# Unstoppable force meets impeccable logic: measuring the impact of offense and defense across sports and time

Here in the U.S., it’s the time of year where the learned philosophers of the American Football have once again emerge from their regular season hibernation to bicker about playoffs. They are here to witness football’s newest chapter in a never-ending saga, the greatest existential struggle of sports: offense vs defense.

“Defense wins championships!” declare the gnarled old coaches, pointing to the mangled corpses of the 2007 New England Patriots and the 2013 Denver Broncos.

“No, Rodger Goodell already ruined the league with his stupid forward passing! Booooo!!!” sayeth the hipsters.

Meanwhile, in the basketball world, walking offensive highlight reels like Lebron James and Stephen Curry duke it out against the disciplined defending minions of Greg Popovich. In soccer, it’s South American strikers vs European back lines.

We don’t always think about it directly, but this philosophical struggle between offense and defense is one of *the* central themes that pervades all of sports. It’s not far fetched to say that your stance in this discussion in part reflects who you are as a person, incorporating everything from your temperament to your nationality and political affiliation. At the end of the day, what makes the subject so enticing is that it ultimately comes down not to some objective statistic, but to the personal mindset and body of experiences through which every sports fan sees their beloved game.

Or so you thought.

To kick off the inaugural month of Scribes of 505, I’m here to make some objective statistic. Call it the OVD (offense vs. defense) index. So don your thinking caps, put on your copies of *Moneyball*, and prepare to be the most insufferable know-it-all at your local Buffalo Wild Wings joint. It’s time to crunch some numbers.

## The Problem

The goal in any sport is to win. As a result, what we are looking for is a quantifiable number that can answer the following question:

*Is offense or defense more important to winning games?*

To keep things simple, we’ll just look at typical games in the regular season without trying to make any statements how it translates to “winning championships” or anything like that. Also, nothing that we discover will have any bearing on what managers/coaches/players *should* do; we’re just looking to describe the historical results.

On the other hand, the metric that we use must be sufficiently flexible so as to describe how things change over time, for instance, whether the NFL was more “defensive” back in the 80’s. In addition, it will also be nice to see how things compare across different sports, to say whether basketball is really more about “getting buckets” than football is about getting touchdowns.

If you do some research in this topic, then most of the results produce a bunch of seasoned sports fans arguing over inconclusive anecdotal evidence. The more “quantitative” discussions cite changes in specific stats over the years, like the fact that yards per play are at all-time highs in the NFL and that pace is similarly rising in the NBA. While these number seem superficially impressive and may well be correlated with a growing importance of offense, they mean very little if *every* offense is benefiting from the high numbers.

Dig a little deeper and you’ll finally come across a sprinkling of obscure blogs that explore statistical distributions in figures like Football Outsider’s *DVOA* and basketball *WPA*. These discussions come much closer to addressing the real question. However, my main complaint is that advanced stats are a bit overkill for our simple question. Furthermore, none of these analyses translate across different sports nor can they be applied to historical data.

## The Approach

The approach we take relies on far simpler data, in fact, the simplest stat there is: points scored by each team. With only this information, I claim that we’ll be able to unify every season of every league across the sport-time continuum into one single OVD framework: one stat to rule them all.

Here is the central chain of logic:

- The role of offense in any sport is to score points. The role of defense in any sport is to prevent the opposing offense from scoring points.
- A good offense scores a lot of points all the time and a bad offense scores very few points all the time. Likewise for good/bad defenses.
- The final score for a team is influenced by both its offense and the opposing defense. Whichever side has a greater influence on the points scored is the more important unit.

What does this all mean? Well, in a single game, it’s impossible to tell which side of the ball “has more influence” on the final score. Did the Cowboys get shut out because their offense sucked or because the Colts defense was amazing? The answer is nobody knows, at least not without watching the game.

The magic happens when you look at the aggregate numbers across an entire season. In one extreme, suppose that offense determines 100% of the outcome and defense is just about luck. By rule (2), we should expect that there is a wide range in average points scored by offenses. The high-flying Chiefs will *always* score a lot of points and the hapless Cardinals will *always* put up stinkers regardless of what defense they play. On the defensive side, we’d expect that the average points allowed by each team would be pretty uniform in the long run. Some weeks you play the Rams, some weeks you play the Bills, but eventually everything evens out and your average points allowed is, well, average. Most importantly, the same exact argument can be said in reverse about defense.

And there it is: the key intuition to our simple metric. By rule (2), good/bad offenses are labeled as such by how many points they score over the course of a season. Good/bad defenses are labeled by how many points they allow. By rule (3):

*The more important side is the one with the greater variance in points.*

In other words, if the statistical variance across points *scored *is higher for any given sport, then the offense is more important. If the variance across points *allowed *is higher, then defense is more important.

