*This is Part II of a multi-part series. Please check out the Prologue and Part I covering the relationship between payroll inequality and the distribution of regular season wins.*

A couple of weeks ago I posted my findings on the relationship between regular season win distributions and payroll inequality within and across the four major American sports leagues. My conclusions generated a great deal of discussion. This is awesome. Some of it (as always) was more thought-out than usual. Before moving on, I shall address some of the most common objections, but those who are uninterested should feel free to keep scrolling.

**Objection: Football will naturally have a more unequal win distribution because the season is much shorter and the schedule is unbalanced.**

The latter part of this statement is entirely true. In fact, I said as much in my piece, taking several steps to account for this in my calculations. The full statement itself is only partially true. As noted in Part I, this is certainly true comparing a 16-game season to a 162-game season, but it shouldn't be (equally) true when comparing the distribution of wins per football team over 10 seasons (160 games) and the distribution of wins per baseball team over a single season (162 games).

Yes, the best football teams will usually win around 80% of their games, while the best baseball teams win around 60% percent, and so in any one football season the win distribution will appear to be unequal compared to any one baseball season. However, while the distribution of wins in football evens out as we add seasons to the sample, after 160 games the distribution is still less equal than any single baseball season.

Also relevant is that the NFL schedule is necessarily unbalanced, in the sense that all 32 teams don't have an opportunity to play each other. But the MLB schedule is also unbalanced, and has been since 1997, as an artifact of the introduction of interleague play and the desire to restrict its scope. In other words, both leagues make decisions about who plays whom, which can obviously affect win outcomes.

But it's worth noting that football tweaks its schedule based on previous year records (less so in the four-division era than during the three-division era) and that baseball does not. Moreover, this should (maybe doesn't) wash out over 10 years. What this means is that schedule structure should either A) privilege football over baseball in terms of win distribution, or B) have no effect in the long run. In light of the data, conclusion B seems potentially valid, but Conclusion A does not.

Finally, most of these arguments simply reinforce my point: that

**game fundamentals and schedule structure are the primary drivers of competitive balance (or the lack thereof), not payroll disparity**. Yes, payroll equality is a statistically significant explanation of win inequality, even when controlling for time and league effects. That said, I was remiss in not presenting the beta coefficients in Part I's findings, and they tell a more detailed story.

IV (Win Distribution) | Coefficient | Beta | Std. Error | P-value | *NHL Dropped | ||

Payroll Inequality | 0.1347 | 0.1439 | 0.0603 | 0.031 | |||

Season | 0.0000 | -0.0004 | 0.0005 | 0.992 | |||

MLB | -0.0422 | -0.3665 | 0.0076 | 0.000 | |||

NFL | 0.1139 | 0.8092 | 0.0080 | 0.000 | |||

NBA | 0.0565 | 0.3686 | 0.0075 | 0.000 | n = | 48 | |

Y-Intercept | 0.1035 | 0.9874 | 0.917 | Adjusted R^2 = | 0.9342 |

What the beta coefficient tells us is the relative effect of each independent variables on the dependent variable. In this case, the OLS regression statistics indicate that league effects are far stronger in this model than payroll effects. We can legitimately say that the (negative) league effect in baseball on win inequality is 2-3 times as strong as the (positive) effect of payroll inequality. The league effect in football is 5-6 times as strong as the payroll effect. Thus, payroll inequality matters, but its effect is swamped by the factors that make the MLB different than the NFL, as well as the fundamental differences between football and baseball.

**Objection: The distribution of regular season wins is not an appropriate proxy for competitive balance.**

Fair enough. Typically, those who don't see a problem with competitive balance are talking about the distribution of wins, while those who do see a problem are looking at postseason chances and persistent dominance/failure.* While I agree that the using Gini coefficients as I have is problematic, this is a multi-part series. I did not intend those findings to be the final word, but rather to raise questions questions about the relationship between payroll effects, league effects, and competitive balance.

**There is a social science analog: we can use Gini to measure economic inequality in one society at one point in time, but not the capacity of a household can improve its lot. A household in a quantitatively more equal society is not necessarily better able to improve their lot than in a quantitatively less equal society, depending on the structural context in which it exists.*

I also intended to use that piece to set up this one (about mobility) and the next one (about playoff chances), so here we go...

**Competitive Mobility**

Just as in social science research we must differentiate between economic equality and social mobility, in sport we must differentiate between competitive equality and competitive mobility. Both are measures of competitive balance, but those of you who disagreed with me were more interested in the latter. As it turns out, you were right: teams are far more

*mobile*in the NFL than in the NBA or NHL, while teams in the MLB are the least mobile. See the chart below:

*Methodology: My measurement of mobility is not all that different than a measure of standard error. Essentially, I calculated the absolute change in win percentage for each team between season*

*y to season*

*y+1. I then averaged that change for all the teams in a league in each season, arriving at my mobility calculation. While Part I's chart looked at the year in which each season started, the year in this chart indicates the period of time leading up to the year in which the season starts. For instance, the value for the NBA in 2007 is based on the average absolute change in win percentages between the 2006-2007 season and the 2007-2008 season.*

As you can see, the average NFL team's win percentage varies about 0.200 every year. That's a great deal more variance than the average NBA team (~0.100), NHL team (~0.075) or the MLB (~0.050). Critics of baseball's competitive balance have a point: bad baseball teams more commonly remain bad than do bad football teams (or basketball or hockey teams, for that matter). Of course, if you're from Pittsburgh, or Kansas City, or Baltimore, this is hardly news to you.

**Payroll Effects vs. League Effects**

So baseball has a competitive mobility problem. Why? The chart below plots mobility against payroll disparity for each league-year. Overall, there seems to be a negative relationship between mobility and payroll inequality. Looking at each league separately, however, the relationship seems to be much weaker.

