Scarcity Pricing: Why Discount When Supply Is Constrained?

I prefer soaps with no additives, scents or other assorted chemicals. Accordingly, I have purchased Tom’s of Maine natural soaps for almost 20 years after a dermatologist introduced me to this friend of sensitive of skin. The soap is a bit expensive and sometimes hard to find. So when I find a reliable source, I stick with it and buy in bulk. Unfortunately,, my latest supplier, recently restricted orders to 3 bars of soap per person. I am not sure whether the company is suffering supply constraints as a result of the coronavirus pandemic, but I am mystified by the company’s approach to scarcity pricing. Despite the supply constraint, Vitacost discounts the price of this Tom’s of Maine soap.

I first emailed Vitacost for more information on the ordering policy. Customer service explained: “Unfortunately, due to the high demand of this product, we have placed a limit on how many you can order at once. This is in place so that every customer is able to enjoy the product.” The demand is relatively high because Vitacost cannot supply all the soap customers want. Still, this rationing policy surprises me. The soap is not a critical, life or death product. After my last order, I realized the company’s scarcity pricing is inconsistent with such high demand.

Vitacost warns customers about an order limit on this Tom's of Maine soap while at the same time discounting the price of the soap.
Vitacost warns customers about an order limit on this Tom’s of Maine soap while at the same time discounting the price of the soap.

I emailed Vitacost again for answers. Customer service responded with a non-answer:

“Thank you for contacting We appreciate your candid comments about the quantity limit and pricing of the Tom’s of Maine Sensitive Natural Beauty Bar Fragrance Free — 5 oz. . We are always looking for ways to improve your experience, which is why I’ve sent your comments to the appropriate department for further discussion.”

Companies should charge higher prices for high demand products. The price should increase until demand balances with supply. Vitacost should not discount the price. For example, the company could raise the price until the average order reaches around 3 bars of soap. Vitacost could even use those profits to motivate its supplier to invest in more capacity or divert supply from other retailers. (I would love to know whether the wholesaler is also under-pricing the soap!). So why does Vitacost apply a discount for its scarcity pricing?

Perhaps Vitacost uses this soap as a kind of “loss leader.” The reasonable cost keeps customers coming back to the site to shop for other products. Those other purchases should deliver more profits than Vitacost loses from the discounted scarcity pricing. However, the company risks losing single-product customers like me who are now hunting for alternative retailers. For example, I will pay retail price if I can get a lot more soap.

I prefer to buy in bulk both to make sure I have plenty of supply on hand and to reduce the per unit cost for shipping. Now, I pay $4.95 to ship just three bars of soap. This kind of ordering increases my costs. I pay more to ship each bar of soap. I also spend more of my time ordering soap. Moreover, the odds go up I will experience the frustration of running out of soap at exactly the wrong time.

Plenty of room left in this box for more Tom's of Maine Soap!
Plenty of room left in this box for more Tom’s of Maine Soap!

Can you think of any other (rational) reasons that explain Vitacost’s discounted pricing on a highly popular product? I would love to hear about it!

Football Analytics: Kick Extra Point, Worry Later About 2-Point Conversion

The Football Game Scenario

The football game was early in the fourth quarter on November 15, 2020. The home team Carolina Panthers were down 32-17 to the visiting Tampa Bay Buccaneers (Bucs). Hope came alive for the Panthers after quarterback Terry Bridgewater ran up the middle for a 3-yard touchdown. With over 11 minutes to play, the Panthers were down 32-23 and faced a key decision. Should the Panthers go for the near guarantee of the extra point kick and pull within 8 points? If so, the Panthers would next need a 2-point conversion after another touchdown to get even with the Bucs. Alternatively, the Panthers could try the 2-point conversion NOW to pull within a touchdown (and an extra point).

The Basic 2-Point Conversion Scenarios

Traditional NFL rules tell coaches they should only try the riskier 2-point conversion when absolutely necessary to get a win or a tie. Here are some standard scenarios toward the end of the game:

  • Down 1 point: kick the extra point for the tie. If the other team will not have enough time for additional plays and the coach has a strong preference for going for the win, then go for the 2-point conversion. A coach may have a strong preference, if, for example, the team’s defense is exhausted and not likely to perform well in overtime.
  • Down 2 points: go for the 2-point conversion. Whether the team comes away with one or zero points, the team will still need a field goal to win. Go for the tie now.
  • Down 3 or 4 points: kick the extra point so the team can go for the win or the tie with a field goal on the next offensive possession.
  • Down 5 points: go for 2 points so the team can get a tie with a field goal on the next possession. The team will still need a touchdown whether it comes away with one or zero points, so trying for the extra point is pointless.
  • Down 6-8 points: kick the extra point as the team will need a touchdown to tie or win no matter what. When down 7 or 8 points, the extra point has the added bonus of positioning the team for a win or a tie without resorting to a 2-point try on the next touchdown score.

Note that these scenarios do not take into consideration the potential for the other team to score. As a result, these scenarios are most useful toward the end of the game. They can also be useful when the coach is “relatively” confident that the defense will stop the other team from scoring any more points.

The More Tricky 2-Point Conversion Scenario

The 9-point deficit after scoring a touchdown begins the trickier scenarios. If the Panthers kick the extra point, the team stills need a touchdown and a 2-point conversion to tie. In the past, the decision was easy: bank the “sure” extra point now and worry about getting the 2-point conversion later. According to the sports announcers, modern “football analytics” recommend going for 2 points right away. Apparently, the goal is information discovery. The coach gets to find out now instead of later whether the odds of winning remain promising. However, I disagree with this approach. The 2-point conversion is not a neutral prize sitting behind curtains awaiting discovery. The announcers made a good point: the decision is complicated by the costs potentially incurred by sports psychology.

If a team pulls within 8 points on a successful extra point, the entire team gets an extra boost of hope. The game remains within reach. The defense stays focused on preventing further scoring as the biggest chance to win the game. Upon receiving the ball again, the offense can focus on a single mission: use the time available to get one more touchdown.

If the team fails the 2-point conversion, it faces the daunting task of scoring twice to avoid losing. This scenario creates a higher hurdle to overcome for sports psychology. If the defense doubts its offense can score twice, it may not play quite as hard. The defense will more likely become aware of its exhaustion. Upon receiving the ball with two scores to go, the offense needs to hurry more. It will be more prone to mistakes. The opposing defense gets the advantage of a lower bar of performance. The defense just needs to slow the offense down as much as possible.

In other words, the football analytics do not seem to take into account the high cost of failing to convert the riskier 2-point conversion. Depending on the team and the specific game scenario, those potential costs can be too high to risk. Ironically, in this case, more information is bad, not good.

Putting the fuzziness of sports psychology aside, the slightly less fuzzy world of assessing odds provides another way of understanding the likely wisdom of kicking the extra point now and worrying about the 2-point conversion later.

Quantifying the Cost of Failing A 2-Point Conversion

The odds for the different scoring options are also important considerations. In today’s NFL, the extra point is harder to convert. Starting with the 2015 season, the NFL moved the line for the kick from the 2 to the 15-yard line. The odds of making an extra point fell from near certainty (26 of 32 teams made 100% of their extra points in the 2014 season) to somewhere around 94%. The worst team in the 2019 season only made 85% of its extra points.

The odds of making a 2-point conversion these days is reportedly just under 50%, but the range of actual outcomes in 2019 was extremely wide. Excluding the teams with 0% success (in some cases these teams did not attempt any 2-point conversions), the success rates ranged from 17% to 100%. Depending on the team, the 2-point conversion can be quite speculative. The Panthers only made 25% of their 2-point conversions in 2019. Before this game at hand, the Panthers had a 100% conversion rate.

For argument’s sake, I assume the Panthers had a 70% chance of making the 2-point conversion. The Panthers converted 90% of extra points to-date. So the “expected value” of a 2-point conversion is 1.4 (0.7 * 2). The expected value of an extra point is 0.9 (0.9 * 1). These values suggest that the Panthers should always go for the 2-point conversion. Since the team kicked 19 extra points to-date, I assume that the Panthers consider the odds of making the 2-point conversion to be too low to replace kicking extra points. Even so, this expected value does not take into consideration the cost of failure. With the above odds, the cost of failure must be lower than “-2.5” to advantage the 2-point conversion. (If x is the cost of failure, then the two options are equivalent when 0.9 * .1 + 0.1 * x = 0.7 * 2 + 0.3 * x).