## The Method

With this understanding, we can now start to gather and analyze the data. This section can get a bit dry so if you trust my math and would like to just see the results, then feel free to skip forward to the pretty graphs.

The data collected reflects regular season points scored/allowed per game dating back the 1970 across four different leagues: NFL, NBA, MLB, and La Liga. Here is an example of the 2018 data from the NBA:

**Offense (points scored)**

113.5, 112.4, 111.7, 111.7, 110.9, 110.0, 109.8, 109.5, 109.0, 108.2, 108.1, 107.9, 106.6, 106.6, 106.5, 105.6, 105.6, 104.5, 104.1, 104.0, 103.9, 103.8, 103.4, 103.4, 103.4, 102.9, 102.7, 102.3, 99.3, 98.8

**Defense (points allowed)**

99.8, 99.8, 100.4, 102.9, 103.0, 103.9, 103.9, 103.9, 104.2, 104.4, 105.3, 105.4, 105.5, 105.8, 106.0, 106.8, 107.3, 107.5, 108.0, 108.0, 108.2, 108.5, 108.8, 109.0, 109.6, 109.9, 110.0, 110.3, 110.4, 113.3

Note that we don’t care at all about which values correspond to which team.

Okay, so between the four leagues, we now have data spread across a weird mix of points, runs, and goals. Although the intuition is the same for each sport, we need to do some data processing to get each data set down to the same dimensionless meaning of “score”. Here are the steps.

**Log-Ratio:**If we just calculate the variance of the raw scores, then there is subtle trap of overvaluing offense. The problem is that a perfect offense can, in theory, score up to an infinite number of points, but a perfect defense can at best “only” allow 0 points. But if we take the raw difference, then a score differential of*infinity*is far more impressive than ~100 points for the perfect NBA defense. Incidentally, this mental mistake happens everywhere in sports. Websites always, always give a linear score differential, but most fans don’t realize that the same score differential means a lot more for a low-scoring team than for a high-scoring one. To fix this problem in the analysis, we take a*log-ratio*for each score, where**log-ratio = ln(score / mean)**. Intuitively, what this implies is that holding a team to 50 points in the NBA is about impressive defensively as scoring 200 points is offensively, assuming the league-average is about 100.**Standard Deviation:**Now that we’ve calculated the log-ratio, we can take the standard deviation for both offense and defense for each season. So, taking our example 2018 NBA dataset, the result is 0.0351 for offense to 0.0308 for defense. And there we have it! The first time we can say with conclusive confidence that offense*is*more important than defense in the modern NBA.**Normalization**: We now have two numbers, one each for offense and defense, which can be compared. However, we don’t care much about how big or small these deviations are in a vacuum. The magnitude of these numbers partly reflects the*parity*of teams in a given sport, but this blog post only cares about offense vs defense. So, the next step is to go through each season and linearly normalize both deviation numbers so they add up to 1.0. That means the offensive deviation for the 2018 NBA season becomes 0.533 and the defensive deviation becomes 0.467. Now, we finally have numbers that can be compared across eras of varying parity and across sports of drastically different rules.**Smoothing:**Since this kind of data tends to be relatively noisy, the last recommended step when plotting OVD across time is to smooth out the data with a 5-year moving average so we can capture long term trends rather than single-season noise.

This concludes the full description of the metric. The OVD index is a number between 0 and 1 that measures relative importance of offense vs defense. It follows from this convention that **0 indicates perfect defensive dominance, 1 indicates perfect offensive dominance, and 0.5 indicates perfect balance.**

## The NFL

Without further ado, I am now proud to present the first definitive OVD graph for the NFL. For comparison, I added the average points per game, also a 5 year moving average, over the same time period.

What do you know? The NFL isn’t ruined after all! Despite the very obvious fact that scoring and offense in general has been going up over the years — evidenced by the second graph — OVD shows that defense is more or less within the same range as it has been since 1980, and is even more important than it was in the mid 2000’s. More surprising to me is that football has so consistently favored the offense for nearly the last 40 years. I was expecting more from a so-called blue-collar sport whose spiritual animal is an overweight shirtless man with a “D” and picket fence.

It’s also interesting to see where we go forward in this annoyingly QB-centric league. If you squint really hard at the OVD “bubble” between 2001 and the present, you can almost Peyton Manning’s Forehead next to the silhouettes of Brady, Brees, and Rodgers in the golden age of elite QBs. As the league is now being flooded with a new generation of good young QBs, it seems to have paradoxically lowered the relative importance of good offense.

## The NBA

The OVD for the NBA was probably the most surprising to me. There seems to be a prevalent belief among casual sports fans that the NBA is somehow all about superstars making flashy dunks and no defense. I’ve met a number of people who claim that they prefer college basketball because “NBA players don’t play defense”. The data suggest otherwise. But feel free to keep watching freshmen brick short 3’s if you want.

