Fun Stuff: April Edition

Hi everyone!  Today I’m sharing some of our favorites from our lives this month.

I made a huge easter dinner even though it was just the two of us.  Ham, sweet potato and chard gratin, deviled eggs, green beans with candied pecans, and a beet, citrus, and mint salad.  For dessert we had lemon mascarpone and mango sorbet parfaits.  And a Bellini bar.  It was a beautiful day, so we had dinner outside and enjoyed the nice weather.

We had so much fun at the Tar Heel 10 Miler!  It was a tough race, including a 1 mile climb up Laurel Hill at the end of the race.  They gave us separate splits for Laurel Hill, and Nick finished third in his age group!  Afterwards we explored Chapel Hill and Carrboro.  We looked at plants at the North Carolina Botanical Garden (they have carnivorous plants!), then sampled some beers at the Steel String Craft Brewery, and had a lovely dinner at Kipos.  We are definitely going to sign up for this race again next year!

Coming off of the race, Nick has decided he wants to run a mile PR (his PR was 6:14 back in high school) and will be using this plan.  We’ll keep you updated!

I cannot wait to make this pad thai salad.  I LOVE pad thai, and this looks perfect for the hot summer months.

In girly news, I finally bought this Garnier BB cream.  I’m now wondering why I waited so long to try BB cream.  This stuff is amazing–the moisturizer is light enough so that I don’t break out, and the tint covers small blemishes.  I’m obsessed.

I’ve been looking for closed toe shoes that look good with shorts.  I run a lot, and a weekly pedi just isn’t a thing for me.  I ended up with a pair of sperrys and a pair of toms.

This year was the one year that I got my veggie garden in the ground on time, but we got frost April 15 and 16!  I covered the plants with plastic bags each night, and everything survived.  I planted Greek basil, Thai basil, mint (in a planter!), rosemary, crookneck squash, grape tomatoes, yellow tomatoes, cucumbers, and jalapeños.  I am wishing I had more bed space so I could plant more stuff!

We hope you had a wonderful month!

 

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On Cramming Workouts into a Hectic Life

I have a not-so-secret secret: I deal with stress a million times better when I work out regularly. Even just getting a couple miles in at the gym can instantly change my day for the better.

In an ideal world, we’d all have time to do every single thing we wanted. However, life is chaotic, so we need to arm ourselves with strategies to stay fit. Here are my top suggestions for dragging yourself to the gym (or outside!).

Note: I have a math degree, and am only here to describe what works for me as well as for people I know closely. This is not intended to be medical advice. Please consult a physician before starting a new exercise plan.

1. Make a Goal

What kind of exercise do you like? Is there something on your bucket list, like finishing a triathlon? How many days a week (in the real world, people) do you see yourself making time for workouts? Can you exercise after work, or will family/work commitments mean you have to exercise at lunch or in the morning? Ask yourself these questions and make yourself a workout schedule to accomplish your goals. And remember, you can always add more later.

2. Find a Workout Buddy

Accountability can be the difference between working out or sitting on the couch and ordering pizza. Find a friend, and make a date to run or even just drive to the gym together. Chances are, you’re not comfortable standing someone up, which equals lots of workouts. If you’ve had a long week, grab dinner/drinks afterward, too.

3. Use an Online Fitness Tracker

While we’re on the topic of accountability, remember that you can use social media to motivate yourself. Try logging workouts in an online tool such as MapMyRun, then add some of your friends who use the same tool. I see social fitness tools as having a dual purpose–first, I feel guilty if I don’t log anything, and second, it helps me keep track of how much I’ve been running.

4. Runners–Sign Up for Races

I usually run a couple miles on the weeknights no problem, but when it comes to the longer runs on the weekends, sometimes I’m just not motivated. Signing up for races gives me a reason to get those miles in on the weekends. (Bonus: people within a reasonable drive of the Triangle should check out the Fat Ass run series. They do about 3-4 FREE races per year. Find information about the next one here.)

Here are a few of my favorite races:
City of Oaks
Richmond Marathon, Half, & 10k 
Charlottesville 10 Miler

Some of my upcoming races:
Medoc Meltdown
Richmond Half 
Tar Heel 10 Miler 

5. Get a Real Pair of Athletic Shoes

No matter what type of exercise suits you, you’re going to need real shoes. Consider going to a running store, where the salespeople can analyze your gait and suggest a pair of shoes that complements and/or corrects your stride. I roll my ankles in when I run (technical term: pronating), so I buy motion control shoes.