What does -2.5 mean in this context? This value can represent a proxy for measuring the impact of missing either the extra point or the 2-point conversion. Either miss presents the team with a 9-point deficit at the subsequent kick-off. In addition to the touchdown the team needs in either case, a lack of extra points means the team must score one more time after the touchdown.

For simplicity, assume the coach decides the odds of scoring an extra field goal is 30% and an extra touchdown (with the extra point) is 10%. The expected value of this scenario is 0.3*3 + 0.1*7 + 0.6*0 = 1.6. This value is too low to compensate for (zero out) the -2.5 cost of failing to convert. The coach needs, for example, to conclude that the odds for the extra field goal are 60% and the touchdown 10%. The expected value for this assessment of probabilities is exactly +2.5.

These odds of course require a lot of optimism. For the Panthers facing one of the toughest defenses in the NFL, these odds sit precariously at the extremes of optimism. Note well that these stylized assessments do not even include the cost incurred for the lower odds of scoring the first required touchdown when the offense is rushed and the coaching staff is thinking through more game scenarios.

Conclusion: Kick the Extra Point Now

Putting everything together, I recommend that a team just kicks the extra point when facing a 9-point deficit after scoring a touchdown. Bring the deficit to 8 points and live to think through one more offensive series. In this case, postpone going for the 2-point conversion until it is necessary to tie the game.

So what happened in the actual game? The Panthers followed the football analytics but failed to convert the 2-point conversion. The team went on to lose the game 46-23. The Panthers did not score again even as the Bucs continued to pile up points.

Grocery Pricing: When A Sale Is Not A Sale

The topic of pricing is one of my favorite on this blog. Over the years, I have developed a keen sense of pricing dynamics. So when I find (apparent) pricing anomalies, I feel compelled to talk about and explain them.

I made a quick 2019 New Year’s Eve run to Target and decided to take a quick trip through the grocery aisle for some breakfast options. My eyes soon landed on an old favorite, Corn Chex from General Mills. The cereal was one of the few sales Target offered at the time. Almost without a thought I reached for the 12-ounce box which was attractively priced at $2.50, a whole $1.49 lower. The 37% discount looked like a steal!

However, me eyes drifted to the even bigger 18-ounce family size Corn Chex, and I got distracted by a decision. At $3.79 a box, this jumbo-sized offering surprisingly cost 20 cents less than the regular price of the 12-ounce box! The 18-ounce box cost 21 cents/ounce. At the sales price, the 12-ounce box also cost 21 cents/ounce. Suddenly, Target’s sale did not seem so attractive. Since I love Corn Chex, I put the smaller box down and put the bigger box in my shopping cart. If I am paying the same effective price, I do not need the sale.

So what gives? Most likely, Target charges slightly more for the smaller box to encourage consumers to buy the bigger box of cereal. Surely the decision is easy for large families with a lot of corn Chex eaters. The only people who would pay 20 cents more for 6 ounces less of cereal are people who have no room in the pantry for the bigger box. Consumers who are solely focused on quantity over price might also pay more for less. Either way, Target makes a sizable margin on those sales. When customers purchase enough of the bigger box, Target uses the appearance of a sale to push the smaller box out the door. Target “anchored” consumers to the $3.99 price point for the 12-ounce box, so $2.50 looks like an incredible deal. With the “sale”, the only people who will buy the bigger box are people like me who truly want to eat a LOT of Corn Chex.

Retail stores use regular prices to anchor their customer’s measurement of value. Anyone who shops regularly at Target looks at the Corn Chex sale and sees a fantastic bargain. Target just sees the end of their opportunity to gain out-sized profits from people who are not paying attention.

The lesson? Pay attention to your price per unit of measure and decide accordingly! Sometimes a sale is not really a sale…sometimes a sale is just the end of a non-bargain.

Target's sale on the 12-ounce box of Corn Chex just brought the price per ounce in-line with the 18-ounce box of corn Chex.
Target’s sale on the 12-ounce box of Corn Chex just brought the price per ounce in-line with the 18-ounce box of corn Chex.

A Football Story: The Brittle Logic of Kicking Away A Scoring Opportunity

Football coaches are notoriously conservative play callers, especially at the professional level. While this behavior can produce sub-optimal game strategies, the precautions are understandable given the precarious nature of the job. A coach’s audience is prone to judge decisions by outcomes instead of the situation and information available at the time of the decision. Coaches can receive too much blame for executional mistakes and the ravages of randomness in cause and effect analysis. Conservative play calling buffers these crosswinds because it conforms to conventional thinking; it is more resilient because it references an orthodox body of work that has withstood prior scrutiny. So there is almost nothing like a sportscaster or analyst to remind me of the unfair punishment coaches can receive from actually taking a chance or stepping outside the bounds of standard expectations.

Such an occasion happened during an NFL game between the Detroit Lions and Green Bay Packers on Monday Night Football on November 6, 2017 at Lambeau Field. I was listening to the game on the radio during an extremely long drive through heavy traffic. I had no visuals to distract me from the game announcers. They were my entire window onto the game. I had little else to do but reflect critically on the scrutiny the announcers applied to the game. It is possible this audio focus increased my sensitivity.

Sportscaster Boomer Esiason, former quarterback for the Cincinnati Bengals, caught my attention with a scathing reaction to the decision of Lions coach Jim Caldwell to kick a long-distance 55-yard field goal. Esiason sounded scandalized as he explained why Caldwell should have instead punted the ball back to the Packers. This strategy is conservative because it trades in the immediate opportunity to score for the potential of receiving a better opportunity to score later. Esiason argued that Caldwell’s strategy should focus on pressuring the young Packers quarterback Brett Hundley. A punt would pin the Green Bay offense deep in its own territory. With his back against the wall (near his own endzone), Hundley would presumably execute even more poorly. This strategy includes some key assumptions delivered with no supporting data or references:

  • The punter successfully kicks the ball deep, AND the Packers fail to return the ball down the field.
  • A bad quarterback’s performance significantly varies by field position.

A conservative coach would indeed assume the odds of a great punt and poor return are better than the odds of a long field goal. Yet, the Lions possessed the football at the Packers’ 37-yard line. Such a close-range punt can easily result in a touchback because the room for error is so much smaller. A touchback occurs when the ball goes into the opposing team’s endzone, and it gives the opposing team the ball on its 20-yard line. With the Lions at the Green Bay 37-yard line, a touchback would result in a net 17-yard punt. Esiason ignored these risks in his analysis and said nothing about the skill of the Lions punt team.

Given the poor quarterback play, the Packers coach was very unlikely to allow Hundley to make any risky throws. Notably, Hundley never turned the ball over the entire game. The Packers suffered three sacks but only lost 12 total yards as a result. Packers coach Mike McCarthy seemed prepared to call a game crafted for his inexperienced quarterback. A bad player will force any coach to get and stay conservative. In other words, the Packers coach would likely neutralize pressure by very conservative play calling. Esiason assumed that the Packers coach would be unable to neutralize this pressure.

Overall, Esiason’s strategy has multiple points of failure. It feels and looks brittle compared to the simplicity of attempting a long field goal. I argue that relying on your team’s resilience in the case of a failed kick is the better risk/reward course of action, especially against a much weaker opponent.

Even without these assumptions, Esiason’s analysis fails under the weight of a critical logical flaw. If a legendary high-performer like New England Patriots quarterback Tom Brady replaced Hundley, Esiason’s strategy implies that the coach should kick the long field goal. However, the skill of the quarterback has NO impact on the odds of making the field goal. So if a coach fears a field goal miss, why would that coach risk giving a highly skilled quarterback a short field (meaning a shorter distance to make a touchdown)? I claim that Esiason should REVERSE his logic. If the opposing offense is weak, then a coach should take MORE risks: the downside costs should be lower. The potential penalty for giving a short field to a bad quarterback is much lower than giving a short field to a good quarterback. If Esiason then objected to the conditional on the skill of the quarterback, then his strategy effectively reduces to a ban on all long field goal kicks unless perhaps to win a game in the final minutes or seconds…an extremely conservative strategy!

Esiason’s error is more glaring considering the record of Matt Prater, the kicker for the Lions. Over his career, Prater has a 79% success rate with field goals of 50+ yards (the other announcer provided this statistic – perhaps in the hopes of assuaging Esiason?). That is, Prater is a good and strong kicker. He is a kicker a coach can trust with riskier kicks. Esiason complained that the weather was cold and not conducive to making long field goals, so perhaps the odds under those circumstances were somewhat lower. I doubt significantly lower given Prater’s overall record. (Note that the Lions are an indoor team, so Prater plays at least half of his games in the relative comfort of room temperature).

