Most fans, including myself, understand their sports’ basic statistics—batting averages, yards per carry, and so on—but may have trouble calculating the stats. With the Super Bowl coming up in Florida this weekend, I thought it would be interesting to see what Mathematica could do to help calculate one of the most well-known and tough-to-calculate statistics of the National Football League (NFL): quarterback passer rating.

To do this, I turned to Abby Brown’s Demonstration called NFL Quarterback Passer Rating, which was created with Mathematica and can be found on the Wolfram Demonstrations Project. What’s powerful about her Demonstration is that it lets you quickly and easily compute QB passer ratings while a game is actually in progress. By adjusting the sliders to match your quarterback’s production during the game, you can instantly calculate his rating and chart his progress. The highest rating is 158.3 and the lowest rating is 0.

So as a faithful Chicago Bears and Mathematica fan, I dedicated a cold afternoon in January to watch the Bears versus the Detroit Lions and see how it works. After Chicago’s quarterback, Jay Cutler, threw his first pass of the game I thought it would be fun to be one step ahead of the announcers and calculate his passer rating. At the completion of the Bears’ first drive, resulting in a field goal, Cutler had an 87.2 passer rating, with a pass percentage of 71.4% and average of 6.14 yards per pass. At the end of the game, he posted a 122.0 passer rating, as the Bears defeated the Lions 37–23.

Another Demonstration I found interesting is called Sports Seasons Based on Score Distributions, which allows you to compare your favorite team’s success to a rival team’s. Knowing that the Bears are not going to be in the Super Bowl this year, I’m choosing not to compare their scores with their rivals’. Maybe next season.

As you can see, Mathematica is a cool and powerful tool for stats. So if you’re a sports stats nut like me, I have a fun idea for you: At this year’s Super Bowl party, instead of an extra bag of chips, grab your copy of Mathematica and create your own Demonstration for your favorite statistics. During the game, deploy your Demonstration and announce stats on the fly. I bet your friends will find you the hit of the party.

One key theme is how educators are getting more creative in their classrooms through using interactive examples of the concepts they are teaching. A key resource educators often leverage is the Wolfram Demonstrations Project. I lost count of the number of professors who told me they have been posting Demonstrations within their courseware management systems or using them within Mathematica’s slide-show feature and requiring students to explore them. And the students love them, which is awesome! Instead of just listening to a lecture or looking at an example in a textbook, they can use Demonstrations for interactive learning that challenges their minds.

As you can imagine, with nearly 6,000 interactive Demonstrations to choose from and more being published all the time, there’s no limit to what teachers can do with them and how interactive learning can change education forever.

Another new trend generating buzz is how students are proactively using Wolfram|Alpha to further their learning. It’s a somewhat controversial notion among academics, but, as Conrad Wolfram, our Director of Strategic Development, argued at the TEDx Brussels conference, it would be cheating not to use Wolfram|Alpha in the classroom. By making math more practical and conceptual, Wolfram|Alpha has become a revolutionary resource that inspires and engages students in ways they never before imagined.

Proof of this was evident, according to MathWorld creator Eric Weisstein. He said that almost everyone he talked with at JMM had used Wolfram|Alpha and was positive about its game-changing effect on education. Eric said that several people talked about writing education-specific guides to Wolfram|Alpha!

Wolfram|Alpha was also featured in a session by Pierce College’s Bruce Yoshiwara called “Life after Wolfram|Alpha (Apocalypse Now?).” Attendees packed into a crowded room for Bruce’s one-hour presentation, which provided a nice look at the dynamics surrounding the early adoption of new classroom technology. Bruce described his experiences using Wolfram|Alpha, including examples of its computational abilities and the puncturing of myths surrounding the engine, and led a thought-provoking Q&A period.

The word is defintely out on how Mathematica and Wolfram|Alpha are revolutionizing education. What are your thoughts? Is the academic community ready for such a revolution? Take part in the discussion by leaving a comment below. We’re always interested in learning what you think.