6. Find a Gym that Works for You

There are all kinds of gyms out there, and finding one that suits your needs is key. If you have children, consider a gym that has child care. Always aim for a gym that is close to your home or work. Nick and I belong to a Planet Fitness that is 1 mile from our home, which consequently eliminates the excuse of “its too far away.” Many gyms offer free passes for a week or two, so play the field and find your gym. Also, don’t be afraid to break up with your current gym if it just isn’t working for you.

7. Set Up Ways to Exercise at Home

You don’t have to spend thousands of dollars on gym equipment to be able to exercise at home. Youtube has tons of free yoga videos, and pinterest has numerous fitness pins. My favorites:

Bryan Jones Power Yoga
PopSugar’s Dumbbell Blast
Vinyasa Flow Yoga-Intermediate

8. Use your Crockpot

Sometimes, by the time I’ve worked a full day and gone to the gym, I’m exhausted and really freaking hungry. Consider prepping a crockpot dinner before you leave for work if you know you’ll be short on time and energy. Pinterest has tons of good ideas.

9. Hydrate, Hydrate, Hydrate!

Drink lots of water.  Dehydration makes me sluggish and more likely to blow off a workout.  If you work a desk job, buy yourself a plastic tumbler and get up and refill it every time it is empty.

10. Don’t Beat Yourself Up

Your body needs time to recover after workouts. Give yourself a day off when you need one! On that note, some weeks are just plain crazy and you may not get to the gym as much as you intended. It happens to all of us, but remember that a lifelong commitment to health and fitness is far more important than a few missed workouts.

What are your favorite tips for staying motivated to work out?

The Final Four: Why You Should Bet “On Wisconsin”

Florida is the Vegas favorite to cut down the nets Monday night. But that doesn’t mean betting on them gives the best odds for bettors. I preview each match-up from a statistical point of view, and provide the chances each team has of moving on to the title game, and becoming the NCAA basketball champion.

Wisconsin v. Kentucky (-2)

This game pits a talented, yet under-performing Kentucky squad full of future NBA players coached by the legendary John Calipari against the last Big Ten hopeful, Wisconsin, in its first final four in the 13 years Bo Ryan has been at the helm. Vegas has jumped on-board the Kentucky bandwagon and has made them a 2 point favorite over Wisconsin. My numbers disagree.

The cluster analysis I performed last week, I have enhanced by including tempo into the equation. This gives me two sets of clusters. The first set has eight clusters of teams where tempo is not included, while the second set has seven clusters with tempo included. We can then group the teams into a possible 56 clusters (eight clusters multiplied by seven clusters), however, only 28 clusters of teams are formed. This isn’t unexpected, as the only difference was the inclusion of tempo, so teams that were similar in the first cluster analysis often will be similar in the second cluster analysis. Wisconsin is a Type 7 team in the first analysis, and a Type 6 team in the second analysis; I notate this as (7,6). Kentucky falls into group (5,4). As it turns out, (7,6) vs. (5,4) has occurred 164 times in the 2013-2014 NCAA basketball season, with (5,4) winning 83 times and (7,6) winning 81 times. Additionally (5,4) teams have won more despite being ranked lower on average according to Pomeroy’s ratings. Type (7,6) teams had an expected winning percentage of 54.0% so combined with a 164 game sample size, the 83 wins by (5,4) teams could have occurred by pure chance (p = 0.13). Thus, we cannot prove that (5,4) teams match-up well against (7,6) teams, so we provide no match-up bonus to Kentucky.

This is confirmed by the fact that Wisconsin has been quite successful against Kentucky-type teams this year, going 7-1 against (5,4) teams with the sole loss coming to Minnesota on the road (they beat the Gophers two other times). This 87.5% win rate is in line with a 79.0% expected winning percentage. Wisconsin recently dismantled Baylor, who as Mike Portscheller at btn.com points out, is quite similar in style to Kentucky. In fact, they are so similar that my two cluster analyses indeed pitted Baylor as a (5,4) team, just like Kentucky. Kentucky, on the other hand, has gone 1-1 against (7,6) teams, with a win over Boise St. and a loss against Michigan St.

