

In our data there is just 1 team that does not fall within the expected range (2011 Saints).

319/320 = .9968 or 99.7%

Summing up a bit:

– The data is random (no year-to-year persistence).

– The data is Normally distributed (hits the 68%/95%/99.7% mark almost exactly)

The 2012 Eagles recovery rate of 35% is almost exactly on the 2 standard deviation line.

Therefore, since we expect 95% of teams to fall within 2 standard deviations:

The 2013 Eagles have a 97.5% chance of recovering fumbles at a higher rate than they did last year.  (95% + half of the 5% distribution beyond 2 standard deviations)

One last bit for today, how does this rate business effect actual fumbles?

Here is a chart showing the correlation between fumble recovery rate and fumbles differential (Gained – Lost).  In other words, to what degree are “creating” fumble turnovers and “protecting the ball” a result of fumble recovery percentage (which is luck)?

I’ll have more on this tomorrow, when I’ll take a more detailed look.  The chart above should give you a strong hint of where this is going though.

I’m going to stop there for today.  This section is a lot longer than I intended and I’m guessing very few people have the time/patience to read through a 3000 word post on expected fumble recovery rates.