Skip Your Mortgage, Punk. I Dare You!

As I sit here listing to my “Closing Time (by Semisonic)” radio station on Pandora – and all its iterative loops of similarly-styled music in the Pandora algorithm – trying to hear the actual song “Closing Time” as frequently as possible, it reminds me a series of commercials I often hear on traditional radio stations each day. First, let me caveat the commercial by stating that I listen to exclusively talk radio. I literally don’t ever listen to music-based radio in the car and couldn’t even tell you a station that plays music in the central Indiana area. So if you’ve not heard these commercials, trust me, they’re played several times on every single break on my stations.

The advertisement to which I refer above is one perpetuated by seemingly every retail bank that does business with consumers in the Midwest – each is relatively the same, stating something like “Choose us for your mortgages and loans because we allow you to skip two payments. Aren’t we so connected to and caring for our customers?” Now, I can’t verify this is the exact phrasing used in each ad, but it’s always something similar. “So?”, you ask, “Why isn’t this a good thing? I like to skip payments!” Good question. You see, as I sit here listening to the song “Closing Time”, it reminds me of one of my only jobs where I ever actually worked until the closing time – at a very reputable , good, conservative Indiana bank. At this bank, we featured a very similar service, and having just completed my first ever finance and time-value of money course when I worked there, I spent some time one day considering the impact on consumers.

Since this banking trend is now becoming grossly popular, let me spend a little here explaining my findings and why you, at ALL costs, should avoid this “friendly” practice of “skipping” mortgage payments.  In order to do this, let me present a specific scenario that gives you an overall idea of the costs of engaging in the mortgage-skipping process.

In my scenario, the customer is a relatively new homebuyer or someone who relatively recently re-mortgaged. Let’s say this homebuyer conformed to the following constraints in the scenario:

Purchase Price - $150,000 (the average home purchase price for a home in the Midwest)

Mortgage Loan Value - $120,000 (assuming the person followed the convention of putting 20% down payment)

Loan Terms – 30 years at 5.5% (I think these are reasonable terms for a home buyer today)

Skipped Loans – After 4 years (This is a fairly new home owner and he wants to skip two payments after 4 years of making his monthly payments)

In this scenario, the dollar cost of skipping the two payments after 4 years is $5,128! That means, over the course of the entire mortgage, it will cost the buyer an addition $5,128 over what it would have been initially. Instead of paying $245,284.84 for the $120,000 loan (because of interest and amortization), it will cost $250,412. I don’t know about you, but for me, skipping the $681 monthly payments for two months is not worth the extra $5,128.

The worst part about this entire process is that many of the advertisements inform the consumer that the loan payment may actually decrease after the skipped payments, which is extraordinarily deceptive. Although the bank may actually decrease the monthly payments it’ll be marginally less and will simply eat a little into that additional $5,128 paid. For example, if the monthly payments began at $681 and are decreased to $671, that will decrease the additional $5,128 down to about $2000 extra paid. So even though it seems as though the consumer is paying less, the extended terms of the loan position it such that the bank earns an extra $2,000 over the course of the loan.

None of this, however, is to advocate for abolishing this kind of practice. I fully acknowledge that, to some people, it’s more beneficial to skip a couple payments now for more prioritized matters, and paying the additional money over the course of the loan is acceptable because of the time-sensitive nature of the reason why the payments are skipped. However the majority of the individuals who select to skip payments do so because they don’t understand the full implications of the decision. They operate under the assumption that the bank is simply being nice and the loan is being placed “on hold” for the two months. While that may be true in some circumstances, in most, the principle of the loan is still accruing interest and the consumer is expected to pay that interest at an amortized rate.

So, my friends, be careful when considering if YOU are going to skip your mortgage. Make sure to ask for a complete adjusted mortgage schedule and calculate the difference out yourself.

Performance Under Pressure – Why All the Quant Models Agree that AROD’s Playoff Metrics are Abysmal

For those of you who frequent the sports television radio stations in hopes of witnessing highlights relative to your teams-of-interest, there is no doubt you were exposed to all of the analysis and comments surrounding the most recent round of MLB playoffs – the ones where Alex Rodriguez (AROD) seemingly individually competed against some other team of no apparent significance.

