Archive for category Uncategorized
Bulky-bonneted NFL players—not a Super look
Posted by mark in sports, Uncategorized, Wellness on February 6, 2026
On Sunday the Seahawks play the Patriots in the Super Bowl. I will be on the lookout for any with oversize “bobbleheads”—a derisive term by J.J. Watt of the Cardinals for fellow players who wear Guardian Caps to protect themselves against concussions. The manufacturer of these soft-shell, foam-padded, helmet claims a 40% reduction in HARM—head acceleration response metric,* That is a very clever acronym, but does it really lessen brain trauma? The NFL thinks so, citing nearly 50% reduction in concussions for players wearing them. Many position players, for example, running backs and linebackers, must wear Guardian Caps during all practices involving contact—use in games remaining optional.
However, as recently reported by the New York Times,** “independent neurologists are generally skeptical, if not outright dismissive, of the benefits of any product claiming to reduce concussions because few rigorous studies have been done to demonstrate their effectiveness.” The rate of concussions in NFL preseason practices from 2018 to 2023—after the advent of Guardian Caps—declined between 54 and 62 percent. However, the statisticians who gathered the data admitted that the use of the protective covering did not significantly reduce concussions from helmet hits.
“There’s no question that every injury or injury reduction strategy is multifactorial.”
– Jeff Miller, NFL’s chief spokesman
I’ve suffered several concussions—the first one in 3rd or 4th grade (I forget) gym class diving at a dodge ball and smacking into the wall.
After that I joined a football team at a small playground that in my 8th grade made it to the Saint Paul City ‘superbowl’ the year of Superbowl I. However, every full contact practice and game caused me such headaches that I shifted over to playing ‘pickup’ touch football. This saved me (I hope) from persistent post-concussion syndrome turning into chronic traumatic encephalopathy (CTE).
Many years later playing with me buddies from General Mills Chemical R&D I knocked myself out diving for a softball hitting my noggin on a sprinkler head. (I am a bit too competitive at sports!)
My third concussion, the cause of which I’d rather not discuss, sent me to ER for dozens of stitches and a night in intensive care at Hennepin County Medical Center.
So, I can feel the pain and very much hope that further developments in head protection will protect contact-sports players of all ages from concussion and CTE.
*See their video on The Science Behind Guardian Caps
**“The Questionable Science Behind the Odd-Looking Football Helmets,” Ken Belson, Feb. 3, 2026.
Fresh-made mac and cheese—the ultimate comfort food
Posted by mark in food science, Uncategorized on November 5, 2025
The New York Times Wirecutter team came out with a report in early September that rated Kraft Mac & Cheese Original their favorite out of the 19 boxed options tested, saying that its “buttery and silky-smooth sauce clings to each soft noodle.” If that doesn’t make your mouth water for a fresh hot bowl of gooey orange pasta, nothing will. But as writer Ciara Murray Jordan reveals in her video recap of the Wirecutter test, even a comfort food like mac and cheese becomes nauseating when binged.
Two decades ago, I ran statistically design of experiment (DOE) on Kraft Mac & Cheese Original versus their recently released Easy Mac—a more convenient, single-serve microwavable variation on their traditional stovetop, boxed brand. My goal was to see how two experimental recipes for canned mac and cheese from a Stat-Ease client (confidential) performed against King Kraft.
My wife Karen cooked up the four competing foods and presented them in random order for blind taste testing by me, my three daughters—Emily (age 21 at the time), Carrie (16), Katie (14) and three of her friends—seven in all. We rated the mac and cheese on a scale of 1 to 5—higher the better.
As you can see from the one-factor plot produced by Stat-Ease software, my client made great improvements via application of DOE on the recipe and processing of their canned product. (The numbers by some points indicate multiple results at that rating.)
Unfortunately, as you can see by the least-significant-difference bars (essentially a 95% confidence interval), this project failed to meet its goal—a canned mac and cheese just cannot best a fresh made one. As seen in the scatter plot by taster, Kraft (in one form or the other–the red and blue points) consistently came out on top.
So it goes for researchers and process developers—you win some and lose some (more of the latter). However, I did feel good seeing the original recipe (green points) rated so low by all the tasters and their far greater liking for the DOE-enhanced product.