So how did things turn out? Prater missed the field goal.

Detroit Lions kicker Matt Prater misses a 55-yard field goal against the Green Bay Packers on Monday Night Football (November 6, 2017).
Detroit Lions kicker Matt Prater misses a 55-yard field goal against the Green Bay Packers on Monday Night Football (November 6, 2017).

Source: NFL

Esiason essentially lost it after the miss. Without acknowledging that Prater missed the field goal by a small margin – the ball hit the crossbar and would have made it over with a few more inches of lift – Esiason took the miss as proof of the soundness of his strategy. For the next several plays, he found several opportunities to remind the audience of coach Caldwell’s perceived negligence.

After the miss, possession returned to the Packers. They gained all of one yard in three downs before punting the ball right back to the Lions. The result was not surprising given the poor play of the Packers offense. I would not have expected the good field position to somehow enhance Hundley’s play. The Lions ended up with the ball deep in their own territory (on the 9-yard line), and Esiason bitterly pointed out that this positioning was the fault of Caldwell’s poor decision-making. Even as the Lions methodically marched the ball up the field, Esiason continued to complain that Caldwell forced his offense to work harder than needed. The Lions ended this drive with a touchdown and took a 14-0 lead. The success of the Lions suddenly diminished the power of Esiason’s argument which relied so heavily on the post-decision results.

Sportscasters straddle a fine line between descriptive recitals of the moment in real-time and sober consideration of a myriad of decisions emanating from coaches and players. That line can blur enough such that heat of the moment observations appear to prove the claims of the previous moment. I understand the pressures. Yet, a football game unfolds through multiple possibilities, and sportscasters can become overly focused on one particularly compelling path. In THIS game, Esiason made strong claims and did not consider alternative realities or sufficient data points. I think if he went back to review the entire context, he might reconsider.

Fortunately in business and in life we usually have the opportunity to take some time to challenge our gut instincts and consider the full context. We can collect some hard data on key assumptions behind our preferred decision. We can use our playbook as an initial map to the game, but we do not have to lock into a single course of action or commit to a single set of pre-conceived set of probabilities. When our field goal is waiting for the call, we can ask for the odds of success. We can look to the defense and assess the odds of stopping a poorly playing offense. We can inspect the offense and uncover its ability and determination to score from any point on the field.

Try that kick!

Jeff Bezos and More: In Defense of the Value of Valedictorians

Jeff Bezos is one of the most successful valedictorians in American history.
Jeff Bezos is one of the most successful valedictorians in American history.

Source: Steve Jurvetson – Flickr: Bezos’ Iconic Laugh, CC BY 2.0

Jeff Bezos is known as the founder and CEO of (AMZN). The stock for his company is toying with the $1000 level for the first time ever and is close to pushing Bezos past Bill Gates as the world’s richest man. (AMZN) trades near an all-time high as it flirts with a historic $1000 level. (AMZN) trades near an all-time high as it flirts with a historic $1000 level.


As of May 25, 2017, Bezos had an estimated $82.8B net worth. Bezos also graduated from Miami Palmetto High School as his class’s valedictorian. You would never believe this combination of information after reading headlines like this recent one from CNBC: “This is why class valedictorians don’t become millionaires.”

In this article, CNBC interviewed Eric Barker, author of the recently released book “Barking Up the Wrong Tree: The Surprising Science Behind Why Everything You Know About Success Is (Mostly) Wrong.” Barker made the following strong claim:

“[Valedictorians] do well…but they don’t actually become billionaires or the people who change the world.”

Given the fame, fortune, and impact of Bezos, I wondered how could Barker make such a strident claim with no qualification and how the claim could be accepted with no critical review (CNBC was far from alone). I decided to do a quick internet search. In the top results, I discovered several sites which list famous, impactful, and even very rich people who were the valedictorians of their respective high school classes. I provide the list, edited by own cross-referencing, at the end of this post. This list is far from comprehensive. Given the readily available information, I have to assume that Barker started with a theory or hypothesis and focused on confirming data. It seems he mainly relied on the work of one researcher from Boston College, Karen Arnold. Again from the CNBC article:

“[Barker’s] assessments are based on research by Karen Arnold, a professor at Boston College and the author of ‘Lives of Promise: What Becomes of High School Valedictorians: A Fourteen-year Study of Achievement and Life Choices.’ She tracked 81 high school valedictorians and salutatorians after graduation…

…’Valedictorians aren’t likely to be the future’s visionaries,’ says Arnold. ‘They typically settle into the system instead of shaking it up.'”

I put aside the technicality that Arnold included salutatorians in her study and not just valedictorians. Instead, I was left unclear about the implicit relationship Barker drew between “billionaire” and “visionary” when Arnold did not appear to do so in her research. As far as I can tell from some references to Arnold’s 1995 book which followed graduates from the class of 1981, Arnold did not create monetary quantifications of success. However, I can definitely understand why someone with a money-based view of success would make the connection. Indeed, the hurdle Barker offers up as a definition of success is extremely high. The CNBC article produced this related quote from Barker’s book:

“There was little debate that high school success predicted college success. Nearly 90 percent are now in professional careers with 40 percent in the highest tier jobs. They are reliable, consistent and well-adjusted, and by all measures the majority have good lives.

But how many of these number-one high school performers go on to change the world, run the world or impress the world?

The answer seems to be clear: zero.”

Zero impact. Nada. Not Jeff Bezos. Not Conan O’Brien. Not Sonia Sotomayor. Not W.E.B. Du Bois. And do not dare include General Douglas MacArthur. (See the end of this post for descriptions of these and other notable high school valedictorians).

Barker’s mistake was not just an over-reliance on a single, very old study. Barker also over-extrapolates and fails to consider the frame of reference for these strong claims that box valedictorians into a corner of inconsequence. (Ironically enough, Bezos seems to have graduated in 1982, one year after Arnold kicked off her study). Arnold’s sample is extremely small; the sample is too small to reliably test for the kinds of rarefied achievers that Barker highlights.

First of all, there are currently at least 22,000 high schools in the U.S. My estimate comes from the number of high schools referenced by the rankings of the U.S. News and World Report. So the U.S. presumably produces at least 22,000 valedictorians a year. For the sake of argument, I will reduce that number to 20,000 valedictorians in 1981. Arnold’s research subjects are 0.4% of the population for a given year and with each passing year, the numbers of valedictorians quickly overwhelm her longitudinal snapshot. If Arnold’s research were a survey, her results would include a whopping (minimum) margin of error of 11% for the class of 1981 assuming her sample was randomly selected (without bias). In other words, if the conclusion from this one study is that 0% of valedictorians grow up to be “world changers”, we could assume that repeating this study multiple times would generate observations of roughly as many as 11% (or 9) valedictorians of consequence in each trial.

Quantifying “world changing” is not easy, so it makes sense that Barker used the short-hand of billionaires. Yet, billionaires are like needles in a haystack. There are so few billionaires that in 2016, Forbes was easily able to list all 540 of them…and this is across DECADES of high school classes, not just one. I would love for someone to categorize this list by academic achievements and class years. Anyway, according to the Census Bureau estimate for 2016, the adult population of the U.S. was about 249,485,228. So the rate of billionaires in the adult population in general is 0.0002%. Using a sample size calculator, I find that I need 1,920,726 adults to conclude that my study group produces zero billionaires with 95% confidence.

The hurdle for millionaires matches Arnold’s sample. CNBC reported earlier this year that there are 10.8M millionaires in the U.S. That amount produces an incidence rate of 4.3% in the adult population (for the sake of simplicity, I am assuming all these millionaires are adults). The sample size calculator produces a study group size of 85. Yet, the only mentions of millionaires in the CNBC article are in the title and in a reference to a different study. I quote Barker’s use of this study from an article Barker wrote in Time’s Money to promote the book with the hyperbolic title “Wondering What Happened to Your Class Valedictorian? Not Much, Research Shows“:

“School has clear rules. Life often doesn’t. When there’s no clear path to follow, academic high achievers break down. Shawn Achor’s research at Harvard shows that college grades aren’t any more predictive of subsequent life success than rolling dice. A study of over seven hundred American millionaires showed their average college GPA was 2.9.”

Barker again produced surprisingly strong conclusions based on a single result. Yet, this single result, a GPA of 2.9, is actually pretty good: just a small fraction below a B grade. Assuming that 2.0, a C grade, is average, this study showed that millionaires are above average academic achievers in college (putting aside grade inflation!), hardly a roll of the dice. I am willing to bet that the top academicians are partially responsible for pushing that study’s results above a 2.0 average.

