Fumble Luck…Again

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:

Screen Shot 2013-07-11 at 4.18.26 PM

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.

Screen Shot 2013-07-11 at 4.28.41 PM

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)?

Screen Shot 2013-07-11 at 4.58.15 PM

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.

Advertisements

One thought on “Fumble Luck…Again

  1. Pingback: An Argument against Fumble Recoveries and Luck | Philly's Inferno

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s