Behind the ScoreboardApril 13, 2010
Structural Unfairness In Baseball's Divisions
By Sky Andrecheck

A couple of weeks ago, I had planned on penning an article for SI.com on MLB's wild-haired proposal to reshuffle the divisions in order to make them more equitable. My thesis was to be that there was little reason to do so. Teams ebb and flow and the shuffling is unnecessary. The record of AL East teams against the other divisions is barely over .500 since 1996, so the AL East isn't that much of a powerhouse anyway. To boot, when looking at 90-win teams that missed the playoffs, the AL East housed fewer of these teams than either of the other two AL divisions. I'm glad I didn't write that article, because I'd have been wrong. Here, I'll show why.

Let it be known, I still think the proposal is a hare-brained scheme. Swapping strong AL East teams with weaker ones would be tantamount to just handing the flag to Boston and New York. Additionally it wouldn't be fair to those "weak" AL teams - after all, maybe they'd surprise people and make a run. Plus the whole thing just seems jury-rigged and unseemly. Still, there is a real question of what structural advantages and disadvantages are built into the current system.

The Effect of Market Size on Winning

Certainly some teams figure to be better than others long-term. Market forces are a very real phenomenon, and the fact is that big-markets and owners with deep pockets can have a strong effect on a team's performance. How those big-market teams are distributed among the divisions can have a strong impact on the game.

As a first step, I ranked all 30 teams based upon "market size", and when I mean market size, I mean not only the size of the market, but also things like ownership's willing to spend money, etc. This was somewhat subjective, however I think my ordering was reasonable. I then assigned each team a market "value" according to the normal distribution, so teams like the Dodgers and Yankees got the highest scores, and teams like the Rays and Pirates got the lowest. I then did a regression to predict WPCT (data pulled from 1995-2009) from this market size variable. As expected, the two were significantly correlated. The predicted WPCT for the biggest team (the Yankees), was .558. That translates to about 90 wins, which I think is a pretty good over-under for a future undetermined future Yankees team. The market size advantage drops off quickly after that. The Red Sox have an average WPCT of .537, translating to 87 wins. Meanwhile, most teams are clustered close to .500. As you can see, market size matters but doesn't hand a team anything. Overall, the WPCT's predicted from market size had a standard deviation of .027.

True Talent

Now, the standard deviation of team WPCT as a whole since 1996 has been .072. The factors adding up to this .072 SD can be described in the following equation:

Total Variance = (Between Franchise Variance Due to Market Size) + (Within Franchise Variance Due to Other Factors) + (Team Variance Due to Luck)

The "Other Factors" translates to teams' ebb and flow of talent - sometimes the same franchise will produce a good team, and sometimes it will produce a bad team. Since we know all of the other variables except this one, we can easily solve for it and we get the following values:

Total SD = .072
Market Size SD = .027
Within Team SD = .054
Luck SD = .039

And it all adds up: (.072)^2 = (.027)^2 + (.054)^2 + (.039)^2

Knowing all of the factors that go into a team's performance, I set up a simulation to estimate the probabilities of each team making the playoffs. The simulation was set up to play a balanced schedule against each of the other teams in the league, plus a handful of "interleague" games against a .500 opponent (I didn't have time to program in the unbalanced schedule unfortunately, although I think this is a relatively small issue). So, how much structural disparity is there in baseball? Are teams like the Rays really at a huge disadvantage due to playing in the AL East?

Long Term Playoff Probabilities

The following chart shows what happens in the simulation:

divisions.PNG

Indeed, the Rays are at the biggest disadvantage of any team in baseball. As one of baseball's smallest market teams, and in one of baseball's toughest divisions, they have just a 7% chance to make the playoffs. To clarify, these percentages are for some theoretical year in the future, NOT taking into account the personnel currently on the club, the quality of the management, etc. The team with the biggest advantage is the Yankees, who have a 57% chance to make the playoffs in any given year. Of course, these numbers are quite dependent on the market size ratings I assigned teams earlier. And, my guesses aren't exactly the gold standard.

Additionally, it's not Bud Selig's fault if the Rays and Pirates are small market clubs. A large part of the reason for the small probability for teams like the Rays is due to their own small-market nature. That's useful to know, but the impetus of the piece was whether the divisions themselves were unfair to certain teams.