A quick internet search helped me turn up another study of millionaires and their academic achievement. In 2016, Bloomberg reported on the work of economists at the Federal Reserve Bank of St. Louis who used data from the Federal Reserve’s Survey of Consumer Finances for 2010 and 2013:

“According to the sample, a black person’s odds of being a millionaire increase from less than 1 percent if he or she doesn’t complete high school to 6.7 percent with a graduate degree. White Americans without a high school diploma start out with slightly better chances—1.7 percent—that rapidly improve with more school: A graduate-level education increases their probability of amassing a net worth greater than $1 million to 37 percent.”

These differences are significant. Since it typically takes above average academic performance to get admitted to graduate school, THESE results seem to suggest that academic performance in college does matter in one’s drive to millionaire status. However, academics are obviously not the ONLY path to success.

The fact that there are multiple paths to success and riches tripped up “Rich Dad Poor Dad” author Robert Kiyosaki when he leveraged Arnold’s results to come to even stronger conclusions about success than Barker did. Back in 2013, Kiyosaki really slammed valedictorians when he wrote “Why Valedictorians Fail“:

“Professor Arnold discovered that, ‘while these students had the attributes to ensure school success, these characteristics did not necessarily translate into real-world success…. To know that a person is a valedictorian is only to know that he or she is exceedingly good at achievement as measured by grades. It tells you nothing about how they react to the vicissitudes of life.’

Translation: real life is not measured by grades but by your bank statement—and they don’t teach that in school.”

Kiyosaki has an even clearer money-based definition of success than Barker; if you are not rich, you have failed in life. Kiyosaki also slams valedictorians for being too timid: “Valedictorians don’t make good entrepreneurs and investors because they’re afraid of risk. They make great employees.” Poor Bezos!

Kiyosaki’s effort to portray valedictorians as failures buries the valuable message of resilience, boldness, and adaptability.

“The message is simple: Success in the classroom does not ensure success in the real world. The world of the future belongs to those who can embrace change, see the future and anticipate its needs, and respond to new opportunities and challenges with creativity and agility and passion.”

I would respond that academic success also does not exclude you from being the kind of wealthy success that Kiyosaki elevates. The list of valedictorians at the end of this post validate my claim.

After all this belittling of academic brilliance, I found humorous irony in a piece that featured Arnold defending the distinction of valedictorian as a way to honor academic achievement (emphasis mine):

“…being valedictorian is the one academic honor that does matter to students. We understand that athletes and performers merit special honors because their achievements represent hard work, focus, and motivation. So why shy away from awarding honors to students who succeed in academics?

…In 1995, I co-authored a book on what becomes of valedictorians later in life. We studied 17 years of data and determined that valedictorians become hardworking, productive adults whose educational and career achievements remain outstanding.”

Arnold is clearly not one to devalue valedictorians in the ways that Barker and Kiyosaki do. I daresay that Arnold’s main point was to build character profiles of top academic achievers and not to establish a hard and fixed ceiling of life achievement for these people. I further claim that using research in isolation, without considering a full context of data and analysis, and/or failing to review multiple possibilities leaves us vulnerable to confirmation bias and weakens our ability to lean against counter-arguments.

So overall, I say “GO!” to all of you star academicians who wish to walk in the footsteps of Bezos and so many other extremely successful people!

A LIST OF FAMOUS HIGH SCHOOL VALEDICTORIANS – a healthy mix of successful, impactful, non-conformist, and even wealthy academic achievers

(List compiled from and Newsday with cross-checking from Wikipedia and High school names and graduation years were not available for all personalities.)

  • Jeff Bezos: founder, CEO, and Chairman of – Miami Palmetto High School, 1982 (?).
  • Douglas MacArthur – general known for World War II battles: West Texas Military Academy.
  • W.E.B. Du Bois – sociologist, historian, civil rights activist, Pan-Africanist, author, writer and editor, first African-American to earn a Ph.D. from Harvard: “an all-White high school in Massachusetts” late 19th century.
  • Sonia Sotomayor – U.S. Supreme Court Justice: Cardinal Spellman High School in the Bronx, 1972.
  • Coretta Scott King – civil rights activist (wife of civil rights leader Martin Luther King, Jr.): Lincoln Normal School, 1945.
  • Conan O’Brien – comedian, last night talk show host: Brookline High School, 1981.
  • Weird Al Yankovic – music artist specializing in parodies: Lynwood High School.
  • Kevin Spacey – actor: Chatsworth High School in Chatsworth, California, 1977 (co-valedictorian).
  • Mare Winningham – actress: Chatsworth High School in Chatsworth, California, 1977 (co-valedictorian).
  • Cole Porter – music composer: Worcester Academy in Massachusetts, early 20th century.
  • Jodie Foster – actress: the Lycée Français de Los Angeles, a French-language prep school, 1980.
  • David Duchovny – actor (made famous by the X-Files): the Collegiate School in Manhattan.
  • Chevy Chase – comedian, actor: Stockbridge School.
  • Cindy Crawford – model: DeKalb High School, 1984.
  • Bette Midler – actress, singer: Radford High School.
  • Alicia Keys – singer: Professional Performing Arts School.
  • Johnny Bench – major league baseball player: Binger-Oney High School in Binger, Oklahoma
  • Tiffani Thiessen – actress: Valley Professional High School in Studio City, Los Angeles, 1992.
  • Emmylou Harris – singer and musician: Gar-Field Senior High School.
  • Harry Anderson – actor: Buena Park High School then North Hollywood High School, 1970.
  • William Peter Blatty – author (wrote the Exorcist): Brooklyn Preparatory, a Jesuit school, 1946.
  • Troian Bellisario – actress: Campbell Hall School in North Hollywood, California.

{Addendum: title changed and small corrections made on June 5, 2017}

Still Not Worth the Cost: A Follow-Up Case Study of Congestion Pricing in the SF Bay Area

Over three years ago, I wrote “Not Worth the Cost: A 17-Month Case Study of Congestion Pricing in the SF Bay Area” as an analysis of congestion pricing on the Express Lane for Highway 237 in Milpitas, CA. I concluded then that the opportunity for saving time was not worth the price of the toll on the Express Lane. Road conditions have changed dramatically since then. Traffic has become so bad that I can now imagine scenarios where paying the price of the toll is worth the savings in aggravation alone. However, one caveat is that at certain points in the commute period, even the Express Lane can become extremely congested, especially during the approach to the Express Lane. Such congestion erodes some of the value proposition of the Express Lane.

For this post, I focus on an update of the data. In a future post, I plan to do some deeper analytics and wax poetic on the poor operations of the Express Lane (for example, cheaters abound with near complete impunity). The bottom-line for the update: commute times are longer, the tolls have shot up, YET the expected drive time for a given toll cost has decreased.

First, here are some general parameters of the data collection:

  • Date range: June 18, 2012 to January 24, 2017.
  • Time range: 7:28am to 9:53am. The median time was around 9:04am with 50% of the drive times occurring from around 8:41am to 9:20am.
  • Total measurements: 160. Nine measurements occurred on days when the Express Lane was not available to toll payers (HOV-only presumably because of capacity problems). I took measurements when I had to drive to work when my schedule did not accommodate taking my vanpool (family schedule, personal appointments, work events, etc…)
  • Measuring tool: stopwatch. Note that until the 21st measurement, I used the car clock.
  • Measuring points: from the solid white line that identifies the off-ramp from southbound 880 onto 237 to the point where the carpool restriction drops from 10am to 9am (near the Great America Parkway exit).
  • Length of drive: 3.2 miles
  • Driving rules: stayed in the leftmost non-Express lane.
  • Congestion: no observed accidents. I started to observe and experience congestion on the Express lane in late 2013 with the problem worsening over time. In the future, I plan to start measuring this congestion when I am riding in my vanpool.

Below are two charts using the same data. The first chart juxtaposes the time period starting from January, 2012 to the time period starting January, 2014. The trend lines are linear. The second chart compares the time period from June, 2012 to December, 2014 to the time period from January, 2015 to January, 2017. The trend lines there are also linear.

Highway 237 Express Lane Drive Time Versus Cost - split at January, 2014.
Highway 237 Express Lane Drive Time Versus Cost – split at January, 2014.