Even serious NBA fans and front offices are always ready to forgive supremely talented stars like Harden, Westbrook, Jokic, and even Lebron James in recent years for their less than stellar defense. Should we value defensive stalwarts like Andre Robertson and Rudy Gobert with similar regard? Probably not, because conventional wisdom says that offensive superstars have more impact than defensive superstars. However, if that logic holds true, then it follows that good defensive role players should be proportionally more valuable than offensive role players.

**The MLB**

Moving on, we’ll look at batting vs pitching/fielding in the MLB, where batting appears to be rapidly losing ground in recent years. I’ll tag in Zach, our resident baseball authority, for his input.

Thanks for tagging me in here Thien-nam. First of all, it is definitely not surprising that the OVD leans towards defense in baseball, especially in the past 5–10 years. Any die hard MLB fan such as myself knows that baseball teams have been valuing defense a lot more in recent years. Since first introduced by former Rays manager (and current Cubs manager) Joe Maddon around ten years ago, defensive shifts have become highly prominent among all MLB teams and have been used increasingly more each and every year. The use of analytics has provoked managers to change up traditional defensive schemes for different individual batters in order to decrease the chance that the batter will get on base. Not to mention, teams have also increased the use of defensive substitutions late in games to prevent the excess scoring of runs (e.g. a player that is highly valuable on defense replaces a valuable offensive player with sub-par defensive skills).

Also, baseball has placed a high importance on the effectiveness of bullpen pitchers and bullpen units as a whole. Bullpen pitchers are more talented than ever with a high amount of them being able to throw 95 mph or greater along with a multitude of great breaking balls. This has resulted in contending teams spending more money than ever trying to secure the best bullpen pitchers they can in order to prevent runs late in games and hold on to leads, which results in lower scores as a whole.

On the other side of the ball, offense has been increasingly focused on “launch angle” and hitting more home runs. In consequence, strike out rates are higher than ever before which means that less runners are getting on base. Therefore, by relying more on the home run, scoring in baseball can vary drastically with an increased number of both higher and lower scoring games. Teams are trying to capitalize on a pitcher’s mistakes instead of methodically getting hits and producing more runs.

Honestly, the only surprising thing about the OVD statistic is the lack of offensive importance during the steroid era (late 1980s through the mid 2000s). Many hitters took steroids and increased their offensive statistics like crazy. However, it is obvious that many pitchers took steroids to combat this, resulting in a stalemate and a consistent lean towards defensive importance, just as in basically every other era of baseball. This is just another interesting tidbit in a slew of curious facts about that time in this sport.

Good stuff Zach, thanks.

## La Liga

Finally, last but not least, we’ll hop across the pond… border… other pond… whatever. Wherever people watch soccer. Although I would prefer to look at the English Premier League for this section, I wanted a league that dates back to at least 1970 to match the other graphs.

The data shows that soccer takes the crown for most offensive sport. Thanks dad, I see now why you were so disappointed that I wanted center back in my AYSO (American Youth Soccer Organization) league.

This graph only reflects one league, of course, but its obvious offensive bias relative to American sports is quite large. Unlike in the NFL, where offensive skill positions get an unfair amount of press, the Neymar’s and Mbabbe’s of the world are clearly earning both their salary and their attention. Based on my soccer expertise as a person who is aware of the existence of Lionel Messi and Christiano Ronaldo, I have to assume that they are single-handily responsible for that offensive bubble from 2006 to 2018.

## The Conclusion

If you’ve read this far, then you are most likely interested enough for me to sneak in a couple caveats about the analysis, the “don’t forget to eat your vegetables” advice section of OVD, if you will.

- The absolute scales on the OVD index don’t mean much other than that 0 is perfect defense, 1 is perfect offense, and 0.5 is perfectly balanced. In other words, an OVD of 0.6 isn’t somehow “twice as offensive” as an OVD of 0.55 in any meaningful way, as far as I can tell. All you can say is that the 0.6 OVD is “more offensive” than the 0.55 OVD and be happy that this guarantee holds regardless of sport or era. That being said, if anybody with a statistics background is reading this and
*can*come up with a meaningful interpretation, then I would be happy to hear about it! - This analysis only works because I define offense and defense in the simplest way possible (see rule 1). In the conventional definitions of American football, for instance, the actions of the “offense” can have a huge impact on the opposing team’s score. I’m asking you to accept that such actions still count toward the defensive side of OVD.

Given these caveats, we can now take a step back and appreciate the usefulness of this statistic. It applies across all time and across all sports. With simple scoring information, you can finally show Toby from HR that nobody gives a crap about defense in your rec league. We can even calculate an OVD for Laser Tag or Yu-Gi-Oh tournaments; any competitive game where two sides are trying to outscore each other.

The ultimate power of measuring scores, and only scores, is that the results are universal. Games rise and fall, legends live and die, but OVD measures all.