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As the story goes, 
the legendary marksman William Tell

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was forced into a cruel challenge
by a corrupt lord.

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William's son was to be executed


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unless William could shoot 
an apple off his head.

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William succeeded, but let's imagine
two variations on the tale.

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In the first variation,

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the lord hires a bandit to steal
William's trusty crossbow,

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so he is forced to borrow
an inferior one from a peasant.

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However, the borrowed crossbow
isn't adjusted perfectly,

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and William finds that his practice shots

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cluster in a tight spread 
beneath the bullseye.

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Fortunately, he has time 
to correct for it before it's too late.

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Variation two:

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William begins to doubt his skills
in the long hours before the challenge

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and his hand develops a tremor.

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His practice shots still cluster
around the apple

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but in a random pattern.

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Occasionally, he hits the apple,

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but with the wobble,
there is no guarantee of a bullseye.

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He must settle his nervous hand


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and restore the certainty in his aim
to save his son.

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At the heart of these variations
are two terms often used interchangeably:

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accuracy and precision.

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The distinction between the two

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is actually critical 
for many scientific endeavours.

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Accuracy involves how close you come
to the correct result.

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Your accuracy improves with tools
that are calibrated correctly

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and that you're well-trained on.

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Precision, on the other hand,

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is how consistently you can get 
that result using the same method.

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Your precision improves 
with more finely incremented tools

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that require less estimation.

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The story of the stolen crossbow
was one of precision without accuracy.

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William got the same wrong result
each time he fired.

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The variation with the shaky hand
was one of accuracy without precision.

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William's bolts clustered 
around the correct result,

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but without certainty of a bullseye
for any given shot.

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You can probably get away 
with low accuracy

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or low precision in everyday tasks.

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But engineers and researchers
often require accuracy

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on microscopic levels with 
a high certainty of being right every time.

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Factories and labs increase precision

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through better equipment 
and more detailed procedures.

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These improvements can be expensive,
so managers must decide

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what the acceptable uncertainty 
for each project is.

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However, investments in precision

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can take us beyond 
what was previously possible,

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even as far as Mars.

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It may surprise you that NASA
does not know exactly where

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their probes are going to touch down
on another planet.

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Predicting where they will land
requires extensive calculations

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fed by measurements 
that don't always have a precise answer.

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How does the Martian atmosphere's density
change at different elevations?

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What angle will the probe
hit the atmosphere at?

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What will be the speed 
of the probe upon entry?

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Computer simulators run thousands
of different landing scenarios,

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mixing and matching values
for all of the variables.

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Weighing all the possibilities,

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the computer spits out 
the potential area of impact

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in the form of a landing ellipse.

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In 1976, the landing ellipse
for the Mars Viking Lander

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was 62 x 174 miles,
nearly the area of New Jersey.

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With such a limitation,

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NASA had to ignore many interesting
but risky landing areas.

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Since then, new information 
about the Martian atmosphere,

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improved spacecraft technology,

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and more powerful computer simulations
have drastically reduced uncertainty.

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In 2012, the landing ellipse 
for the Curiosity Lander

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was only 4 miles wide by 12 miles long,

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an area more than 200 times 
smaller than Viking's.

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This allowed NASA to target 
a specific spot in Gale Crater,

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a previously un-landable area 
of high scientific interest.

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While we ultimately strive for accuracy,

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precision reflects our certainty
of reliably achieving it.

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With these two principles in mind,

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we can shoot for the stars

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and be confident 
of hitting them every time.