In this view, the red dots signify drives starting from January, 2014. The remaining black dots are drives starting before January, 2014. The trend lines are not very accurate because of the huge range in drive times for a given toll cost (R-squared of 0.47 and 0.50 respectively). For example, when the toll is set at $7, the drive time in the standard lanes can range from 14 to 21 minutes. In other words, the drive can be 50% longer than the best case scenario. At $5, the range goes from 8 to 18 minutes, a truly horrible spread. The spreads do not improve until the lowest toll costs at which point congestion is negligible in the standard lanes. Fortunately, there is just enough clustering to make the data usable. So, for example, from $6.50 to $7.00, I expect the drive to last around 18 minutes in the regular lanes.

The most interesting finding is that since January, 2014, the drive time for a given cost is, on average, below the implied drive time when averaged across the entire date range. This result surprised me. This result technically means that taking the Express Lane makes even less financial sense than before – at least at the lower toll costs say below $4.50 which represented the maximum observed cost from my first analysis. For example, I used to expect a $4 toll to imply a 13 minute drive. Now, I should expect that $4 toll to imply a 12.5 minute drive.

The difference in time periods becomes more stark when I make a clean break between a before and an after period. For this view, I used January, 2015 as the dividing line. Anecdotally, drive times in the regular and carpool lanes began their dramatic increase sometime in 2015.

Highway 237 Express Lane Drive Time Versus Cost - split at January, 2015.
Highway 237 Express Lane Drive Time Versus Cost – split at January, 2015.

This chart shows that before January, 2015 a $4 toll implied a near 14-minute drive. Since January, 2015, that same $4 toll implies a near 12-minute drive. The Valley Transportation Authority (VTA) has essentially dropped the price for taking the Express Lane. I am assuming the VTA made this move to increase utilization on the Express Lane. I will need to read the VTA’s financial reports to verify this hypothesis. Note that the VTA can well afford the drop in price because the dramatic increase in commute times gives more people, at the margins, the incentive to hop onto the Express Lane. Presumably, there are also a lot more cars on the road which equate to additional revenue opportunities.

Before January, 2015, the maximum drive time I experienced was 18 minutes ONCE. The next three longest drives were 16 minutes long. Since January, 2015, the maximum drive I experienced was 21 minutes (just this month in fact!). Three other drives were worse than the previous maximum. This worsening in commutes is also reflected in the maximum observed toll which went from $5.50 to $7.00.

I also note that the two trend lines are essentially parallel: the slopes are equal. In other words, the incremental drive time for an incremental increase in toll has remained the same even as the base cost has gone down (think of where the graphs cross the vertical or y-axis when the toll equals $0).

Finally, I include below a chart from a friend of mine who loves the Express Lane and takes it regularly. These data are from recent drives. The chart just confirms an apparent toll maximum at $7 and the slight tendency for tolls to increase later in the morning.

The cost of the Express Lane tends to increase later in the commute.
The cost of the Express Lane tends to increase later in the commute.

I still do not consider the toll for the Express Lane worth paying except in those dire emergencies where I need to shave any number of minutes from my drive. Such a dire emergency has yet to occur. I am otherwise content just to get extra minutes listening to my latest podcast. The unattractiveness of paying up shows in stark relief when a $6 to $7 toll may save just over 10 minutes. The growing congestion on the Express Lane adds to the baseline uncertainty of the value proposition presented by the toll.

Next up – a deep dive into the VTA’s own analysis.

Uber Uses Economics 101 And A Natural Experiment to Justify Surge Pricing

I have several beefs with Uber and its ilk. One beef I do NOT share with some is the controversy over Uber’s surge pricing. Surge pricing sounds exotic, but the pricing process is relatively basic in operation and in principle. It comes from the economics of bringing supply and demand into balance when demand surges beyond available supply.

Some critics say surge pricing is “not fair” as if Uber is providing or controlling a public good. These critics fail to recognize that pricing IS the way to generate fairness ESPECIALLY when resources are scarce. Uber’s latest defense of surge pricing comes in the form of an Economics 101 lesson accompanied by an interesting case study including what is called a natural experiment. A natural experiment is a scenario where circumstances align to provide a control to compare against an object of study. Comparing the object of study versus the control can provide some understanding of the impact of whatever characteristics make the object of study different from the control (the treatment).

In a recent press release called “The Effects Of Uber’s Surge Pricing,” Uber explains the basic economic principle:

“Surge pricing has two effects: people who can wait for a ride often decide to wait until the price falls; and drivers who are nearby go to that neighborhood to get the higher fares. As a result, the number of people wanting a ride and the number of available drivers come closer together, bringing wait times back down.”

Surge pricing delivers improved service levels by working through incentives. When supply and demand are in balance, a person who wants a ride at the given price P can generally get one in just a few minutes. At this price, every driver who wants to drive is theoretically waiting by the Uber app ready to accept a request. The potential drivers who have chosen not to drive have presumably decided that their time is better spent doing something else given current pricing.

When demand surges out of this state of equilibrium, wait times for riders soars as the number of drivers becomes insufficient to deliver the typical high service level. An increase in price constrains demand AND increases supply. As Uber notes, those people who prefer to pay the lower pre-surge pricing will wait out the surge (or find alternatives). Some drivers who previously preferred to do something other than drive will find the higher price attractive enough to get on the road. The surge price continues to increase until demand comes down and supply goes up enough to return service levels to a more reasonable level.

For Uber, this process of surge pricing achieves operational efficiency. It is a particularly important tool for providing incentives for drivers to get on the road when they are most needed. Uber does NOT note that for those riders who decide to wait out the surge, THEIR wait times increase tremendously. It is not clear theoretically or from the accompanying case study whether some customers are unhappy enough about the poorer service level at the non-surge price P to stop using Uber in the future. Given Uber’s on-going success, the answer seems to be “no.” Customers are always free to come back to Uber whenever prices meet their preferences.

The controversy over Uber’s surge pricing is not just peculiar because of the basic economics that underly the practice. I find the controversy particularly peculiar given the market’s ready acceptance of similar pricing practices throughout the economy. Airlines increase airfares during the busy holiday season. In sports, the tickets for playoffs and championships are much higher than the regular season as the demand from fans soars to participate in a unique experience. The most popular concerts command higher ticket prices. In entertainment in general, when performances sell-out, the price of tickets in the “after-market” are typically much higher than the prices from primary vendors. Hotels cost a lot more during busy tourist seasons. The examples go on and on. Uber’s surge pricing is a well-accepted and well-established process for pricing. Uber’s need to defend the practice likely comes from the company’s transparency in using the pricing and the lack of similar pricing in many traditional transportation services.

The accompanying case study, “The Effects of Uber’s Surge Pricing: A Case Study“, is written by researchers from the University of Chicago: Jonathan Hall, Cory Kendrick, and Chris Nosko. The research is called a case study because the data come from just two examples. The paper is not a comprehensive investigation of Uber’s surge pricing. Yet, the work is still powerful in that it compares a typical example of what happens during surge pricing with a time when Uber suffered an outage in its system for surge pricing. The contrast in service levels is clear and demonstrates the usefulness of surge pricing.

The paper shows what happens during a surge in demand at the end of a concert by pop music star Ariana Grande at the Madison Square Garden on March 21, 2015. In the 75 minutes following the concert’s end, demand surged over 4x normal as represented by the number of times users opened the Uber app in a given 1-minute window. Surge pricing kicked in and sent prices as high as 1.8x the pre-surge price. Specifically, Uber surged prices for 35 minutes: 1.2x for 5 minutes, 1.3x for 5 minutes, 1.4x for 5 minutes, 1.5x for 15 minutes, and 1.8x for 5 minutes. The supply of drivers increased as much as 2x during this same time period.

As a result of bringing demand and supply closer, the percentage of requested rides that resulted in a completed trip (the completion rate) remained unchanged and wait times did not increase “substantially.” The study could not adjust for drivers who already planned to make themselves available only after the concert’s completion. The authors did not explain why surge pricing was only in place for 35 of the 75 minute surge, but my guess is that a non-price related increase in supply might at least be part of the explanation.

This is all fine and good but even better with a point of comparison like a control. Uber cannot recreate an Ariana Grande concert at the Madison Square Garden for an exact comparison. However, some high demand period of similar scale without surge pricing can provide a sufficient substitute. Such an event occurred during last New Year’s Eve in New York City. For a 26 minute period, a technical glitch prevented the surge pricing algorithm from working. Surge pricing was in effect before the outage. This period is a great natural experiment to study because:

“New Year’s Eve represents one of the busiest days of the year for Uber and illustrates why surge pricing is necessary in inducing driver­partner response. At the same time that demand is unusually high, driver­partners are simultaneously reluctant to work because the value of their leisure time (e.g., their own celebrations of New Year’s Eve) is high. Put bluntly, people do not want to drive on NYE, and, in the absence of surge pricing, we might expect the gap between supply and demand to be large.”