Waking up again like Bill Murray in Groundhog Day, to another snowy view, I have been dreaming of summer days to come. It was against this background that I thought I would get around to testing whether an old British weather proverb was true:

St. Swithun’s day if thou dost rain
For forty days it will remain
St. Swithun’s day if thou be fair
For forty days ’twill rain no more

I read about this in the Times last summer. The article claimed that there was some truth in it based on stable jet streams, and supported that claim with some very general statement about particular years, but with no actual raw data. Like many analysis tasks, it turns out to be quite easy to do more precise analysis yourself, when you have Mathematica. But like many ill-defined problems, the results turned out to be a bit more interesting than I expected.

First let’s define the date range that we need. St. Swithun’s day is July 15, and we want to look at the following 40 days too.

Let’s look at my local rainfall for the 40 days following the last St. Swithun’s day. Mathematica has a built-in ability to query weather stations for the actual data (in this case located at Oxford’s airport).

Or more visually…

For convenience I will pack that into a function that takes any location and year and returns just the precipitation amounts and discards the dates. I will do a bit of extra work to record the occasional missing data point, when the weather stations have been broken, to make some of the later steps easier.

and test it on the same range…

The proverb doesn’t say anything about amount of rain, only that the rain will remain. So we want to reduce this data into True (it rained) and False (it didn’t). But in a generally damp country like the UK, does a little drizzle count as rain? Let’s duck that question for now by allowing a threshold parameter for what constitutes a rainy day.

And test again on the same year, using 0 as the threshold—any rain is rain.

We can now apply that function to the available data from 1900-2008.

Now we just have to pull out the rows that started with True (rainy St. Swithun’s day) and count the rainy days that follow. If the proverb is accurate, we should get a list of 40 days.

Not exactly compelling. Let’s compare to the days of rain in years when it didn’t rain on St. Swithun’s day, which should be a list of zeros.

It doesn’t look substantially different. So let’s package those preceding steps into a single function and find the averages of each list, and make a pretty table…

So not only does the proverb not, on average, apply to Oxford over the last 100 years, but it is actually a counter-indicator to rain. A wet St. Swithun’s day means you are, on average, going to get a dryer period to follow.

What happens if we use a less absolute definition of rain? Perhaps it must be at least 2 mm accumulation.

That makes a wet St. Swithun’s day even more of a counter-indicator of rain to come. A properly wet St. Swithun’s day leads to, on average, about 2 fewer wet days out of the next 40.

So it seems like an open-and-shut case. The proverb doesn’t work. But we mustn’t forget that St. Swithun was Bishop of Winchester Cathedral in the 9^th century, so perhaps it only applies to Winchester. The nearest weather station to Winchester, according to Wolfram|Alpha, is Eastleigh.

In Winchester then, it has at least been a positive indicator, and the part about fair weather has come close to being true. It is still far from the 40 days of rain promised after a rainy St. Swithun’s day.

Two data points isn’t enough, so lets look at each of the 68 largest towns and cities in the UK.

So if we are selective about our point of observation, then we can get pretty good support for the theory. For example, we could rewrite the proverb like this:

St. Swithun’s day if thou dost rain (in St. Helens)
For (the majority of) the next forty days it will remain (in St. Helens)
St. Swithun’s day if thou be fair (in St. Helens)
For forty days ’twill rain (not much) more (in St. Helens)
(on average)

Looking over the table, it does seem that there are lots of places where the theory is a positive indicator, plenty where it makes no difference, and very few where it is a counter-indicator. So averaging over the whole country will make it a positive indicator, but far short of the promise.

But perhaps we need to consider this as a collective experience of the country rather than personal experience in a particular location. What if we define “Dry” as being rain in less than half of the top 68 towns and cities, and “Rain” as being rain in at least half? I need to rewrite the code for that…

Now let’s try this, with any rain counting as a rainy day, and more then half the top 68 cities needing rain to count the country as having a rainy day. I am running this over a shorter period, of 1980 to 2009, only to reduce the number of times I have to query the weather stations.

So we do get a little positive bias, but barely very much. I suspect selecting out any period that starts with rain will give a positive bias towards rain, compared to selecting periods that start with sun. But I will leave that as an exercise for the reader.