Also, I built a predictive model to predict offensive and defensive efficiency using a regression model with Pomeroy’s four factors as inputs in predicting offensive and defensive efficiency for each team. Normally, I’d adjust Pomeroy’s four factors for strength of schedule, but the difference in each team’s schedule strength is negligible to this analysis, so I stick with unadjusted values. The model predicts Wisconsin to score 110.2 points per 100 possessions and Kentucky to score 108.1 points per 100 possessions. With no match-up adjustment, this means Wisconsin should win 60.9% of the time.

Throw in the injury to Willie Cauley-Stein (who hasn’t been ruled out, but I’m counting as out, or at best ineffective) and Wisconsin definitely has the edge, expected to win 63.1% of the time. Wisconsin moves on.

Prediction: Wisconsin 69, Kentucky 63.

Florida (-6) v. Connecticut

The earlier game produces a rematch from earlier in the year where the home Huskies edged out a one-point victory over Florida in Storrs. Since then Florida has not lost, reeling off 30 straight wins en route to the #1 overall seed in the tournament.

Florida falls into the (6,5) group of teams while Connecticut is a (7,2). Here, the cluster analysis again predicts no match-up difference. Adjusting for missing players actually gives a slight advantage to Florida. One of Florida’s losses (to Wisconsin on the road) came with Dorian Finney-Smith and Scottie Wilbekin sidelined, giving Florida a small boost in each area of the four factors when accounting for this. On the other hand, while two of the Huskies’ losses came while missing key players, they also went 3-2 in other games when their opponents were missing key players. This produces a near neutral net effect, with minimal changes to each component of the four factors. Using the regression model using the missing player adjusted four factors, Florida is expected to win 75.1% of the time.

UConn’s Cinderella run comes to an end, and the Gators advance and cover the six point spread.

Prediction: Florida 65, Connecticut 56.

NCAA Championship Game

Using the probabilities above it’s easy to calculate each the odds for each potential match-up. Here are the probabilities for each match-up, with match-up chances that are better than Vegas odds noted with the expected yield return on a dollar.

  • Florida v. Wisconsin 47.4% chance (Vegas odds 1.6 to 1), $1.232
  • Florida v. Kentucky 27.7% chance (Vegas odds 1.2 to 1)
  • Connecticut v. Wisconsin 15.7% chance (Vegas odds 6 to 1), $1.099
  • Connecticut v. Kentucky 9.2% chance (Vegas odds 5 to 1)

NCAA Title Odds

The only significant adjustment to Pomeroy’s ratings for potential championship game match-ups comes from a possible Florida v. Wisconsin game. Here, Wisconsin, a (7,6) team would face Florida a (6,5) team, where (7,6) teams have won 36.2% more than expected against (6,5) teams. This holds true for Wisconsin, as they are 3-1 against (6,5) teams having beaten Virginia, Florida, and St. Louis, with the lone loss to Ohio State. The only other adjustments are the aforementioned missing player adjustments to Kentucky, Florida, and Connecticut. The missing player and match-up adjustment move Wisconsin’s chances of a victory to 45.5% over Florida.

The missing player and match-up adjusted winning percentages produces the following championship probabilities, with favorable noted with the expected return on a dollar:

  • Florida 45.5% (Vegas odds EVEN)
  • Wisconsin 30.8% (Vegas odds 3.5 to 1), $1.386
  • Kentucky 13.0% (Vegas odds 2.75 to 1)
  • Connecticut 10.7% (Vegas odds 7 to 1)

Wisconsin is being undervalued both against Kentucky and in a potential championship game against Florida. The result is them being highly undervalued, especially as national champions. Given a one-time shot Florida is the expected team to win it all, but if the Final Four is played 100 times, you’d make the most money betting “On Wisconsin”.

An Introduction + a Cocktail

Hello there! Since my wonderful husband dove right in with the sports analysis, it is my turn to write and I figured we should actually, you know, introduce ourselves.