During the outage of the price surge, completion rates plunged severely. Prices fell from 2.7x normal prices to 1.0x the standard fare. The artificially low fares caused a surge in demand that sent completion rates hurtling downward. At its worst, the completion rate dropped below 25%. Sure, a few people got a good deal, but the vast majority of people wanting a ride could not get one. This kind of poor service level is very bad business for Uber. Without proper pricing, Uber could quickly get a reputation as a system that does not provide good service and has few actual rides to offer at the moment users strongly desire one. Drivers were also not properly compensated for providing such a valuable service during this time (the authors do not mention whether Uber “made good” with those drivers).

This valuable Economics 101 lesson from Uber reminds us of the power of pricing to allocate scarce resources in an efficient manner. It also demonstrates how proper pricing provides strong incentives to bring supply and demand into balance to maintain good service levels for those people who participate in the market. The study does NOT cover what happens to those people who withdraw from the surge pricing period. For example, do they return after pricing returns to normal? This kind of loyalty would be good for Uber longer-term. Or do consumers priced out during surge pricing pay for alternative transportation options which are presumably cheaper but not quite as convenient? Studying retention after such defection would be key for Uber to understand how to price even more efficiently in the future.

Using Machine Learning To Tease Out A Dynamic Pricing Algorithm

On November 29, 2013, I wrote a piece titled “Not Worth the Cost: A 17-Month Case Study of Congestion Pricing in the SF Bay Area.” In that piece, I presented data I manually collected on toll costs for the westbound Express Lane on Highway 237 (running from Milpitas to Sunnyvale, CA) versus the drive time on the highway’s general purpose lanes. I was disappointed to find that the relationship between the two was not very reliable. Moreover, I concluded that neither the toll nor the overall projects costs are worth paying.

Motivated by comments and questions from a reader, I decided to take a deeper look at the data to see whether I could tease out some more complex relationships. I will be doing this analysis in stages. In this first stage, I developed a simple machine learning model using a regression tree to predict drive times based on a full array of variables.

I broke up the data into the following independent variables:

  • Cost: price of the toll on the Express Lane in dollars.
  • Month: index for month of the year (1=Jan, 2=Feb, etc…) using the date of the data collection.
  • DayofWeek: index for the day of the week (2=Mon, 3=Tue, etc..) using the date of the data collection. Note that the tolls only apply on non-holiday weekdays.
  • WeekOfYear: index for the week of the year (1=the first week which is Jan 1st, 2 = the second week, etc..) using the date of the data collection. Note that the week starts on Monday.
  • Hour: the hour component of the start time of the drive on the general purpose lane.
  • Minute: the minute component of the start time of the drive on the general purpose lane.

The dependent variable (what the model is trying to predict/classify) is the duration of the drive on the general purpose lane in seconds. I coded this as DriveTimeSeconds.

I used the e1071 package in R for creating the best regression tree using 10-fold cross-validation.

The initial results are promising. The regression tree below shows that drive time on the general purpose lane is influenced by the day of the week and the fraction of the hour (but NOT the hour itself!). Adding these variables to the cost information from the toll lanes provides a richer understanding of resulting drive times. Of course, the model cannot know whether congestion itself depends on the day of the week and the time, but, for now, congestion does not appear to be material to this model since I generally did not observe congestion in the Express Lane during my data collection. Ironically, the last two days that I added to the data – December 3rd and 6th – DO include some observed (very minor) congestion in the Express Lane.

Classification Tree Applied to the Dynamic Pricing Algorithm on the Highway 237 Express Lane (San Francisco Bay Area)
Classification Tree Applied to the Dynamic Pricing Algorithm on the Highway 237 Express Lane (San Francisco Bay Area)

Here is how to interpret the branches of the tree (from left to right of the leaf or end nodes):

  1. If the cost of the Express Lane is less than $2.05, then I can an average drive time of 479.2 seconds (8.0 minutes).
  2. If the cost is less than $2.55 but at least $2.05 AND the weekday is a Wednesday, Thursday, or Friday, then I can expect an average drive time of 641.5 seconds (10.7 minutes).
  3. If the cost is less than $2.55 but at least $2.05 AND the weekday is a Monday or Tuesday, then I can expect an average drive time of 700.7 seconds (11.7 minutes).
  4. If the cost is at least $2.55 AND the time is before half past the hour AND the time is at least 15.5 minutes past the hour, then I can expect an average drive time of 701.2 seconds (11.7 minutes).
  5. If the cost is at least $2.55 AND the time is before 15.5 minutes past the hour, then I can expect an average drive time of 766.8 seconds (12.8 minutes).
  6. If the cost is at least $2.55 AND the time at least 30 minutes past the hour, then I can expect an average drive time of 803 seconds (13.4 minutes).

With these results, I can move beyond the disappointing scatter of the 2-dimensional graph of drive time versus cost and see the more complex relationships at work. It is VERY interesting to see that while the tolls ranged from $0.85 to $4.25, the tree only contains two branching points based on cost. This verifies that cost is not a sufficient determinant of average driving time from the perspective of the driver in the general purpose lane.

The chart below recasts the original chart: it color-codes the points according to the rules from the regression tree. You can now visualize how the algorithm partitioned the data. The “nodes” in the legend are ordered and numbered as shown in the list above.

Highway 237 Drive Time Versus Cost of Express Lane (Random Dates from Jun 18, 2012 to Dec 6, 2013)
Highway 237 Drive Time Versus Cost of Express Lane
(Random Dates from Jun 18, 2012 to Dec 6, 2013)

With this format, you can also visualize which parts of the model have the highest error rates. The very first rule, “Node1”, has the highest error rate given that with a cost less than $2.05 drive time can range from 200 to 800 seconds (3.3 to 13.3 minutes). If I had additional variables at my disposable, I might be able to reduce the error rate of this region of data. This model can also be a starting point to help the VTA generate a more consistent congestion pricing model (again, from the perspective of the general purpose driver).

In a future analyze, I will apply k-means clustering to these data to see whether I can generate even richer results. I think the partitioning routine of k-means should be well-suited to this problem. I will also explore metrics of performance of these models. Stay tuned!

(Author’s addendum for December 7, 2013: I neglected to include a variable for the year in the above analysis. Such a variable is very effective in detecting whether the VTA’s pricing algorithm has experienced significant change over time. After adding in the year, the model did not change. However, going forward, I will keep this variable so that any significant changes do get flagged.)

Not Worth the Cost: A 17-Month Case Study of Congestion Pricing in the SF Bay Area

On March 20, 2012, the Valley Transportation Authority (VTA) implemented congestion (or dynamic) pricing on a critical San Francisco Bay Area thoroughfare called Highway 237 that primarily connects commuters from the East Bay to the South Bay. This change converted an existing car pool lane into an “Express Lane” which now allows solo drivers access to the lane for a fee (or toll). This project is part of a two-phase rollout of congestion pricing on Highway 237 and one part of a grander push to implement congestion pricing across the state’s clogged highways. Government transportation officials with the (VTA) have marketed the following benefits for this change:

  1. Provide congestion relief through more effective use of existing roadways
  2. Provide commuters with a new mobility option
  3. Provide a new funding source for transportation improvements including public transit

The conversion to an Express Lane came with some unpopular changes including expanding the carpool hours by an hour (from 9 to 10am) and restricting westbound access to the Express Lane to commuters directly connecting from Highway 880. The expansion of the carpool time seems like a revenue-generating move. It greatly inconveniences commuters (like me!) who had planned their work schedules to enable hitting the freeway after the 9am expiration of the carpool lane. The change forces these commuters back onto the one lane available for merging from 880 onto 237 (two lanes each way). The restricted access provides better and orderly traffic management to keep the expressway moving smoothly. This change change is very unpopular in Milpitas whose residents cannot use the Express Lane even though it runs right through their city (for example, see “Milpitas officials protest new Express Lanes on Route 237“, February 29, 2012).