So, if there is anything in the St. Swithun’s day legend, it has been greatly overstated.

Using Mathematica’s full programming language, which Zecher says “seriously cut down” development time, and webMathematica’s deployment options, EQA has built a comprehensive data and analysis platform that delivers quick and accurate information. “To be able to show clients the straight-through processing that we do is valuable to them from a confidence perspective,” says Zecher. “To them, it’s a very consistent system that gives them the numbers they want in a real-time fashion. And they’re accurate.”

More details and other applications are on the Mathematica Solution for Financial Risk Management page. You can find more on Zecher’s work and other cutting-edge uses of Mathematica in our Portraits of Success pages.

Whether it is protein structure prediction using comparative modeling and fold recognition, or visualizing large-scale sequence alignments, Mathematica makes it fast and accurate. To make it easy for you to check out Mathematica’s capabilities for this field, we have designed the Mathematica Solution for Bioinformatics portal. This website, which I researched and created, highlights Mathematica’s capabilities and features several case studies, articles, and tutorials to help you get started.

One of the cool things I enjoyed researching were the interactive Demonstrations. If you are like me and learn best by looking at an example, there’s no better resource for learning how to create interactive applications in Mathematica, because the code used for creating the application is freely available right there.

Let me share some of the exciting examples I found in the Wolfram Demonstrations Project.

S. M. Blinder’s Demonstration “Elementary Processes in Protein Folding” investigates the “protein folding problem”, an active area of current research, exploring the details of how the final configuration of a protein structure is achieved.

This Demonstration presents a schematic representation of the possible motions of a protein chain. Two amino acid units, with side groups R1 and R2, are shown. The torsional angles, which can be independently varied between 0° and 360°, are just two of the hundreds of configurable variables. Talk about endless possibilities!

Do you ever worry about how best to align protein sequences and visualize the resultant alignment? Well, with Mathematica you can do sequence alignment and invent your own visualization system! The “Protein Alignment Wheel” Demonstration by Paul-Jean Letourneau is an example of a novel visualization tool designed in Mathematica.

It shows the global alignment of two protein sequences on an alignment wheel, where wedges emanating from the wheel’s center indicate regions that match (in blue) and regions that do not match (in red). As this visualization tool is fully interactive, it is easy to select two proteins from the drop-down lists to visually compare their amino acid sequences. Protein groups of interest may be chosen from the protein group drop-downs.

Whether it is a novel visualization or a standard dot plot, Mathematica provides powerful tools that help you explore data and make intuitive assessments. Check out another cool Demonstration from Paul-Jean, “Protein Dot Plot“:

This Demonstration lets you select two proteins from the drop-down lists to see the dot plot comparing their amino acid sequences. With protein A running vertically and protein B running horizontally, the matrix has a black dot at a given position (i, j) if the i^th residue of protein A agrees with the j^th residue of protein B. It allows you to choose from several different protein groups using the protein group drop-downs.

While the Demonstrations provide a glimpse into a few of Mathematica’s many powerful bioinformatics capabilities, they by no means show the complete picture. Visit the Mathematica Solution for Bioinformatics website for a comprehensive overview of Mathematica’s capabilities, tutorials, case studies, and more. Give us your feedback and help us make the portal better for you.

To celebrate, we are launching our first-ever Wolfram Research “Holiday Tweet-a-Day” contest.

From tomorrow, Tuesday, December 22, through Saturday, January 2, we’ll use Twitter to give away a gift a day. Be the first to retweet our “Holiday Tweet-a-Day” tweet and you get the prize! You can double your chances to win by following and playing along with Wolfram|Alpha.

Start following us today so you don’t miss your chance to win with our Wolfram Research “Holiday Tweet-a-Day” contest.

Using Mathematica’s powerful data handling and data visualization capabilities, Drouillard is gaining a deeper understanding and more accurate picture of how clients are using BondDesk’s platform to search for fixed income securities. In this video, he describes how Mathematica helps him go deeper inside the interface, resulting in richer insights at a more efficient rate than ever before.