Nick and I are both mathematicians by trade. Nick works for a biotech company and I am about 15 months from completing my PhD. During the day we write code, analyze data, fit parameters, and curse at our laptops. When we aren’t working, we enjoying running, cooking, watching sports, entertaining, and enjoying the Raleigh nightlife. We were married in March of 2013 and live in the suburbs with our four crazy cats.

We created this blog to share a little of our life with the outside world. I’ll be sharing workout tips and schedules, (mostly) healthy recipes, and other random things that happen in our day-to-day life. Nick has always been interested in sports analytics, so he will be writing about everything from fantasy football to college basketball to NASCAR.  We will also write about things that pertain to us as a couple that many normal people go through, such as balancing work and life.

Now, onto the fun part. Cocktails! Since we live in a huge (to us) house, we love having people over. We’ve hosted many gatherings, and one way I’ve found to get things started is to serve a signature cocktail. It’s a great icebreaker and you get to expose your friends to something they may not have otherwise tried.

Today, we’re infusing vodka. Sounds fancy, right? It is actually very easy, the only catch is that it involves some advanced planning.

cocktail1
Vodka + ginger in a mason jar, ready to be infused!

Like most of the rest of the United States, we’ve had insane weather and cannot wait for spring. For the moment, we’re forgetting about all the snow and cabin fever by making an upbeat and fresh cocktail. Craft vodka is infused with fresh ginger, then combined with lime juice and simple syrup to make an elegant yet easy cocktail.   The ginger is present but not overpowering, which makes this perfect for porch sipping.

Ginger Lime Sippers

Makes 2 drinks

Ginger infused vodka (recipe below)
Simple syrup (recipe below)
1 lime
Ice

Combine 4 oz. ginger vodka, 1 tbs. simple syrup, and the juice of 1 lime in a cocktail shaker. Add ice and shake.

Fill 2 highball glasses to the top with ice. Strain the mixture into each glass, dividing evenly.

The best hosts are ones who take all of their guests’ needs into account. If you have girlfriends who are pregnant or friends who don’t like to drink, consider serving a mocktail version. Replace the ginger vodka with a non-alcoholic ginger beer such as Reed’s ginger brew. Skip the shaking step and simply combine all ingredients and serve over ice.

Inspired by the Moscow Mule at Beasleys Chicken + Honey

cocktail2
The final (delicious) product

Ginger infused vodka

3-4 inch knob of ginger
10 oz. vodka

Remove the skin from a 3 to 4 inch piece of ginger.  Dice.  Meanwhile, add 10 oz. vodka to a glass jar.  Add the ginger.  Cover and let sit in a dark place, 48-72 hours.  To serve, use a sieve to remove the ginger from the vodka.

Simple syrup

2 c. sugar
water

Bring a kettle of water to a boil.  Place 2 cups of sugar in a glass jar.  Add boiling water until all of the sugar is dissolved, stirring frequently.

Virginia vs. Michigan State: Diving Deeper and a Prediction

Last time I discussed two improvements to Ken Pomeroy’s rankings. One adjustment was for missing players, and the other was a new approach to adjusting for on-court match-ups using a technique called cluster analysis. Applying these adjustments, I determined that Michigan State had a 51.9% chance of winning, with an average margin of victory predicted around 1 point. However, even this of course neglects two very important factors. The first factor is that after Virginia’s loss to Tennessee by 35 points, Joe Harris went to coach Tony Bennett’s house on New Year’s Eve to discuss the team’s issues. This seemingly has resulted in a new, transformed Virginia team. The Wahoos have only lost two games since: a close loss to Duke at Cameron Indoor Stadium, and an overtime loss at former ACC rival Maryland. The other 21 games have all been wins, including the ACC regular season and tournament championships, and quality wins over North Carolina, Pittsburgh (twice), Duke, Syracuse, and Memphis. Second, Michigan State played a significant portion of the year with injuries to key players. Branden Dawson, Keith Appling, and Adreian Payne have all missed time this year to one injury or another. Experts argue Michigan State is a better performing team with all three healthy and 100%.

I looked at a couple metrics to rate Virginia since the course of their season changed with that New Year’s Eve meeting. First, the Cavaliers have posted a BPI of 93.0 since the Tennessee loss, compared to an 87.0  yearly average, an increase of 6.9%. Pomeroy’s metric (adjusted for injury in the full-year case), also shows Virginia has played better since the Tennessee game. Their rating since the Tennessee game is 3.2% higher than their yearly rating. So indeed, Virginia has played better since the Tennessee game.