Here is a VTA video from December, 2011 from the web page for the SR 237 Express Lanes Project; it includes maps and video shots of the area:

Congestion pricing enables commuters who can afford the tolls, a method for traveling around congested travel chokepoints. Those who do not pay are forced to deal with the congestion. I like to think of this system simply as tolled highways with a tiered-feed system: people who are either willing to pay a fee or carpool get privileged access to reserved lanes with a low likelihood of congestion. Everyone else fights for space on the remaining lanes. (Note that traffic in the SF Bay Area is so bad these days that at certain times of the commute, even some carpool lanes are heavily congested!). Theoretically, a commuter should only pay the toll if the value of the time saved is worth at least as much as the toll. However, I suspect most people do not make this calculation. Given this particular stretch of highway is only 3.2 miles long and given the VTA collected about $900M in the past year from over 550M commuting vehicles (based on the averages the VTA supplied), I strongly suspect a lot of people are wasting their money. This waste is even more pronounced when comparing the paltry time savings to the length of the overall commute. Many commuters crowding onto Highway 237 must drive for 45-60 minutes and more just to travel 20 miles, including the small stretch on 237.

Here is how the VTA describes the economics:

“This project has already served close to 2 million carpool users and has provided a new travel option to another half million toll paying commuters. This has improved travel times (between Dixon Landing Road on I-880 and North First Street on SR 237) on general purpose lanes in the Express Lanes segment by about 7 minutes. Travel time savings for using Express Lanes in comparison to general purpose lanes ranged between 5 to 15 minutes (Fall 2013). The toll rate ranged between $0.30 and $5 with an average toll rate of $1.62. The estimated gross revenue after one year of operations is just over $900,000.”

Note that the VTA claims that commute times have decreased on the general purpose lanes as a result of transferring cars onto the carpool lane, a sure sign of under-utilization of the carpool lane. Also note that on average the time savings is costing commuters $13.88/hour. The minimum wage in California is $8.00/hour. Nearby San Jose is increasing its minimum wage from $10.00 to $10.15 in 2014. So for the bottom tier of workers, this toll is extremely costly just from a dollar and cents perspective.

For the typical tech worker making $85K and up per year, the absolute cost of the toll is minimal. I believe the VTA is counting on these more wealthy workers to pony up the few bucks to save a few minutes. Here is a testimonial the VTA provided from an IT contract worker as a part of its a November 12th (2013) press release announcing the one millionth toll-paying customer.

“Jonathon Quist…who has been using the lanes since inception stating ‘I use the lanes pretty much every day. In the morning, it shortens my commute by 20 to 30 minutes. My commute from Pleasanton used to be an hour and 15 minutes to an hour and a half, now it ranges from 50 minutes to a bit over an hour. The tolls range from $2 to $4, and considering I’m a contract IT worker who gets paid by the hour, paying the toll is much less expensive than losing a half hour of pay.'”

There are several things wrong with this story, but I like it because it demonstrates what a real and valuable time savings looks like. We know this testimonial is extreme at best and most likely wrong because VTA’s own data show a time savings range 5 to 15 minutes. My own data that I show below suggest a similar a range of savings. Next, Quest’s own math does not even quite add up. By his own estimates, his true range of time savings runs from a low of 15 minutes to a maximum of 40 minutes. If Quist really was spending upwards of 40 minutes stuck on three miles of freeway, it would sure be a no brainer to pay $2 to $4 to avoid that timesink! I would also expect a lot MORE people to use the same escape hatch, thus driving the price of the Express Lane much higher. Finally, the nature of Quist’s work seems odd: it seems the amount of work he gets to do is determined by the time he arrives at work and not by the amount of work to do.

Perhaps the VTA needs to interview more than one person. Maybe this person stretched out his story to make it sound good for the public; I have come to believe that people’s perception of commute delays is exaggerated because traffic jams are so incredibly annoying and painful (here too the VTA has an advantage in convincing commuters to pay the toll – pain avoidance is a powerful thing!). Regardless, I love Quist’s testimonial because it demonstrates what kind of savings it really takes to firmly rationalize paying the toll for those who can truly afford it: the time savings needs to be significant relevant to the overall commute time. The data I have collected from my own driving experience demonstrate the toll is not worth paying at all. Here is what I did and my results…

Soon after the rollout of the Express Lane, I decided to collect data on the cost of the toll and actual time to drive through the congested lanes. Unfortunately, I did not collect travel times before the implementation of the Express Lane. I originally just wanted to approximate VTA’s pricing algorithm in order to estimate my travel time based on the toll charge. I quickly realized that these data also show the difficulty of making a good assessment for the economics of paying the toll. It turns out that the time savings per dollar paid is extremely variable. I presume this is a result of dynamic pricing based on the congestion in the Express Lane and not the congestion of the general purpose lane. (I have been told that the golden rule is to keep traffic flowing in Express Lanes at about 55 miles per hour).

The Express Lane is currently about 3.2 miles long. For my study, I measured from the start of the solid white line that identifies the off-ramp from southbound 880 onto 237 and measured to the point where the carpool restriction drops from 10am to 9am (near the Great America Parkway exit). Traveling at the 65 miles-per-hour speed limit, an unencumbered commuter takes 3 minutes to drive this stretch of highway. Traveling at 70 miles-per-hour, the commute takes 2 minutes and 45 seconds. On a typical congested day, the first mile or so is the most congested portion of the drive, consuming maybe 60 to 80% of the entire time. On the days I measured toll costs and commute times, I never observed congestion in the Express Lane. I also never observed car accidents on any lane. I did however observe plenty of cheaters in the regular carpool lane on southbound 880 and plenty of commuters who illegally passed over the double white lines separating the Express Lane from the general purpose lanes.

For consistency, I not only measured between the same start and end points, but also I stayed in the left of the two general purpose lanes for the entire trip.

My first measurement day was June 18, 2012 and the last was November 26, 2013. I typically hit Highway 237 between 8:50 to 9:15 in the morning. The last measurement day was my earliest at 7:35am. I took a total of 88 measurements over the data collection period. For the first 20 measurements, I used my car clock to mark time. For the first 4, I did not attempt to account for the lack of a measure for seconds. In the next 16, I estimated a rounding to the nearest half minute. Starting with the 21st measurement, I used a stopwatch get a precise measure of driving duration. On one occasion, no toll information was available as the express lane was restricted to carpoolers.

On most days during the measurement period, I used a vanpool for my commute. I did not take any measurements while in the vanpool. However, I will note that in recent weeks, congestion has finally started showing up in both the southbound 880 carpool lane AND the 237 Express Lane. As you can imagine, this is a very disheartening change of events for carpoolers! (I noticed in the October 17, 2013 VTA board meeting that board member Esteves {the same Jose Esteves, mayor of Milpitas?} complained about traffic delays on westbound 237. Perhaps this new congestion has already caught the attention of officials.)

Highway 237 Drive Time Versus Cost of Express Lane (Random Dates from Jun 18, 2012 to Nov 26, 2013)
Highway 237 Drive Time Versus Cost of Express Lane (Random Dates from Jun 18, 2012 to Nov 26, 2013)

The x-axis shows the cost of the toll for the Express Lane. The y-axis shows the duration of the drive time on the general purpose lane for the length of the Express Lane. The red dots mark the most recent measurements. I did this because of the recent apparent increase in travel times in the carpool and express lanes and because I took no measurements between May 2, 2013 and August 17, 2013 as my use of the vanpool greatly increased. The diagonal line is a trend (or regression) line that provides an estimate of the time to travel based on to the toll shown in the formula at the top of the chart.

The chart clearly shows the dilemma for the penny-pinching, economizing commuter. It is next to impossible to know how much time s/he will really save by paying any given toll. For example, when the toll is $2.40, the drive time in the general purpose lane may be anywhere from 8 to 13 minutes. Thus, the Express Lane may save me 5 to 10 minutes of driving. Between $2.80 and $3.00, the drive time variation is particularly bad: from 10 to 16 minutes. Between $1.80 and $2.00, the drive time variability is at its worst: from 4 to 13 minutes. The overall variability in time savings improves above $3.00. The VTA’s pricing scheme is so dynamic that commuters cannot make a rational purchase decision except perhaps at the highest toll rates. Couple this difficulty with the small size of the savings compared to the overall commute, and I see a situation where it makes little to no sense to ever pay the toll.

The VTA of course sees it differently. Again, from the press release on the one millionth customer (note how the benefit statement is slightly different yet again):

“Each month, VTA has seen at least 3,000 new first time FasTrak users in the lanes and has consistently seen no fewer than 10,000 and as many as 14,000 repeat toll-paying customers. These commuters are benefiting from a travel-time savings between 5 and 20 minutes compared to those driving in the general purpose lanes during the peak commute periods. Over 21% of the cars commuting through the SR 237/I-880 interchange are tolled vehicles, meaning that one out of every five drivers are choosing to pay for and benefitting from travel-time reliability and a better commute.”