Now, I am by no means a Yankees fan, however, I feel as though I have recently become the expert on AROD’s playoff capabilities as a result of the exhaustive commentary regarding how poorly he performed. Accordingly to literally all of the analysts – especially you, Stephen A. Smith - AROD is incapable of even crawling out of bed correctly when the playoffs roll around. Since I haven’t followed AROD with any legitimate consistency since his days of glory when he was paired with Griffey Jr., I can’t say whether or not I agree with all of the analysts who think his contract is sunk and he should be traded for any ol’ bench player off the street. As I know analysts have a tendency to sensationalize player performance on popular teams (see: 2010 when Michael Vick was touted as the best QB of all time), I’ve decided to put the quantitative gears to work to see if AROD really does suffer from “playoff collapse syndrome”.

In order to determine if AROD is simply unable to perform in the players, let’s first look at his nominal statistics – or “descriptive statistics” as titled to the left. These are some key batter metrics over his entire career (controlling for playoffs in his early career where he only batted once), and the difference in performance between the playoffs and regular season. After some cursory investigation, it is apparent AROD does, indeed, perform worse in the playoffs. In fact, he performs 20-30% worse in almost all significant batting categories. While this is certainly cause for some concern (and maybe even assertions that he performs poorly in the playoffs), looking at simple statistics like these can elicit false perceptions because of outliers and anomalous events.

In order to ensure statistical significance of AROD’s playoff performance, I performed a brief OLS regression, where the dependent variable is the batting category in question and the independent variable is a dummy to represent whether the statistic is assigned to the regular season or the playoffs. The results of these are reported to the right, but for the cliff notes version: effectively, AROD statistically significantly performs worse in all batting categories – with the exception of OBP.  In fact, all of these are significant at the 5% level, which is evidence that there is a nearly certain relationship between performance and the playoffs. Even more, you’ll notice the estimators are all negative, which means the inclusion of the playoff dummy variable resulted in negative performance.

“But, wait!”, you AROD fans say. “Just because he doesn’t perform well in the playoffs doesn’t mean he’s not valuable to the team.” This is correct, my friends. Although many of the analysts and commentators have asserted AROD’s salary is egregious given his inability to perform in the playoffs,  it is possible that his salary is actually justified by the fact that he continually contributes to his team’s regular season success and subsequent birth in the playoffs. After all, most teams make the playoffs very infrequently, and just making the playoffs is considered a success by most fans (believe me, I’m a White Sox fan just happy to get into October in any year).

In order for me to test if AROD contributes to his team’s success throughout the year such that they make the playoffs because of his existence, I ran another model – this time a logistic regression. The model measures a metric called “Wins Against Replacement” (WAR) against a playoff birth or not. This will determine if AROD’s contributions over a standard minor league replacement resulted in playoff births at a statistically significant level. Indeed, it did not. In fact, there is almost no relationship between ARODs WAR and his team making the playoffs in that year. Given that, one can conclude AROD hasn’t added value such that a minor league replacement (ostensibly making about $22million a year less than AROD) wouldn’t have lessened the chances of his team making the playoffs.

In total, here we’ve learned that AROD does, indeed, perform worse in the playoffs than he does during the regular season – which was proved statistically. We also learned that his contributions to the team above an average minor league replacement weren’t significant such that the team’s playoff contention would have been altered in his absence. But still, teams continue to pay the man obscene salaries for his presence in the line-up. Why is this? Most likely because he helps to fill the seats and couches of spectators, and ultimately, that’s what it’s all about.

Absence Makes the Wins Grow Stronger

There are so many times in life when we all wish we would have abstained from a decision or response because it would have elicited a more desirable outcome. Whether in business, sports, politics, or everyday life, there are those situations where a null activity is better than one which requires some exertion. These situations are often most evident, however, on that stage that is perhaps the most widely observed – sports. While it’s often speculated that a coach would have been better served to take the conservative route or detracted from his pressure during a game, I’ve never seen it proven statistically that it’s advantageous. Given recent events, though, I decided to take some time here to determine whether doing nothing would have actually been better than doing something.

If you follow the NFL in any capacity, you’re probably familiar with the Week 6 Monday Night Football game where The Sheriff (Payton Manning) reared his majestic head and orchestrated a comeback victory on the road – the likes of which, we’ve never seen before. The game took place in San Diego, against the Chargers, where the Broncos achieved 35 unanswered points in the second half to overcome a 24-0 halftime deficit. Following the game, the majority of the storylines discussed Manning’s superior abilities as a quarterback, the Broncos stout defense, and Philip River’s inability to avoid interceptions. There was, however, no discussion about the efficacy of the coaching decisions. There were no commentators considering whether it would have been prudent to simply kill time – you know, the way a leading team typically does in the final two minutes of the game – for the entire second half. Would it be that absurd for the Chargers to effectively concede each down for the entire second half, simply to run the clock? Let’s find out.