Michigan State also sees its ratings boost. It’s ESPN BPI for games where both teams were fully healthy is 91.1 compared to 85.4 for the year. This represents an increase of 6.7% over their yearly average. Using Pomeroy’s metrics (adjusted for injury in the full-year case), Michigan State plays better by 3.9% over their yearly average when they and their opponent are fully healthy.

I let these values represent each team’s ceiling. However, these ideal scenarios aren’t the only way these teams played this year, and I will still use their full-year metric in some way. To do so, I weight the ideal scenario (since this game will be played under the ideal scenario for both teams) twice that of the full-year. Doing so gives Virginia a 63.7% chance of winning before the match-up adjustment. The match-up adjustment knocks this down to a 50.9% chance of Virginia winning.

Considering the way the teams have performed at their peak, and combining peak performance with full-year performance puts Virginia at a slight edge. So, given that this game is virtually a toss-up, what can give one team the edge over the other?

Analyzing the teams’ styles, we see that Michigan State is a highly efficient shooting team, with an effective field goal percentage of 54.7%, good enough for 13th in the nation. They do not really stand out in any other area of offense, although they are in the top 100 in protecting the ball, turning the ball over on only 17.2% of possessions. In MSU’s two fully healthy losses, they lost to Illinois with an eFG% of only 45.7% and a TO% of 28.6% and to Ohio St. with a turnover ratio of 24.6%. Both Ohio State and Illinois play somewhat similar defensive styles to Virginia, with a slow-pace (all are 298th or lower in defensive pace) with top 11 defensive efficiencies. However, pace is where the comparisons end. Virginia’s strengths are minimizing eFG% and dominating the defensive boards, while generating a turnover rate that is only mid-pack. Ohio State is also strong in limiting the opponents shooting and strong at generating turnovers, while being relatively weak on the defensive boards. Illinois is not dominant in any area defensively, but above average to good in each category. To win this game, Virginia will have to continue to dominate the defensive glass, and either limit Michigan State to an eFG% under 50% or force a turnover ratio over 20%.

Virginia should have no trouble winning the battle on the glass, being a great defensive rebounding team (5th in the nation, limiting opponents to offensive rebounds on only 25.9% of missed shots), while Michigan State is a mediocre offensive rebounding team (104th in the nation, grabbing only 33.4% of their missed shots). Since the Wahoos are not a team that tries to create turnovers, this game looks like it will come down to Michigan State’s shooting against UVa’s shooting defense. Virginia must contest as many shots as possible, and even then hope the Spartans aren’t knocking down shots left and right. As was evident against Coastal Carolina, Virginia struggled when its opponents hit shots. Coastal started out 5 for 9 on three point attempts in the first half, despite two of those made attempts coming with a hand in the face.

When Virginia is on offense, there doesn’t appear to be a game changing match-up. Virginia’s offense is above average to good in all areas. Michigan State’s main defensive strength is defensive rebounding. The offensive glass is an area Virginia has all but given up on in NCAA tournament play. Virginia had NO offensive rebounds against Coastal Carolina, and only six against Memphis. Instead, during tourney-time, Tony Bennett seems to have instructed his team to get several players back in favor of a set defense over an offensive put-back opportunity.

Finally, in a game as much of a toss-up as this, it could come down to free throw shooting. Neither team is particularly great from the line. Michigan State generates only 34% as many free throw attempts as they do field goal attempts, good for 300th in the nation, and only shoot 70.4% at the charity stripe (163rd in the nation). The Cavaliers, meanwhile, shoot a paltry 67.1% from the line (272nd in the nation) but at least get to the line more often, attempting 42.4% as many free throw attempts as they do field goal attempts. Whichever team is ahead at the end of the game might not necessarily win it. With a 50.9% chance of winning, Virginia has the higher chance to be ahead in the waning minutes. However, toward the end of the game when the losing team MUST foul, Michigan State has the higher chance to hold on to a lead due to their higher FT%.