By the way, I am now quite hungry for mac and cheese.
You too?
Today’s Major League Baseball batters all hit below average
Posted by mark in sports, Uncategorized on October 24, 2025
This headline gets your attention if you like statistics. It makes no sense without the context: See Baseball Reference’s report on batting average (BA) by year. In 2000 MLB batters averaged .270 (expressed as “two seventy”), but after years of decline they bottomed out at .245 (two forty-five) or so. This reflects a more analytical approach to hitting that disrespects batting average as a metric, it being likened to counting the number of bills in your wallet but not amount of money.
Nowadays MLB teams value players who excel at on-base-plus-slugging (OPS). This mashup of stats creates percentages over well over 100 (“one thousand” in baseball terms) for the utmost elite players—in 2025 only Aaron Judge of the New York Yankees and Shohei Ohtani of the Los Angeles Dodgers. MLB adopted OPS in 1984 after Pete Palmer introduced it in the pioneering book (co-authored by John Thorn) The Hidden Game of Baseball, A Revolutionary Approach to Baseball and Statistics.
OPS combines simplicity with reasonable accuracy and I think that is why it is popular.
– Jim Thorn, Why OPS Works, Fall 2019 Baseball Research Journal, Society for American Baseball Research (SABR)
I’ve been a fan of baseball since 1961 when the Washington Senators moved to the Twin Cities to become the Minnesota Twins. I was 8 years old then. My grandpa had been following the Minneapolis Millers since the late 19th century as a young boy. He turned 8 in 1896 when his home team won their first Western League pennant.
Grandpa was an accountant, so, naturally he collected statistics on every Twins game—carefully ruling out rows and columns for the 9 batters and 9 innings and noting each players batting average. Because of that I am a holdout for appreciating players with high batting averages. I would rather see more hits and the strikeouts that come along with trying to hit a home run at every at bat.
On the other hand, I do not doubt that a lot of people will tune in tonight for Game 1 of the World Series to see if Shohei Ohtani lives up to his “Shotime” nickname by blasting at least one home run, if not several as he did in Game 4 of the National League Championship Series. American League fans like me will be rooting for George Springer (3rd in MLB for 2025 OPS at .959) of the Toronto Blue Jays to hit another dramatic home run like he did for in Game 7 of the AL Championship Series.
Baseball is the greatest game!
Optimal airline boarding strategy will never get off the ground
Posted by mark in Consumer behavior, Uncategorized on August 19, 2025
As I waited at the end of a line last week to board the Mount Washington Cog Train with my assigned-seat ticket in hand, it occurred to me that only needing a small backpack made the process far simpler than for a flight burdened with carry-on baggage. A random free-for-all process, providing priority by willingness to wait in line, served well for the 45-minute ride up and down the mountain.
It’s not nearly as simple getting luggage-laden people on board a flight. But there is a solution. In 2008, astrophysicist Jason Steffen came up with “perfect airplane boarding method.” It starts by seating window-seat passengers every other row from back to front along one side and then the same on the other side. Then repeat the process with middle seats and, finally, the aisle.
For a fun ‘Pac Man’ illustration, see this interview of Steffen by News Nation:
An experimental test of airplane boarding methods using a mock Boeing 757 airplane showed that Steffen method cuts the time in half from traditional methods going by zones. But though it would certainly save airlines a great deal of time and thus money to switch their boarding to this innovative method, none are likely to make the change due to its precise control of passenger being impractical. Elite flyers accustomed to priority boarding would be very unhappy. Furthermore, families must be broken up in the Steffen-method lineup—not good.
However, there is hope for a better way on to an airplane. As noted in the News Nation video, United Airlines adopted a simplified Steffen method called “WILMA” that boards passengers first by window, then middle and, finally, aisle. However, as laid out in this June 24, 2025 post by CNBC the airline exempts many passengers from WILMA, including those with United credit cards. Perhaps that’s why they only save 2 minutes per flight with their new boarding process. But at an estimated cost of $100 per minute the savings of $200 per flight times nearly 5,000 flights per day by United adds up to $1 million in daily savings.