How I Did It

In order to determine how effective running out the clock would have been for the Chargers, I used the following methods: First, I collected drive-by-drive data for the Broncos over the majority of this season. Second, I used this data to create cumulative probability distributions regarding the probability of scoring points on a drive (whether 7, 3, or 0 points). Third, I used this probability distribution to create a series of potential offensive drives for the Broncos over the course of the second half – where the result of each drive was randomly selected given the cumulative probability. I then determined how many offensive drives the Broncos would have had given the following three scenarios in order to determine the probability of scoring the requisite points (24). Finally, I employed 2,000 simulations for each scenario to calculate the precise probability of the Broncos scoring more than 24 points and beating the Chargers (2,000 simulations were used because the number is robust enough to eliminate the influence of any outliers).

For the calculations that correspond to the following scenarios, I used a few assumptions. First, I assumed the Broncos didn’t ever score “negative” points. “Negative” points would occur by allowing Chargers defensive touchdowns or turning the ball over in field goal range. I didn’t account for this because it would only really correspond to Scenario 3 and wouldn’t have really changed the result. Second, I didn’t account for Chargers taking any time outs because this all is presuming Chargers are wasting time, not conserving it. Third, I assumed all the Broncos time outs were used in the effort of saving clock consumption and not to frivolously adjust mistakes. This is consistent with the optimal nature of my scenarios below. Finally, I assumed Broncos made all the extra points taken because the probability of missing one is so insignificant, it wouldn’t have changed the results at all.

Scenarios and Results

Scenario 1 – Optimal and Almost Impossible Scenario

In Scenario 1, I calculated the simulations under the situation that Broncos defense stopped the Chargers for a 3-and-out each drive and the Broncos only took 3 full plays to either score or not. As such, each team would have only held the ball for 2 minutes (provided the NFL play clock is 40 seconds and time doesn’t run on the first down).

Probability of Broncos Winning in Scenario 1 = 35.58%

Scenario 2 – Outstanding Play and Slightly Less Impossible Scenario

Since Scenario 1 is somewhat contrived and nearly impossible to accomplish, I created Scenario 2 to represent outstanding play by the Broncos, but to be slightly more feasible. As a result, in Scenario 2, the Broncos are still able to ensure 3-and-outs for the Chargers offense, but take 3 minutes per drive to either score or not. This is more feasible because 3 minute drives, while still extraordinarily short, are much more frequent than 2 minute drives. Still, though, this assumes stopping the Chargers on each play and no turnovers.

Probability of Broncos Winning in Scenario 2 = 8.12%

Scenario 3 – Great Play and Somewhat Probable Scenario

In order to have at least one scenario that reflects would most frequently happens in the NFL, but still maintain the requisite great play by the Broncos to come back from such a deficit, Scenario 3 was created. In this scenario, the Chargers achieve 2 first downs in the half and the Broncos use 4 minute drives. Still, this requires great play from the Broncos, but is more representative of what typically happens around the league.

Probability of Broncos Winning in Scenario 3 = 3.75%

Final Thoughts

So there it is, folks! Had the Chargers simply engaged in a run-out-the-clock scheme for the entire second half, the probability of the Broncos winning, even under the most optimal of conditions, was only around 35%. In fact, in a more likely scenario, the Broncos would have only had a 3.75% chance of winning. Of course, looking at the game ex post, given what the Chargers actually did, the probability of the Broncos winning the game was 100%.

I would be very interested to hear the perspective of some “professional” sports analysts as to whether or not they agree with a potential scheme of draining the clock for the entire half. Given my own anecdotal experience, analysts dislike introducing change into the game they often played themselves. I’d wager most of the analysts would disagree with a proposed strategy that involves running no substantial plays. But the numbers don’t lie – in situations like this, sometimes it’s better to stay out of it!

In this case, absence really does make the wins grow stronger!  

Elasticity and Football...It Doesn't Get Much Better!

“The NFL has no incentive to work out a deal with the real refs because demand for the game is inelastic.” – Steve Young, on the Monday Night Football set directly following the infamous Packers vs. Seahawks game.

