Ben Watson and the Pythagorean Theorem - AFC Divisional Game Patriots vs. Broncos Jan 14, 2006

The 2005 divisional playoff game (January 14, 2006) between the Patriots and the Broncos featured Patriots TE Ben Watson making one of the greatest hustle plays I had ever seen in my life.  Watch below:

 

A great play, though ultimately for naught as Denver maintained possession at the 1 yard line and would ultimately punch it in on a Mike Anderson TD run.  New England would go on to lose the game, snapping Tom Brady's streak of 10 playoff wins without a loss.

How Far Did Ben Watson Run?

Linebacker Tedy Bruschi said, "We saw Ben was on the other side of the field so he basically had to run like 120 yards, even longer than that, to get that."

A great hustle play for sure, but how far did Ben Watson actually run on that play, and how much further did he go than Champ Bailey, one of the fastest players in the NFL?

Positioning of Watson and Bailey at the time of the interception

As you can see in the above photo, Bailey is about 1 yard deep in the end zone and near the sideline when the ball is intercepted.  His path to the opposing end zone is pretty close to a straight line, so we can estimate that it's between 100 and 102 yards.  Watson, on the other hand is on the opposite side of the field, on the numbers.  How far did he actually run?

Finding the Distance

It would be pretty difficult to get out there and use a tape measure to find out how far Watson ran on this play, so instead, let's turn to a good old geometry trick, the Pythagorean Theorem.  The Pythagorean Theorem works with right triangles, and as you may recall from elementary school, the formula for finding a side of the right triangle is this:

A² + B² = C²

where A and B are the lengths of the legs of the triangle, and C is the length of the Hypotenuse.  How does this help us figure out how far Ben Watson ran?  One way to do this is to draw a right triangle which gives us some usable distances to help with this problem.

As you can see, Watson's path to Bailey can be shown here.  Using the video from before, we're approximating Watson's starting position on the far side of the field, roughly around the 9 yard line.  Since Bailey was ruled to have been tackled at the 1 yard line, that makes an easy estimate of 90 yards for length A.

Length B is a little more tricky since there aren't any yard markers across the width of the field, and my diagram is not really to scale.    In the photo, Watson is roughly at the numbers, which we can estimate to be between the sideline and the near hash mark.  The near hash mark is 70' 9" (or 70.75 feet) from the sideline, so halfway between that is 35.375 feet.  That works out to about 11.80 yards. The width of a football field measures 53 1/3 yards, so if we subtract 11.80 from 53 1/3, we'll get about 41.53 yards.  For simplicity sake, let's just call it 41.5 yards.

Why am I fudging these numbers so much?  First off, it's simply an eyeball estimate of where Watson was standing.  Second, moving these numbers by 1 or 2 yards won't change the final answer by that much.  Try it yourself when we get the answer.  How far was the run?

Now we have some distances for A and B, let's try to figure out how far Watson actually ran.  There's actually no algebra we need to do, just some arithmetic and a calculator will be handy here.

90² + 41.5² = C²

8100 + 1722.25 = C²

9822.25 = C²

Taking the square root of both sides, you get:

+/- 99.1 = C

In math, the +/- is absolutely necessary to fully solve a square root problem.  However, since we're not dealing in hypothetical math land, we know the only value that matters here is the positive one.

Conclusion

Ben Watson ran roughly 99 yards to chase down Champ Bailey on that play.  Since Bailey ran over 100 yards, this puts the play in a little more perspective.  Watson didn't have to outrun Bailey but simply catch him from a different angle.

This takes away NOTHING from Ben Watson and his awesome effort.  He made a play where most others would have just given up because he was so far from the ball when the interception happened.  This was also against one of the fastest players in the league as well.  However, using math, we can show Watson didn't run 120 yards to catch Bailey.  Even if our estimates are off, we won't be off by so much that it will turn 99 yards into 120 yards.

If you're a young football player reading this, take to heart what Watson's college coach said.  "Stuff like that doesn't take a whole bunch of talent.  It's just effort."