This is truly a toss-up of epic proportions. Being a Wahoo fan, I have no doubt Virginia will win the battle of the boards by a wide margin when MSU is on offense. I also don’t see Virginia’s defense creating many turnovers. However, I did see in person Virginia contest almost every shot in the first half against Coastal Carolina. This time contesting shots will work in their favor and Michigan State will knock down shots well below their yearly clip. A close game at halftime will be opened up in the second half, as Virginia slowly builds its way to an 8 point lead in the closing minute. An eight point lead will be enough to ensure free throws are not an issue. MSU will not come all the way back in the final minute and Virginia will move on to the Elite Eight. Virginia 67, Michigan State 62

Virginia vs. Michigan State: A Statistical Analysis

The upcoming game between Virginia and Michigan State is intriguing on several levels. First, this is a battle between two contrasting programs. Long established national power Michigan State, with legendary coach Tom Izzo, fields a team of sharpshooters who face off against a Virginia team that has slowly built its way back to national prominence through the grind-it-out style basketball coach Tony Bennett emphasizes. Second, this game is the only Sweet Sixteen matchup where the Vegas betting line favors the lower seed. In other words, Michigan State is considered the favorite. Last but not least, especially in regards to this piece, according to various statistical models Virginia is anywhere from a moderate favorite to the ever so slightest of underdogs. These intriguing points raise three questions: how do these teams match up? What current analytic model is most accurate? And how can we improve upon these existing models to come up with the best possible estimate of each team’s probability of advancing to the East Region final?

Starting with the “simplest” of models, Ken Pomeroy’s formula over at kenpom.com estimates that Virginia is a 63% favorite to advance to the Elite Eight. His model uses tempo-adjusted offensive and defensive efficiencies to assess team strength using Pythagorean Expectation. Essentially, he is calculating the expected winning percentage of one team against an average Division-I team. However, when two teams match up, it’s highly unlikely one of them is the average D-I team. He compares two teams by using what’s called a log5 formula to calculate the expected winning percentage for one team over the other. This is how his formula derives that Virginia should beat Michigan State 63% of the time. His model can also account for home-court advantage using an adjustment to the tempo-adjusted offensive and defensive efficiencies for the home team. However, since this game will be played in a neutral venue, we’ll skip past his adjustments for home-court advantage. Kenpom’s method also has an advantage over purely margin-of-victory-based models such as Georgia Tech’s Bayesian LRMC model or Raymond Cheong’s rankings which do not account for the tempo of play. In these models, a 30 point win is counted the same, regardless of whether this margin of victory was achieved in a 50 possession per team game or an 80 possession per team game. Clearly, achieving such a large margin of victory in a 50 possession per team game shows that the winning team was extremely efficient, reaching this margin with significantly fewer chances to do so when compared to an 80 possession per team game. Pomeroy’s model does predict margin of victory as described before using tempo-adjusted efficiencies.

However, as useful as this model is, Pomeroy himself admits and understands that this model cannot account for several factors. These include things like injuries or suspensions, on-court matchups, and other intangibles whose effects on a particular game are hard to quantify (examples include player experience, depth, coaching, officiating, etc.). We will focus on the two factors that can be adjusted for, injuries or suspensions, and matchups.

Nate Silver at fivethirtyeight.com and ESPN’s BPI are two models that do account for injuries or suspensions. Silver’s missing player adjustment uses a concept called win shares, which is roughly equivalent to measuring the impact a player’s absence has on the point differential per game. The example he gives is that Brandon Davies’ suspension in 2011 hurt BYU by about 1.7 points per game. ESPN’s missing player adjustment de-weights games where one or both teams are missing key players and makes the adjustments on a minutes-per-game basis. This is a good adjustment, because it is tempo independent (whether a game has 80 possessions or 50 possessions per team per game, if a player missed half the game, he missed approximately half of the possessions). One additional item to point out is that Silver’s calculations for 2013-2014 season now include ESPN BPI as one-seventh of his base power rankings, and then the base power rankings are adjusted for missing players. So there is a full missing player adjustment plus another one-seventh missing player adjustment. Since Silver’s missing player adjustment has an extra one-seventh component adjustment in his method, we choose to use ESPN’s BPI, which accounts for tempo and where a specific weight is given for each game.