Based on my experience boarding the Mount Washington Cog Train and numerous studies, a random process serves well by it being fair and fast. When American Airlines tried it in 2011 on all but those passengers with elite status, the random process shaved 20 to 25 minutes off average times. However, according to their flight attendants, it created “complete chaos in the cabin.” As you can see in this April 26 press release, American now goes by a 9-group process. Evidently saving time via free-for-all boarding cannot provide payback for the pandemonium.
Maori manu dive bombers making a big splash
Posted by mark in sports, Uncategorized on June 3, 2025
My daughter Emily and her husband Ryan (pictured) will soon be enjoying a massive upgrade to their above-ground pool.
I am hoping to see him jump off the roof of the house and perform a Maori manu (meaning “bird”) dive like these World Champ bombers in Auckland, New Zealand.
A team of fluid dynamic and biomechanics experts at Georgia Tech ingeniously deployed a quarter-pound, 7-inch high ‘manubot’ to work out how these daredevil divers create splashes exceeding a height of 30 feet. See Mastering the Manu—how humans create large splashes (published May 19 by Interface Focus) for their findings. Figure 1a tells the story: By contorting their body into a V shape, the Manu masters create an air cavity that creates a ‘Worthington’ jet-splash—named after the discover who delivered this discourse on the physics phenomenon in 1894.
“It’s very difficult to master, it can be quite dangerous, and it requires millisecond control.”
– Pankaj Rohilla, co-author of Mastering the Manu
On second thought, I will back off on my son-in-law going dive bombing—best this be done by Maoris or manubots.
Going bananas!
Posted by mark in Basic stats & math, pop, Uncategorized on April 24, 2025
Monkeys are a lot of fun except when they get on the loose, as I experienced once while eating at an outdoor restaurant at a Costa Rican resort (as seen pictured). Unfortunately, another tourist started feeding them, despite numerous warnings posted throughout the patio. This last fall 43 monkeys escaped a South Carolina breeding compound—the last 4 of which ran free for two months. Not good.
On a lighter note, consider the Infinite Monkey Theorem, which states that a monkey hitting keys independently and at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, including the complete works of William Shakespeare. Mathematicians from the University of Technology Sydney did some calculations on this that say no to Shakespeare but provide small consolation by allowing for a 5% chance that a monkey can type “bananas” in its own lifetime. See the stats and math in their December 2024 publication of A numerical evaluation of the Finite Monkeys Theorem.
“It is not plausible that, even with improved typing speeds or an increase in chimpanzee populations, monkey labour will ever be a viable tool for developing non-trivial written works.”
— Stephen Woodcock and Jay Falletta
So no monkeying around will be allowed by mathematicians and/or statisticians.
PS: On the topic of bananas, I plan to blow my entire $2 State of Minnesota 2024 property tax refund (just got word on this windfall from my CPA), to purchase this banana-flavored Laffy Taffy. It’s not easy to find something good like this for $2 or less!
Bulbous bats hit the sweet spot for bashing baseballs
Posted by mark in sports, Uncategorized on April 4, 2025
According to the lore of Major League Baseball (MLB), in 1919 Babe Ruth hit the longest homer run ever recorded—purportedly 575 feet, but probably closer to 540 feet. See the bat he used, which sold in 2003 for over $56 thousand, at this auction site. Notice the clean lines.
In the early days of baseball, batters preferred bats made from hickory and oak due to their durability. But when Babe Ruth played, ash became the preferred choice for its lighter weight, allowing for increased bat speed and power. In 1998, the MLB approved maple, which despite its heaviness and propensity to shatter catastrophically, is now used by nearly all players, in part due to ash becoming very scarce due to invasive insects.*
Now attention to bats has shifted to their shape. The New York Yankees set the baseball world on fire by using “torpedo bats” in game 2 of their 2025 season to hit 9 home runs—a notable exception being Aaron Judge (AJ) who hit 3 of the home runs with a conventional Chandler model AJ99 (aka the “gavel”, ha ha).
Developed by an MIT PhD physicist—Aaron Leanhardt, torpedo bats push their barrel closer to the player’s hands, thus providing a better chance of hitting the ball on the sweet spot. They look like an elongated bowling pin, not elegant like the bats I saw being turned out at the Louisville Slugger factory a few years ago.