Playoff Probabilities Given an Average Team

To take the nature of the particular team out of it, I changed the team in question's long-term average WPCT to .500. For instance, if the Rays were not small market, and instead had an expected WPCT of .500, how often would they make the playoffs? And is that probability higher or lower than it would be in other divisions? Below is a chart showing the probability of making the playoffs, assuming that the target team has an average WPCT of .500.

divisions2.PNG

As it turns out, the Rays are still getting the shortest stick in baseball. Even assuming they have no market disadvantages (or advantages), they have just a 20% probability of making the playoffs in a given year. How does this compare to other teams? The most favorable structural advantage goes to the Los Angeles Angels. Assuming no market advantages, their probability of making the playoffs is 31%. That means that just due to their competition, the Angels will make the playoffs three times for every two times that Tampa makes the playoffs. Not surprisingly, besting the Yankees, Red Sox, Orioles, and Blue Jays is tougher than beating the Rangers, Mariners, and A's. For one, it's easier to beat three other teams than four. And for another, the Red Sox and Yankees are usually tougher to beat than any of the other AL West teams. Those are observations any fan could make, but the effect on the probability of winning is quantified here.

The rest of the AL West is also substantially easier than the AL East. Oakland has a 25% chance of making the playoffs, while the Mariners and Rangers push 30%.

Additionally, the AL Central is a great place to call home. Again, assuming no market advantages or disadvantages for the target team, each team has a 28%-30% chance of making the playoffs. Again, this is a far cry from the Rays' 20%.

How about the Yankees themselves? Again, making their average ability equal to .500, they figure to make the playoffs 26% of the time. These odds are higher than that of the Rays (because they don't have to face a powerhouse Yankee team), but still lower than any AL Central team or most of the AL West. The AL East is tough even for the big dogs.

Now let's move over to the National League. The first thing to notice is that it's generally tougher to win in the NL than the AL. This makes sense because there are more teams to beat in the NL, but the same number of playoff spots. Many of the teams approach the Rays' probability of winning. In the NL East, the Marlins have a 21% chance of making the playoffs, in the NL Central the Pirates have a 22% chance of winning, and in the NL West, the Padres have a 21% chance of winning. However, there is not quite as much disparity among the larger market clubs. Of the large market players, the Cubs have just a 26% chance to make the playoffs, while the Mets have a 25% chance, and the Dodgers have a 29% chance. This is in contrast to the AL, where a number of teams have probabilities approaching 30%. A summary of the average probability of making the playoffs in each division is below.

divisions3.PNG

Conclusion

So what's the conclusion? Yes, some teams face significantly higher hurdles than others. It's not just the Rays that face the problem, but many other National League clubs as well. Paradoxically, because they don't have to play themselves, the large market teams face an easier schedule than their small market counterparts. Situations like these create the imbalances we see here.

The AL East is indeed a tough division, but it's actually about the same toughness as the NL East. It's actually the AL Central and the AL West that are the outliers, in that they are easier divisions than the rest of baseball. If MLB is keen on evening that up, one potential solution is to move Toronto to the AL Central and the Twins to the AL West. That would make the AL East a four-team division and hence easier to win, would toughen the AL Central by adding the Blue Jays instead of the Twins, and would toughen the AL West by adding a fifth team. The NL's division imbalance is solved nicely by having the smaller market teams populate the NL Central. The fact that it has six teams counteracts the fact that the teams are likely to be of a little lower quality, and hence the NL Central is about as easy to win as the West or East.

Is the model perfect? No, because it's difficult to estimate each team's average long-term WPCT. Still, the underlying conclusions, especially regarding which divisions are easiest or hardest, should hold. The teams from the AL East have a legitimate beef, especially the Rays. However, compared to other AL divisions, the National League is also getting a raw deal. These types of inequities are part of the game, but they should be minimized if possible. With these numbers, it hopefully be more clear on how large these inequities really are. Whether baseball will do something about it remains to be seen.

Comments

I would swap Washington and Tampa -- according to your rankings, the former's demographics are better suited for competing in the AL East. You would also have two new natural intra-division rivalries, which might spark greater fan interest in each of the four cities.

I've been using a qualitative version of this to explain to people why it's wrong to make it out that the Red Sox are one of baseball's two superpowers.

Although the Sox do have an edge for the WC, they will always have a much bigger disadvantage than teams like the Angels for making the playoffs due to being in the same division as the Yankees.

This is not meant as a "woe is me" (as the other AL East teams have it far worse), but to make it out like the Red Sox are as "bad/evil" as the Yankees is unfair. To have any shot at consistently competing in the AL East, you have to spend at least as much as most any other team, after the Yankees, and that's what the Red Sox do.

Thanks for the enlightening post.

I'd still like to see 5 teams in every division; for no other reason than it just seems silly to not have symmetry there.

Move Houston to the NL West and bring one of the Rockies/Diamondbacks/Padres into the AL West. I'd vote for the Rockies.

Heck, I'd contract two teams and go with four seven-team divisions, with two division winners and two wild-cards. If one division really was stronger than the other, then it would get both WC slots for that league.

