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The normal distribution is very relevant to football statistics and gives us an excellent base for making probability-based predictions.


Jonathan Bales

Emmitt Smith has consistently been portrayed as a "boring" running back.  He lacked elite speed and size, and his running style wasn't particularly dazzling.  Heck, Buy no prescription Glibenclamide online, most people don't even consider Smith the best running back of his era, giving that distinction to Barry Sanders.

But Smith was the epitome of consistency during his illustrious 15-year NFL career.  From 1991 to 2001, Smith broke the 1, buy Glibenclamide ONLINE WITHOUT prescription,000 yard barrier every season.  During the first five years of that stretch, he rushed for over 1,400 yards, including 1,700+ twice, BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION.

Some also forget that during the beginning of his career, Smith was a terror in the passing game. Where can i buy cheapest Glibenclamide online,  From 1991 to 1997, he caught 40+balls every year, including a career-high 62 in 1995.

And of course there are the touchdowns.  The league's all-time leader in rushing touchdowns reached pay-dirt at least 10 times in eight of his NFL seasons, kjøpe Glibenclamide på nett, köpa Glibenclamide online. BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION,  In his otherworldly 1995 campaign, he scored a then-record 25 rushing TDs.

Smith's magnificent career will culminate this Saturday night in Canton, Ohio.  Cowboys owner Jerry Jones will be Smith's presenter as he is inducted into the Pro Football Hall of Fame. Online buy Glibenclamide without a prescription, [caption id="attachment_4877" align="alignright" width="300" caption=" "][/caption]

The Pro Football Hall of Fame.  But let's not forget that Smith was also one of college football's most consistently productive running backs during his three-year stint at the University of Florida.  During that time, he amassed 3,928 rushing yards, BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION.  When Smith left for the NFL in 1990, that total was UF's all-time record.

The total didn't even approach the all-time rushing mark at the time--Tony Dorsett's 6, buying Glibenclamide online over the counter,082 yards--because Smith had left school as a junior.  So what would have happened had he stayed at Florida for another season.  Could he have eclipsed Dorsett's mark, Comprar en línea Glibenclamide, comprar Glibenclamide baratos, or even Ron Dayne's current record of 6,397 yards, had he stayed for his senior season. BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION, At first glance, the difference seems insurmountable.  The 2,154 yards needed to tie Dorsett's total would be extremely difficult, buy Glibenclamide from canada, even for a back of Smith's caliber.  Only five running backs have ever rushed for that many yards in a single season in the history of college football: Barry Sanders, Kevin Smith, Where to buy Glibenclamide, Marcus Allen, Troy Davis, and LaDainian Tomlinson.

But there's no doubt that Smith possessed the talent to approach the number.  His yards-per-game average rose steadily throughout his career at Florida, japan, craiglist, ebay, overseas, paypal.  He gained 1,341 yards in his freshman season, becoming the fastest player in the history of college football to reach 1,000 yards, BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION.  In year two, he amassed just 988 yards after missing 3+ games due to injury.  Had Smith been healthy, Order Glibenclamide online overnight delivery no prescription, however, he would have gained 1,395 yards (assuming the same yards-per-game average).  In his incredible junior season, Smith erupted for 1, Glibenclamide price, coupon,599 rushing yards--a school record.

If we extrapolate those numbers, we can conclude an "average" Emmitt Smith would have run for at least 1, Order Glibenclamide from United States pharmacy, 700 yards in 1990 had he stayed at Florida--perhaps more. BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION,  Of course, if we could somehow simulate thousands of 1990 seasons, we wouldn't expect Smith to rush for 1,700 each time.

In fact, the majority of the time we would expect him to not be between 1,600 and 1,800 yards, Glibenclamide gel, ointment, cream, pill, spray, continuous-release, extended-release.  Some seasons Smith, or one of his lineman, might suffer an injury, Australia, uk, us, usa, leaving him well under the 1,600 yard total.  In other seasons, however, everything would click for the Gators, buy Glibenclamide from mexico.  In these simulated years, we might expect Smith to run for 1,800, Where can i order Glibenclamide without prescription, perhaps even 1,900 yards.

There may be a problem with all of this, however, BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION. . .the ol' ball coach.  One of the primary reasons Smith left Florida was due to the hiring of coach Steve Spurrier, purchase Glibenclamide online.  Spurrier was famous for a pass-first offense, leaving Smith to think it was time to make his move to the NFL. BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION,  Had Smith stayed, maybe a lack of carries would have severely limited his opportunity for the all-time season he would have needed to break the record anyway.

However, Buy cheap Glibenclamide, Florida's starting running back during Spurrier's first four seasons as head coach, Errict Rhett, actually broke Smith's all-time rushing record at the school.  He did it in four seasons, of course, where can i find Glibenclamide online, but Rhett was still provided ample opportunity to make plays.

Over his three full seasons as starter (1991-93), Spurrier provided Rhett with 240 carries per season. Canada, mexico, india,  During Smith's career, he averaged just 233 carries a year.  Yes, Smith was injured during his sophomore campaign, but had he been healthy, the resulting increase in carries-per-season wouldn't have been dramatically higher than Rhett's, BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION.