I would love to show this analysis to those 10-14,000 repeat customers and find out whether their decision-making remains the same!

I conclude this piece by pointing out the difficult decisions ahead for our transportation officials. Not only are the economics questionable for individual commuters, the project economics for these massive conversion projects are also problematic. These projects are extremely expensive and financing is extremely difficult since the tolls collected do not even come close to paying for the projects in the near-term.

For starters, here is a description of how much planning was involved in getting the 237 conversion going:

“In December 2008, the VTA Board of Directors approved the Silicon Valley Express Lanes Program (hereafter referred to as the Program) which had been under development since 2003. The Program, as approved, was the result of 18 months of coordination, analysis and outreach on both technical and policy areas related to implementing Express Lanes as a means to address congestion levels on highways while also looking towards new solutions to accommodate the future growth in travel demand. Outreach activities included reaching out to the general public, key community and project stakeholders to derive public opinion through focus groups, a web survey, open houses, and presentations to business communities and environmental groups.”

Remember, the first year of revenue for the 237 Express Lane was a gross of just $900,000.

Here is the list of current funding as shown on the 237 web page at the time of writing. It is not clear whether this is recurring or one-time funding. Either way, it is clear that toll revenues fall short of requirements.

  • $3.5 million American Recovery and Reinvestment Act (ARRA)
  • $4 million Federal Value Pricing Pilot Program (VPPP)
  • $4.3 million local funding
  • $11.8 million total funding

Now also compare the current revenues to the costs of Phase 2 for the conversion of Highway 237 and other similar projects in the South Bay…

“The key objective of the Implementation Plan is to present a plan for the SR 237 and US 101/SR
85 Express Lanes projects currently under development. For the projects in Attachment B on SR 237, US 101/SR 85, the amount spent to environmentally clear the projects will total around $14 million with the funding having come from VTA CMA Local Program Reserve funds and federal funds acquired by VTA. The remaining cost for final design and construction is approximately $585 million.

The $585 million will fund three additional express lanes projects for VTA. The SR 237 Express Lanes (Phase II) project will convert the remaining 4 miles of existing carpool lane on SR 237 to Express Lanes between North First Street and Mathilda Avenue ($15 million). In addition, the SR 85 Express Lanes project (costing $170 million) will convert entire carpool lane segment on SR 85 (24 miles) to Express Lanes. This SR 85 project will also include adding a second express lane in the segment between SR 87 and I-280. Lastly, the US 101 Express Lanes project (costing $400 million) will convert existing carpool lane segment and also add a second express lane within the existing footprint between Morgan Hill and San Mateo County (34 miles) to express lanes.”

CLEARLY, taxpayers will have to subsidize the lion’s share of these improvements, meaning that commuters are not paying the true costs of their travel unless they are the ones responsible for paying the extra taxes.

This passage confirms that the costs of these projects are very high relative to existing tax revenues and projected project revenues:

“At present, VTA does not have funds for the design phase of work for Express Lanes. Since the mid-1980s much of the highway development work in Santa Clara County has been funded by local sales tax measure, however, there is currently no local sales tax measure that provides for highway work in the county. If funding capacity is available in the upcoming 2014 State Transportation Improvement Program (STIP), it will most likely be in 2018 or 2019.”

The VTA has had to consider alternatives that include private sources of funding and/or ceding some or all control of the projects to other government agencies. Here is one of the lists of considerations as an example:

  • Is VTA willing to forego all toll revenues and control over operational policies for a certain period of time (up to 50 years) in order to accelerate project delivery?
  • Is VTA willing to share toll revenue for repayment to a private or public entity, but still maintain control of operational policies?
  • Is VTA willing to accept construction and revenue risk in order to maintain full control of policies and revenues but be satisfied with potentially significant delays in project delivery while VTA searches for additional grant funding to supplement any debt financing?

There are no simple answers. I am sure politics will play a key role in answering some of them. In the meantime, we commuters and taxpayers should also ask the tough questions on whether these efforts are the best use of our money. As I intimated above, at least from the perspective of the individual toll-paying commuter, my conclusion for now is “no.”

Author’s addendum (December 2, 2013): Please note that the Express Lane also runs in the eastbound direction on Highway 237. I did not study this direction because on most days where I drive, I avoid the commute hours altogether given congestion is typically even worse on the way home; even the carpool lane on Highway 880 northbound is clogged for most of the trip. Traffic often does not start to cool off until after 7:30pm or later (and the congestion typically starts right at 3pm when the carpool lanes are reactivated!). This same congestion can cause traffic to back up into the eastbound Express Lane. Anecdotally, on days where I was forced to deal with the evening commute congestion, I would frequently notice that tolls were turned off. I think the economic proposition for drivers heading east are even worse than the economics heading west.

Does the TouchPad Firesale Teach Some Lessons In Pricing?

On August 18, Hewlett Packard (HPQ) announced its earnings and dropped the following bombshell:

“HP will discontinue operations for webOS devices, specifically the TouchPad and webOS phones. The devices have not met internal milestones and financial targets. HP will continue to explore options to optimize the value of webOS software going forward. “

My first thought was that I should check to see whether I can get one of those TouchPads, first released just a little over a month ago to the market, at a bargain basement discount. My father is an avid browser of the web but struggles with using a keyboard or clicking a mouse. At the right price, a tablet offers him a preferable computing alternative. I was far from alone. HP dropped the price of the TouchPad Tablet with 16GB Memory to $99.99 and the TouchPad Tablet with 32GB Memory to $149.99. Best Buy online sold out quickly and remains sold out today:

TouchPads sold out at Best Buy Online
TouchPads sold out at Best Buy Online


Lines immediately formed outside of Best Buy stores in San Francisco, CA that still had TouchPads in stock. I just called a local Best Buy to inquire about availability of the TouchPad. The recorded message began with an introduction stating that the store had sold out of TouchPads and had no plans to sell any more of them. Even retailers in the United Kingdom quickly sold out of HP TouchPads.

Clearly, consumers think these products are a steal compared to the $500 or so they would otherwise pay for competing products like Apple’s iPad, Samsung Galaxy, or RIM’s Playbook. These consumers are not concerned that they are buying a product with an operating system that has reached the end of its life and may not be supported for long. Moreover, commentary on the product indicates the TouchPad is an inferior product. From CNET (before an update to account for the product cancellation):

“The TouchPad would have made a great competitor for the original iPad, but its design, features, and speed put it behind today’s crop of tablet heavyweights.”

So what pricing lesson does this event teach us? addresses this question on page 2 of its article “RIM Reaffirms PlayBook Commitment After TouchPad Fire Sale.” Firstly, tablets cost $300-500 to build, so HP’s firesale is priced to clear out product – great for consumers, bad for business. The rush to buy at firesale prices affirms consumer expectations that such deals will not be seen again anytime soon. The iPad has sold about 30 million units to-date, so it does not appear Apple (AAPL) has a pricing problem relative to the competition. Competitors could consider undercutting Apple prices to gain some market share, but one analyst thinks it would take a 30% discount to compete with iPad on price. At a $350 price point, such a competitor is most likely going to lose money.

I see the opportunity in multiple layers:

  1. Somewhere below $300 is a price where consumers are willing to trade features for price. A “stripped down” tablet, perhaps focused on a few common tasks like email and web browsing could be a big hit with a lower tier of the market. This product could also be made slightly smaller, slightly slower, etc…
  2. Additional sales could come from selling a cheap product that offers additional products and services to enhance the value of the software and provide recurring revenue streams. mentions something similar regarding’s pending tablet offering. Also see “What HP’s TouchPad fire sale tells iPad rivals.”
  3. Similar to the last point, a low-cost tablet bundled with wireless services, television programming, Netflix (NFLX) subscriptions, etc… could be a huge hit.

In other words, Apple is likely to remain the feature-function leader for quite some time. HP demonstrated that when cheap enough, a large number of consumers are willing to settle for less. The competitor that matches production costs with a low-priced, “budget” offering could have the best chance to compete.

The additional challenge in this marketplace is the proliferation of hardware at many different form factors converging with the increasing ability to pack more features into less. This dynamic blurs distinctions across devices – for example, my suggestions above could end up looking like a cell phone on steroids, a mini-tablet not much different than a netbook with a larger screen, etc.. – and keeps marketers and product managers on their toes trying to manage product cannibalization as well as all the many cross-competitive pressures.