Is it true? Does the NFL really have no incentive to improve operations because demand for the game is inelastic? According to the furor of ESPN analysts who suddenly discovered the economic definition of “elasticity”, it certainly is true. If it is true, what would prompt the NFL to change anything? If the same number of fans will watch regardless, surely there is no incentive to ever improve operations. If, for example, the ticket prices raised 100%, would you still attend the games? Surely Steve Young knows what he’s saying. After all, he did graduate from BYU with both his undergraduate and JD (of course, we all know BYU is the school where they encourage a man to have multiple…utility curves).

Economicseducation

First, let me define demand elasticity in the context of economics. Demand elasticity is the percentage change in demand over the percentage change for a certain variable. For example, if the relative income for the market of an NFL team went up 10% and ticket sales went up 20%, the income elasticity of demand is 2 or (20%/10%). Since the elasticity is greater than 1, it is said to be elastic. If the elasticity was less than 1, it’d be inelastic, and at exactly 1, it’s unit elastic.

Now that we’ve completed our economics 101 lesson for the day, let’s think back to my last blog where I posited a reason that metropolitan GDP in college towns was uninfluenced by team performance. I said this is because of relatively inelastic demand for college football tickets. Given what we’ve just established as elasticity, that seems like a reasonable enough conclusion now – at least I think.  My conclusion effectively stated the performance elasticity of demand was relatively inelastic, or maybe even nearly perfectly inelastic in the short term, to where the same number of fans will patron a team and its hometown businesses the same regardless of performance. Here, though, I’m going to review this paradigm for the NFL and compare it to college football through an equitable qualitative analysis.

In order to do this, let’s first set some parameters. Now, when Steve Young made his remark, he was referring to referee elasticity of demand. However, the influx of analysts who suddenly seemed enthusiastic about this remark didn’t exactly understand this, as they continually regurgitated their Wikipedia definitions of price elasticity of demand. As such, here I’m going to compare only the price elasticity of demand for the NFL and college football. Also, I’m aware the best way to do this would be to gather exhaustive ticket price and attendance data, run the regressions, and estimate elasticity. However, I’m going to assume teams have already done this correctly and I’m going to infer the elasticity from the behavior of the teams and corresponding pricing.

I made this graph, so don't say anything about the aesthetics!

Ok, so first let’s tackle the NFL (pun intended). In short, the NFL is NOT inelastic in terms of price and demand. In a recent article on Yahoo!Finance, it was explained that NFL stadium profits are hurting, and thus, teams are lowering ticket prices to elicit greater profits. Assuming Steve Young was right and other kinds of demand in general is inelastic (thereby assuming no demand curve shifts), this means NFL ticket prices are elastic. If we observe the graph to the left, we’ll notice that profit is maximized at unit elasticity, and thus, lowering prices means the NFL was previously operating in the elastic portion of the demand curve (there could be several other factors at play here, but remember, I’m assuming owners have already controlled for these).

Next, let’s hit college football. Based on my previous blog’s quantitative analysis, I’ll again assume general demand is consistent and no shifts are imminent. As such, it is apparent price elasticity of demand for college football is inelastic. Recent studies have shown that college ticket prices have been steadily rising at abnormal rates (adjusted for inflation, that is), and ticket sales remain incredibly high. This may even suggest college football is nearly perfectly inelastic. Again, if we consult our trusty graph above, we’ll see that raising ticket prices leads to more profits in the inelastic portion of the demand curve (again, there could be other factors, but I’m assuming they’re controlled).

So why does college football get to enjoy price inelasticity and not the NFL? Brace yourself because I’m about to hit you with some marketing here…it’s because of branding. People often assert the NFL is tremendous and powerful brand. While this may be true, its brand doesn’t hold a candle to college football.  College football is able to connect with fans at a much more intimate level, where many of the fans feel a VERY real sense of belonging to the school. College football fans will base their entire year around attending games, and will mortgage their lives to make sure to see top rivalries. While people love the NFL, too, fans aren’t as concerned with attending games. Very rarely do you see the connection between fans and NFL teams that you do with college football teams. In fact, those NFL teams with even a remotely passionate fan base are often compared to a “college football atmosphere”. In that sense, college football has excelled at creating a holistic that brands much more than just the game.

So what’s the lesson here? Connect with your customers and you will control them (with prices at least). Is that cynical?