So far as I’m concerned the ‘jury remains out’ on torpedo bats, especially given the counteracting results by the Judge (see my pun there?). I will be watching for statistical evidence based on a representative and sufficiently sized sample.
Stay tuned!
PS: By the way, baseball bats, specifically their shapes, cannot be patented because they fall within the rules of the game, making them ineligible for protection. That opens up the market for bat-makers to feed the frenzy for torpedo bats, for example Louisville Slugger’s Pro Prime Pink model TPD1. Wow!
A simple statistic reveals amazing wisdom from crowds
Posted by mark in pop, Uncategorized on February 18, 2025
My good friend Rich Burnham, knowing my interest in off-beat science and stats, drew my attention to this video by YouTuber Michael Stevens (aka “Vsauce”) on an experiment that failed to confirm a phenomenon called the “wisdom of the crowds.”
Normally, as demonstrated by Sir Francis Galton in 1906 from data collected at a country fair on 787 guesses at the weight of an ox,* groups of people exhibit a high level of collective intelligence via a simple median (the “middlemost estimate”)—being off by only 9 pounds for the 1,198 pound ox. This amazes me—blowing away my mindset that the wisdom of a crowd degrades to the ‘lowest common denominator,’ that is, the people with the least knowledge.
Experts agree with Vsauce’s hypothesis that the complete failure of his crowd to correctly guess the number of jelly beans in his jar stemmed from the estimates being shared, rather than gathered with no cross-talk.
“The wisdom of crowds requires that people’s estimates be independent. Studies have found that when people can observe the estimates of others, the accuracy of the crowd typically goes down. People’s errors become correlated or dependent, and are less likely to cancel each other out. We follow our peers, to the detriment of the performance of the group.”
– Psychology professor Tania Lombrozo, No Man Is An Island: The Wisdom Of Deliberating Crowds, posted 3/12/18 by WGCU, a National Public Radio-member station on Florida’s Gulf Coast
I made the same mistake in a 2019 contest for my Anderson clan. While vacationing together at a lakeside resort, I gathered individuals’ estimates on the number of aluminum-can pull-tabs I’d collected for donation to the Ronald McDonald House in Minneapolis. See the picture below of my wife Karen (holding Bertie) working with our oldest grandchild Archer do the count. I asked the participants to write down their guesses on a clipboard by the jar, which created more fun via the gaming aspects of going just above or below a competitor, but violated the statistical requirement for independence.
An interesting workaround that allows collaboration for tapping the “wisdom of the crowds” is to first break the group into a number of teams and then average out their consensus estimates. See the research, based on results from a group of 5,180 people asked to estimate the height of the Eiffel Tower or the like, at this 2018 Letter by Nature Human Behavior on Aggregated knowledge from a small number of debates outperforms the wisdom of large crowds.
To keep things simple, the next time my bottle of pull-tabs fills up for another contest to guess the total, I will go with the simpler approach for crowd wisdom by banning cross talk and then seeing if the median estimate wins. If it doesn’t work, I will blame it on our family group being too small (though it does exceed 20—all in one cabin!).
Distance learning vs in-person training—pros and cons
Posted by mark in Education, Uncategorized on January 7, 2025
In March of 2020 when the Covid-19 pandemic came to a head with widespread quarantines, the Stat-Ease training team quickly Zoomed (pun intended) our workshops from in-person (IP) to distance learning (DL). It went amazingly well from the start.
Coincidentally, two of my grandchildren shifted from IP grade-school to DL at our home. The youngest, a kindergartner (Laine), benefited greatly by the oversight of my wife Karen—a retired preschool teacher. I helped the other (Archer), a third grader. It did not start well due to many technical difficulties and troublesome adjustments for teachers and students. We continued our DL home schooling the following school year due to the ongoing quarantine in Minnesota. By the time IP classes resumed, the DL went about as well as could be expected—the most difficult class being physical education, especially in the winter due to our home lacking a gym.