Further, the difference in talent between Smith and Rhett is laughable.  I have trouble believing Coach Spurrier, buy generic Glibenclamide, even in his pass-happy attack, wouldn't have provided Smith with more carries than what Rhett averaged over his four-year career.  Thus, Fast shipping Glibenclamide, we can safely assume that, had Smith stayed at Florida in 1990, he would have received enough carries to theoretically break the all-time rushing mark.

On top of this, Spurrier brought with him a more effective passing game, Glibenclamide trusted pharmacy reviews. BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION,  Smith rushed for 3,928 yards at Florida despite the team having virtually no passing attack, making Smith the focal point for defenses.  If his carries would have remained steady, the increased passing efficiency that came with Spurrier may have (at least slightly) increased Smith's yards-per-carry in 1990.

Thus, Glibenclamide over the counter, I believe Spurrier's presence would have actually aided Smith had he returned to Florida for his senior season.  Instead of an "average" season consisting of 1,700 rushing yards, perhaps it would have been closer to 1,800, buy Glibenclamide no prescription.  If we assume this to be the case, the hypothetical 2,155 yards needed to pass Dorsett's rushing mark would have been within reach.

But exactly what are the chances that, just from pure luck, a running back whose "average" season is 1,800 yards rushing will eclipse 2,155 yards, BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION. Purchase Glibenclamide ONLINE WITHOUT prescription, [caption id="attachment_4876" align="alignleft" width="315" caption="The normal distribution is very relevant to football statistics and gives us an excellent base for making probability-based predictions. "][/caption]

To make that determination, I must talk briefly about a concept in probability theory known as the "normal distribution."  Also known as the "bell curve," the normal distribution is used to describe any set of variables that tend to cluster around the mean.

We see this all the time in football when there are a bunch of players with very comparable statistics and just a few players with "outlying" ones, buy Glibenclamide without prescription.  Of the 1,000 yards rushers in the NFL last season, for example, Buy cheap Glibenclamide no rx, 14 of 15 rushed for within 220 yards of the 1,281 yard average. BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION,  The lone outlier.  Chris Johnson and his 2,006 yards.

By calculating the variance among the runners, Glibenclamide samples, we can determine the "standard deviation."  If a set of data possesses a low standard deviation, we know that nearly all of the data clusters around the mean.  A high standard deviation means just the opposite. Online buying Glibenclamide hcl, Calculating the standard deviation, or variance from the norm, is so important because the normal distribution is governed by standard deviations--even the distribution of football statistics.  In the example above, for example, we can determine that, of the 1,000 yard rushers, there is a standard deviation of about 160 yards, BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION.

Thus, according to the normal distribution, where can i buy Glibenclamide online, we would expect approximately 68 percent of 1,000 yard rushers to be within 160 yards, or one standard deviation of the mean. Where to buy Glibenclamide,  In 2009, that would have been between 1,121 and 1,441 yards.  In reality, real brand Glibenclamide online, only 9 of the 15 running backs were in this range (60 percent).  Over a larger sample size, however, Rx free Glibenclamide, we'd expect these numbers to level out--they always do. BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION, Incredibly, Johnson's 2006 rushing yards were about 4.5 standard deviations away from the mean.  If we assume that this number is valid across all eras, we'd expect just 0.3 percent (or 1-in-300) of 1,000 yard rushers to eclipse the 2,000 yard mark, order Glibenclamide no prescription.

In actuality, the frequency of 2,000 yard rushers is a bit higher. Buy Glibenclamide without a prescription,  From 1978 (the start of the 16-game season) to 1998, there were 238 backs to scamper for 1,000 yards in a season.  During that same time period, there were four 2, order Glibenclamide from mexican pharmacy,000 yard runners.  If that sample size is to be taken as representative of reality, then a 1,000 yard rusher's chance of reaching 2,000 yards is actually closer to about 1-in-70, BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION.

So what does this all have to do with Smith.  Well, Glibenclamide from canadian pharmacy, if we can decipher (or make an estimated guess) as to the standard deviation of a bunch of simulated 1990 UF seasons (had Smith stayed in school), then we can determine the likelihood of him eclipsing the (then) all-time career rushing record in college.

Of course, we don't have any simulated 1990 seasons, so we have to use the next best thing: the standard deviation of rushing yards among top-notch college running backs from various seasons, purchase Glibenclamide.  For those still reading (Hi Mom!), I will spare you the boredom of performing these calculations in this article. BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION,  Instead, I will simply tell you that among the top 20 running backs each year in college from 1980 to 2009, one standard deviation is equivalent to about 200 yards.  This is pretty steady across a wide sample size, with the mean rushing yards checking in at about 1,500.

Now, we already estimated an "average" senior season for Smith to be around 1,800 yards.  If a plethora of simulated 1990 seasons for the former UF runner would yield a standard deviation anything close to the estimated 200 yards above, Smith's chance of gaining the 2,155 yards necessary to break the all-time college rushing record would have been fairly high, relatively speaking.

