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? 

Why Should I Root for the Home-Town Team Again?

Hey there, Busenbarkemetricites (say that 4 times fast, I dare you)! Since all of my previous posts haven’t truly been related to “econometrics” in any explicit way, this week, I spend some time using actual econometric analysis to explore an argument related to one of my favorite pastimes – NCAA College Football. That’s right, we’re  finally getting into the good stuff – D1, true blooded, authentic, and passionate college football….well, kind of.

If you’re at all like me, you have a true passion for college football, as it represents one of the final bastions of true passion in sports. There are certainly fewer ulterior motives to playing the game than there are in professional sports, and for most college athletes, the game is played purely for the love of it and the camaraderie of others who enjoy it. If you’re even more like me, you long for a system that can accurately rank college football teams, or at least approach the quantification of a team’s ability on a purely objective scale. If there is anything I want in college football, it's a method of ranking teams such that subjective assertions from the media and other coaches are removed.

rockymountainnews.com

Growing up in South Bend, IN, of course, I witnessed first-hand the vast inferiority of our current ranking system, as Notre Dame is located in the city and a large majority of the population there and everywhere else in the world has a very real connection with the school. The inferiority of the ranking system was demonstrated time-and-time-again as Notre Dame, over the course of my cognizant lifetime, was continually unjustifiably over-ranked (if you don’t believe me, look here: http://preseason.stassen.com/over-under/teams.html). As the infuriation of this system that would allow such a continually “over-dog” to garner fandom grew, my distaste for Notre Dame football paralleled it.  As a result, I was berated by fellow South Bend townspeople for not supporting the team, as according to them, the success of the team directly impacts the South Bend (Michiana for people from the area) economy. 

Well, my friends, it is finally time for me to investigate whether or not I was doing South Bend a disservice by rooting against the Notre Dame football (when over-ranked – which was almost always).

Very briefly, right here, I’ll discuss how I did my analysis. First, I extracted data from the Bureau of Economic Analysis’ website for metropolitan GDP by year. I gathered data for three college football towns, all with similar characteristics in terms of potential impact of the school, but with glaringly dissimilar economic output. The three towns were South Bend/Mishawaka, Ann Arbor, and Champaign/Urbana. I then gathered the winning percentages of each of the teams in the towns – Notre Dame, Michigan, and Illinois, respectively. I controlled for inflation, chaining all of the GDP dollars to 2001 dollars (the year when the BEA began to collect this data), adjusted for the impact of the recession (which made no difference in the final results), and employed GLS regression analysis on the impact of winning and the towns’ respective GDPs. I did some other things, too, but just email me if you’re interested about that or why I used GLS regression.

….and the results are in, folks.

The performance of a college football team makes no significant difference on the economic performance of a town!

Reviewing the table to the right, it is apparent that there are no significant relationships between the winning percentage of a football team and the GDP of the town – even in Champaign, where the economy is relatively small and almost completely driven by the school. Even when using lagging indicators of team performance, the towns’ economies didn’t respond to any changes in performance of the team (that is, winning in previous years didn't impact current year GDP either). I also estimated Pearson Correlation Coefficients for all of the variables (not reported here), and the only even relatively significant correlations were between each of the towns’ economies – indicating macroeconomic trends are much more significant than football team performance.

So, now that we know the real truth, for those of you like me, don’t be guilted into liking a home-town team just because of potential economic implications. Although college sports have financial implications in the academic and higher education universe, performance of the team is fairly irrelevant to how well-off your local economy is. This is likely because of the inelasticity of college football, which would suggest that only MAJOR changes over great periods of time or the introduction/removal of a football program may be significant.

Next week, I’ll explore the elasticity of college football and compare it to the NFL and a comment continually perpetuated by Steve Young and some others at ESPN.