This unplanned experiment on DL across the range of child versus adult revealed a big interaction effect due to the age of the learners—IP being best for grade schoolers and DL being a very viable alternative for mature students. A few weeks ago, I got reinforcement for this observation when teaching cribbage IP as a volunteer to Laine—now in 4th grade—and two of her classmates. This would have been far harder DL.
The reason I’m bringing all this up is that my colleague Shari Kraber, who retired as our workshop manager but continues to provide training, asserts that “in-person training is not as ideal educationally and that the retention of the materials is BETTER using distance learning.”* I’m also a big fan of DL—far easier for me to teach from my home offices in my summer or my winter home (or on the road between). Google’s AI (Gemini) says that there’s no definitive answer on IP vs DL, and that the biggest factor is quality of the teaching and the materials, which makes a lot of sense to me.
Rachel Poleke, our current workshop manager, suggests that another big factor is the preference of individual students for IP versus DL. I totally agree: Ideally the delivery would be tailored to each student. This being impractical, Stat-Ease instead offers on a class-wide basis to deliver private training either way, depending on the preference of our client. For example, one year ago last September I traveled to Netherlands to teach a DOE workshop for a client headquartered in Leiden’s Bio Science Park. That was fun and very gratifying for the great response. It’s nice to take a break from Dl, benefitting by much stronger feedback from students (e.g., the ‘deer in the headlights’ look when clueless) and the ability to watch them work through case studies (our workshops are computer intensive).
Stat-Ease plans to present a rare IP public workshop—Modern DOE for Medical Devices—at our Minneapolis headquarters this year. This brings a huge advantage of DL training immediately to mind: Anyone from anywhere in the world can Zoom in, thus making it far easier for us to achieve a critical mass for class.
One thing I can say for sure—it’s great to have such a viable option for DL nowadays. When I first began working as a trainer of quality-engineering tools in the 1970’s, the technology for DL existed (e.g., PLATO) but, being pre-Internet and all, it could not compete with IP.
It will be interesting to see how things settle out in coming years for IP versus DL, both for corporate training and schooling at primary and secondary levels. Hopefully, the quality of education (based on subjective measures!) will not be lost in the shuffle of convenience for scheduling and the relative costs.
*1/1/25 Stat-Ease blog Ask An Expert: Shari Kraber
Colors to dye for
Posted by mark in food science, Uncategorized on December 4, 2024
I grew up in the golden age for kids’ cereals, first with Trix from General Mills—introduced in 1954 in three colors: raspberry red, orangey orange and lemony yellow (now also wildberry blue, grapity purple and watermelon), followed in 1963 with Froot Loops from Kellog—also in red, orange and yellow—Toucan Sam style (now also green, blue and purple). Back then nobody worried much about how these manufacturers colored their cereals—artificially or otherwise. However, nowadays a consensus has built up about a “rainbow of risks” caused by synthetic food dyes. Political pressure across the spectrum from Gavin Newsome to Robert F Kennedy, Jr continues to build for banning these presumably harmful additives.
This sets the stage for some interesting history by American Heritage magazine on letting the food industry “poison” us as RFK, Jr puts it. Their Senior Editor Bruce Watson reported in the November/December issue how “many of our first food-safety laws arose after healthy young volunteers became sick when they tried commercial foods containing toxic additives.” These daredevils comprised “The Poison Squad” created in 1902 by Harvey Wiley Washington—who became known as the “Father of the Pure Food and Drugs Act” when it became law in 1906.
“NONE BUT THE BRAVE CAN EAT THE FARE.”
– Sign posted outside the Department of Agriculture building to enlist human ‘guinea pigs’
As historian Deborah Blum noted in her book The Poison Squad: One Chemist’s Single-Minded Crusade for Food Safety at the Turn of the Twentieth Century Washington deserves credit for “one of the most significant experiments in the 20th century.” For example, just prior to his crusading work, hundreds or perhaps thousands of children died from milk “embalmed” with formaldehyde.
Not to lessen the current concern over artificial dyes, we can be thankful for the relative safety of our food compared to the fare in the early 1900s. But I do not advocate going back to the days when potential poisons were tested on human subjects. Though I suppose there’s worse things than being tasked with eating large quantities of Trix and Froot Loops, provided, of course, that the milk is not embalmed. ; )