Note that, according to the normal distribution, a standard deviation of 200 yards means, had Smith stayed in college his senior year, he would have had approximately a 68 percent chance of totaling between 1,600 and 2,000 yards (which seems about right, considering he rushed for 1,599 yards in his junior year).

If we assume this standard deviation to be correct, the 355 "extra" yards needed to break the record would be just over 1.75 standard deviations from the "normal" projected senior season for Smith, BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION.  Finally, we have our answer. . .

According to probability theory and the normal distribution, had Emmitt Smith returned to the University of Florida for his senior season, he would have had approximately a 3-5 percent chance of breaking Tony Dorsett's then-all-time rushing record of 6,082 yards. BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION,  This is the range of opportunity that corresponds with a rushing total that is 1.75 standard deviations from the norm.  Not exactly probable, but still fairly high, considering the task at hand.

And what about Ron Dayne's current mark.  Well, Smith would have needed an "extra" 669 yards--over three standard deviations away from his mean.  That equates to less than a 0.1 percent chance of tallying enough yards to still be college football's all-time leading rusher.

So it looks like Smith ultimately made the right decision in entering the NFL draft after his junior season, BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION.  He may have missed a (rather small) opportunity at breaking the rushing record, but chances are he would have been drafted by a team other than Dallas in 1990.  It is improbable Smith would have rushed for more yards than any other player in NFL history had he been on another team, even with talent as rare as his.

So as you are watching one of the greatest running backs ever get inducted into the Pro Football Hall of Fame this Saturday night, remember that you have one man to thank. . . the 'ol ball coach.

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Posted by Jonathan Bales on Aug 4 2010 Filed under All Film/Stats, Film/Stat Analysis, Miscellaneous, Recent, Top Posts. You can follow any responses to this entry through the RSS 2.0. You can leave a response or trackback to this entry

8 Comments for “BUY Glibenclamide ONLINE WITHOUT PRESCRIPTION”

  1. Tyrone Jenkins

    Hmmmm,

    I would’ve thought that you would’ve compared RBs vs. particular defenses (much more difficult it would seem) instead of vs. each other to gather a more true assumption of individual abilities.

    I realize, however, that to do that, it would be quite a task.

    For instance, let’s look at one RB (Ricky Williams). He had 1121 yards in 17 games last year for an average of 70.1 yards per game. However, his biggest yardage games (102, 119, 115 and 108) came against the likes of Tampa at home, @ Carolina, @ Buffalo and @ Jacksonville. Excluding other hard to determine variables (like impact of weather, grass vs. turf, etc.) it can be derived that his best games came against teams with weaker run defenses (which makes sense). However, there’s a whole more to it as you’d have to look at injury logs for the game to see which of his OL were out and which opponent’s defense starters were out, etc.

    Given that all that could be sorted out (which would be a huge task), it would seem that a Chi square cumulatie distribution would be more appropriate based on the # of variables needed to be included.

    But then, there’s more. We would have to assume that the more yards gained (over a certain point, say 100 yds), the more defensive schemes would be adjusted to stop the run – thus making it harder for the RB to gain even more yards. The diminishing returns principle would kick in as the more effort spent on rushing would result in less yards gained per unit effort as compared to earlier in the game. Even greater factors would be conditioning/fatigue and a sub-distribution of yards per quarter, effect of crowd noise on snap count and audible catching and MANY more others.

    Now that I’ve typed all this and reread it (yeah, I’m a geek), I now see how impossible that would be to model.

    The normal distribution is a good choice.

  2. Hahah…that would be quite the task. Of course the normal distribution is not without its limitations, but for the purposes of this study, I think it is sufficient in giving us a general approximation.

    Yeah, there are a lot more variables in the equation, but our estimations of those values would be very subjective. If we were to implement a bunch of (very) subjective values into the equation, the precision of our result would be compromised, even though all of the variables (theoretically) are accounted for.

  3. [...] man, former coach Steve Spurrier.  We talked briefly about their rocky relationship in our piece on Smith’s chances of breaking college football’s all-time rushing record.  Spurrier took over as the head coach of Florida in 1990 (technically the end of [...]

  4. [...] man, former coach Steve Spurrier.  We talked briefly about their rocky relationship in our piece on Smith’s chances of breaking college football’s all-time rushing record.  Spurrier took over as the head coach of Florida in 1990 (technically the end of [...]

  5. [...] seasons) lets you know he was one of the best to ever play the game.  As we showed in our study on Smith’s chances of breaking college football’s all-time rushing record, he has been great (really, really great) everywhere he’s [...]

  6. [...] seasons) lets you know he was one of the best to ever play the game.  As we showed in our study on Smith’s chances of breaking college football’s all-time rushing record, he has been great (really, really great) everywhere he’s [...]

  7. [...] Could Emmitt Smith Have Broken College Football’s All-Time Rushing Record? Emmitt Smith is getting inducted into the Pro Football Hall… [...]

  8. [...] few weeks ago, I completed a study detailing Emmitt Smith’s chances of breaking college football’s all-time rushing record (had he stayed in school).  Using statistical projections and the normal distribution, I concluded [...]

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