Note that the "mobile-equal" quadrant is almost exclusively populated by the NFL. Also note that there are data points that fall into the "equal-immobile" camp, but no data points that fall into an equivalent "unequal-mobile" camp. This indicates that A) payroll equality is at best a necessary but independent insufficient condition of mobility, and that B) just as with win inequality, league effects are at least equally important as payroll effects. Let's check:

IV (Mobility) | Coefficient | Beta | Std. Error | P-value | *NHL Dropped | ||

Payroll Inequality (2yr) | -0.1065 | -0.1316 | 0.0698 | 0.135 | |||

End Season | -0.0002 | -0.0204 | 0.0006 | 0.733 | |||

MLB | -0.0164 | -0.1595 | 0.0089 | 0.071 | |||

NFL | 0.1012 | 0.7819 | 0.0096 | 0.000 | |||

NBA | 0.0189 | 0.1396 | 0.0086 | 0.034 | n = | 46 | |

Y-Intercept | 0.4788 | 1.1171 | 0.671 | Adjusted R^2 = | 0.9010 |

Well, this is interesting. The OLS regression

*does not*find that payroll inequality is a statistically significant driver of competitive mobility when controlling for time or league effects. This could be due to sample size--46 data points is not a lot to go on when testing five variables (even though we were able to find statistical significance between win equality and payroll equality). So while this is interesting in and of itself, let's assume that payroll inequality is significant for the sake of argument.

League effects are stronger, but they are not so disproportionately important in terms of win mobility as in win equality. With the exception of the NFL league effect (roughly six times stronger than payroll), the league effects of the MLB and the NBA are pretty much in line with that of payroll. But this in and of itself is telling. If we assume payroll matters, we can only measure its importance relative to the impact of other variables. As such, the data show that league effects are at least equally strong as payroll effects, and in one case far more powerful.

And if we bring significance back into it, the effect isn't important at all

**League Effect: Short-season Bias**

Which aspects of league "difference" should effect mobility? We must again reconsider short-season bias. Just as the reduced sample size of the number of games played should increase the level of inequality measured, it should also (paradoxically) increase the level of mobility: the minimum, non-zero change in year-over-year win percentages is 0.125 in the NFL, vs. 0.012 in the NBA and NHL and 0.006 for the MLB.

**League Effect: Postseason Barriers**

Consider that 53.3% of all NBA and NHL teams reach the postseason, as compared to 37.5% of all NFL teams and 26.7% of all MLB teams. Gambling to "win today" is a more palatable bet in the NBA and NHL (15:8 odds) and in the NFL (8:3 odds) than in the MLB (15:4 odds),

*ceteris paribus*. Of course

*ceteris*is not

*paribus*, but that's not the point. The point is that differences between the leagues change the strategic setting for, and thus the incentives for, winning during the regular season. Bringing resources back in, a team that played poorly in season

*y*-1 is far more likely to increase spending to win in season

*y*the marginal benefit of each additional win is greater.

**Conclusion**

The theories I posed regarding league effects are only a couple of possibilities. I shall happily entertain objections and suggestions as to where to look for these effects, but that's not the point of this post. The point is that payroll effects are relatively weak--if at all significant--determinants of competitive balance. That said, those who criticize the level of competitive balance in baseball can draw support from these findings. The MLB is certainly a less mobile environment for teams than the NBA, NHL, or especially the NFL, which is a necessary (but insufficient) condition of a competitive balance problem.

*(Photo Credit: Sports Illustrated)*

## 3 comments:

I have a saying that if the data analysis doesn't reflect your real-life experience, then you must be looking at the wrong data. As a fan of a small-market baseball team, I find these kind of statistical analyses frustrating because they only look at "wins" and "payroll" as the measures of primary of interest. However, nobody ever bothers to study or understand the actual experience of what fans go through in reality. Even if you really believe payroll doesn't matter towards "wins", do you really think small market fans like having to lose all their best players during free agency? Do you understand how much it hurts? Do you think fans like having to compete with half the payroll of their big market competitors? Do you think it feels good to have a tiny window to compete before your team is broken up and you have to go through another super-long rebuilding process? How come Yankees fans never have to endure this? Don't you think small market fans would also like to sign some of the top stars in the game once in a while too? I never believed this nonsense that parity and competitive balance should be measured by the number of wins over a certain time span. To me, the experience of treating some fans like kings and treating other fans like dirt is what the issue is really about. If you don't understand the small market fan experience and how demeaning baseball is compared to other sports, you just don't get it. I would really encourage you to look at variables that actually matter to real human beings with real emotions. Maybe then you will understand the issue better.

@Ajay: Let's be clear here. I'm not saying that payroll doesn't have an effect on wins. I'm not even saying that payroll inequality has no effect on competitive balance. And, above all else I'm not saying that there's no competitive balance problem. If you re-read this post, I think you'll find that it's rather conclusive that baseball DOES have the biggest competitive balance problem.

All I'm saying is that payroll disparity is not the most important determinant of competitive imbalance. Competitive imbalance in baseball is most heavily influenced by how the playoffs and the regular season are structured, and that payroll disparity plays a small role, if any.

This is important, because if we want to improve competitive balance in baseball, and payroll disparity is the main issue, then more revenue sharing and salary caps aren't going to help. As you can see, they haven't really made any difference in the NHL and NBA.

So, Ajay, to answer your question, I do feel your pain. But it's important to note that some teams' fans' pain is more because of inept (KC) or greedy (FLA) ownership and front-office management, and how the current CBA actually incentivizes those team's failures. In other words, I don't think we're going to ease your pain with a salary cap--that's all I'm saying here.

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