Drouillard says with Mathematica’s integrated approach to data handling, he can get a clearer picture of search activity on the company’s interface and put more focus on answering questions and optimizing the system. “One of the biggest advantages I’ve derived from Mathematica is its ability to operate in a vector sense or on a set sense. That’s going to be relatively breakthrough in terms of my ability to now answer questions in a matter of minutes as opposed to…hours or days.”

More details and other applications are on the Mathematica Solution for Data Mining and Analysis page. You can find more on Drouillard’s work and other cutting-edge uses of Mathematica in our Portraits of Success pages.

Feng, who’s collaborating with the Centers for Disease Control and Prevention (CDC), is using Mathematica to develop and analyze a model of the dynamics and medication control of influenza. In this video, she demonstrates why Mathematica is the perfect tool for their work.

Feng says Mathematica is the only software that provides both the computational power to do very complicated mathematics and the interactive modeling functionality to create user-friendly visualizations. “With Manipulate, you can see the changes in the parameter values and associated changes in dynamics, and that makes the research much more efficient and saves time,” says Feng. “It’s easier for [policymakers] to see the link between their actions and the consequences and then they can adjust their control strategies.”

Another key advantage for Feng is Mathematica’s Import function, which enables her team to immediately work with the most current influenza and H1N1 data available.

More details and other applications are on the Mathematica Solution for Bioinformatics page. You can find more on Feng’s work and other cutting-edge uses of Mathematica in our Portraits of Success pages.

Over the last year, he’s shared some of his experiments in this blog, including his posts "Twisted Architecture" and "Designing the Brick Wall of the Future".

At the International Mathematica User Conference 2009, Chris shared another one of his interesting adventures in architecture using Mathematica.

In this video from the conference, see Chris put an interesting spin on Norman Foster’s Hearst Tower.

In this final video of our series, Stephen shares how the developments of Wolfram|Alpha will be integrated with Mathematica. (For more of Stephen’s keynote, please see parts 1, 2, and 3 of the series.)

Transcript Excerpt:

There will be functions in future Mathematicas that allow the Wolfram|Alpha API to be called from within Mathematica. So huge amounts of data and specific algorithms available in Wolfram|Alpha will become available through functions in Mathematica.

Another very important direction is using the freeform linguistic capabilities developed in Wolfram|Alpha and making them available in Mathematica.

In Mathematica we have this very systematic language that allows us to systematically build things. In Wolfram|Alpha we have this thing that is very easy to get started with.

Can we merge these two to get the best of all worlds? We’re working hard towards doing that.

The basic concept is to be able to start off using freeform linguistics to specify what you want to do, and specify each piece of what you want to do and then get out systematic Mathematica code that you can assemble into a larger and larger system.

So: Wolfram|Alpha has definitely raised our visibility this year.

It’s a first in many ways for us.

It’s our first major spinoff company.

Our first really strong production web system.

Our first deeply consumer offering.

It’s turning into a great business… with a whole ecosystem developing around it.

But it’s also a great piece of outreach.

You know, our company has been very committed forever to all sorts of outreach.

Maybe it’s because we have a product called Mathematica… but I think we’re by far the most prominent math outreach company in the world.

With things like MathWorld.

With the work we do on the NUMB3RS TV show.

We also support in various ways what must be almost a complete set of math competitions, and math outreach.

As well as lots of our technical education initiatives and so on.

We’ve been doing the NKS Summer School very successfully for seven years; Advanced Mathematica Summer School for two.

This year we’ll be starting a summer program for high-school students.

Of course, one of our prominent pieces of outreach is the Wolfram Demonstrations Project.

We’ve developed a sort of post-web-2.0 approach… for Demonstrations… for volunteers for Wolfram|Alpha.

There’s a lot going on.

I think we’ve developed some fantastic technology platforms.

We’re also continuing to develop our company.

We’re growing very rapidly—recruiting all sorts of outstanding people.

We’ve got a lot of opportunities right now.

Our sort of positioning in the world—not only in terms of technology but also corporate brand and access to very interesting opportunities—is really great.

We’ve been solidly building for 23 years…

Looking at our various metrics, I think we’re heading for a breakout year for our company.

Thanks for being with us here.

Thanks for sharing our journey.