The second adjustment we explore here is for the type of matchup this game presents. There are no rating methods (to my knowledge) that account for the nuances of matchups. However, there is some recent work in this area as ESPN, in conjunction with Liz Bouzarth, John Harris and Kevin Hutson of Furman University, has led the way in matchup-based analysis. They apply their model simply to identify potential NCAA tournament upsets in what they call their “Giant Killers” model. They use a technique called cluster analysis to group similar teams together and identify which groups of significantly lower-seeded teams have the potential to upset much higher-seeded teams (the seed differential for their model to apply must be at least 5).

We build off their ideas, and use cluster analysis to group all 351 NCAA Division-I teams into 8 distinct groups based on their style of play. We then analyze all the win/loss results from the 2013-2014 season and compare each group’s winning percentage over every other group in relation to the expected winning percentage calculated by Pomeroy using an adjustment to these winning percentages through BPI’s tempo-free missing player de-weighting. In simpler terms, if Group A was expected to beat Group B at a 57% clip (according to Pomeroy and adjusted for missing players), but Group A actually beat Group B 65% of the time, we might conclude, based on the sample-size, that this is a significant difference and that Group B outperforms expectations against Group A based on how they match up. We then apply this to the Virginia/Michigan State game to make one final adjustment to Pomeroy’s winning percentage, giving us two adjustments, one for missing players and one for the matchup.

The missing player adjustment is fairly straightforward. Using BPI’s weightings, we see Virginia’s results are deflated by missing players only slightly as the Wahoos and their opponents played mostly full strength all year. The Cavaliers’ adjusted offensive efficiency increases by 0.1% while their defensive efficiency decreases (they become less efficient defensively) by 0.3%. However, Michigan State was struck by injuries for half the year, so their offensive and defensive efficiencies are boosted by about 0.6% and 0.1%, respectively. Recalculating the projected winning percentage with these additions, Virginia drops from a 63.0% favorite over the Spartans down to a 60.2% favorite. In other words, even accounting for Michigan State’s injury troubles throughout the year, Virginia is still expected to produce overall better results against the rest of NCAA Division-I.

However, we have only adjusted for missing players up to this point. We still need to adjust for the on-court matchup. According to the results of my cluster analysis there are eight distinct styles (or “types”) of teams. Each type has similar features that distinguish it from other types of teams. This produces 64 possible matchup combinations (eight types of teams can face eight other types of teams). UVa is a “Type 6” team. These teams are very efficient defensively, forcing an extremely low effective field goal percentage and a very high rate of turnovers. They tend to be good rebounding teams on both ends, but are only slightly above average in effective field goal percentage. Michigan State is a “Type 7” team. These teams are extremely efficient shooters, usually win the turnover battle, and are great on the defensive boards. Type 6 and Type 7 teams are very good and quite similar overall, with Type 6 teams better defensively and Type 7 teams better offensively, especially at shooting. Type 6 and Type 7 style teams produce teams that have the two highest average rankings according to Pomeroy’s rankings adjusted for missing players.

According to the missing player-adjusted winning expectations, Type 6 teams tend to be slightly higher rated than Type 7 as a whole. For matches played in the 2013-2014 season between one Type 6 team against one Type 7 team, Type 6 teams were predicted to win 64.6% of the time over Type 7 teams using Pomeroy’s ratings that have been adjusted for missing players. However, in reality the win rate was about 20% lower than the expected missing player-adjusted win rate, with a 51.7% actual win rate. Based on the sample size the p-value associated with this is <0.01, and we can indeed conclude that Type 7 teams pose a particularly tough matchup for Type 6 teams. In other words, Type 6 teams tend to dominate teams that are inferior, but struggle more than expected against other top-tier teams who are more efficient offensively and less efficient defensively. As a result, we adjust UVa’s expected win ratio of 60.2% down by the average 20% giving the ‘Hoos a 48.1% chance of winning the game against Michigan State.

When compared to other analytic models, this model actually produces the least favorable chance for a Cavalier victory. Adjusted for tempo, this yields a result of Michigan State winning on average by just over 1 point. Currently, the Vegas consensus is Michigan State favored by 2 points with 67% of the money coming down on the Spartans. Thus, bettors seem to be underestimating the Cavaliers’ chances of victory.

The next entry discusses the intangibles for each team, the impact of which is hard to quantify statistically, and delves into what Virginia needs to do to turn the tables in their favor.