I would question the implied assumption that, in a perfect world, all teams should have the exact same chance of winning over the long term. I think the game is better, and greater "equity" obtains, when larger-market teams do, in fact, enjoy a competitive edge. And that's because larger-market teams, by definition, represent a larger share of the fan base. I think the NYs and LAs and Chicagos should win the WS more frequently than, for example, Pittsburgh or Milwaukee, because the latter teams just don't have nearly as many fans to please.

For the poster who wants to see 5 teams in every division, with 3 divisions in each league this can't happen. You need to have an even number of teams in each division (14/16) which will leave one division with either 6 teams (NL Central) or 4 (AL West). If you split 15/15 between AL and NL, you'd have a team with no team to play every day (with the exception of interleague play)

"As a first step, I ranked all 30 teams based upon "market size", and when I mean market size, I mean not only the size of the market, but also things like ownership's willing to spend money, etc."// This is where I disagree. There is a difference between how much a team spends, a function of its management, and how much a team has to spend, a function of its revenue. They are linked in that the latter puts a limit on the former, and a successful team gets more revenue, but a "small market" team that is "small market" due to the cheapness or incompetence of the people who run the team due not have an inherent disadvantage. And if they do, a mechanism for replacing cheap or incompetent owners would accomplish more in bringing parity than revenue sharing.

Since the Red Sox have been competing fairly successfully against the Yankees for at least a decade, can we assume that any team based in a metropolitan area with a population and income at least equal to that of Boston is competitive? This would leave very few genuine small market teams. And maybe the league should be looking at contraction and relocation with the goal of making sure that each franchise has a Boston, or at least St. Louis, sized base. Take Toronto. This is one of the wealthiest cities in North America, it has a larger population than most cities in the US, and the Blue Jays can market themselves as Canada's team in the MLB. They won back to back world championships in the 1990s. What is wrong with this team that it can't compete with the Yankees and has to move to the AL Central? Since 1995, American League teams that have given the Yankees fits have been based out of Boston, Baltimore, Cleveland, Los Angeles, and Seattle. I would argue that the what the Yankees model does is to allow them to compete every year, since they can bury their mistakes and haven't had to rebuild since the 1980s meltdown. But in any given year they are beatable and have been beaten.

"For the poster who wants to see 5 teams in every division, with 3 divisions in each league this can't happen. You need to have an even number of teams in each division (14/16) which will leave one division with either 6 teams (NL Central) or 4 (AL West). If you split 15/15 between AL and NL, you'd have a team with no team to play every day (with the exception of interleague play)"/// I never understood this argument. Since not all the teams play every day, teams have all sorts of off days and travel days under the current schedule, what is the problem with just scheduling an off day for every fifth team? You don't even have to do this all the time since interdivisional games exist too.

I also agree with BD's comment in that parity is overrated. Imagine a season where all thirty teams won exactly 81 games. Aesthetically, you want some dominant teams that casual fans can root for or against, and yes its probably better that much of the time these come from the places where most people live. There is merit in some of the proposals above to put Tampa Bay in the AL Central, the Twins in the AL West, and putting either the Rockies or Brewers in the AL, but because there are arguments for them other than encouraging parity. Sorry for the multiple posts, I still can't get paragraphs to work.

"For the poster who wants to see 5 teams in every division, with 3 divisions in each league this can't happen. You need to have an even number of teams in each division (14/16) which will leave one division with either 6 teams (NL Central) or 4 (AL West). If you split 15/15 between AL and NL, you'd have a team with no team to play every day (with the exception of interleague play)"/// I never understood this argument. Since not all the teams play every day, teams have all sorts of off days and travel days under the current schedule, what is the problem with just scheduling an off day for every fifth team? You don't even have to do this all the time since interdivisional games exist too.
-----------------------------------------------
Ed, what about weekends? Every team plays Friday, Saturday, and Sunday, but with 15 teams in each league you would need to either have an interleague series every weekend or have a team off on a weekend day. This would lead to lost revenue (I have no evidence to back this, but I would assume that weekend games are more profitable than weekday games, and I am sure this would be easy to prove/disprove)

Well, each team would then be giving up one of fifteen Fri-Sun games. That is one such game per five weeks, or about 5-6 per year. And of the 5-6, only half would be "missed" home weekend games, so were really talking lost revenue on 2-3 games per season.

From 2000 to 2008, the average team had 23% better attendance on Fri-Sun games than Mon-Thu. Lets say the average team also charges more for weekend tickets [or perhaps just has less low $$$ promotions] and lets bring it up to 40%. A team with $75M at the gate would then be looking at about $1.1M per weekend game and $787k from weekdays. Take away 2-3 of those weekend games and make them weekday games and we're looking at a loss of about $630k-$945k for the season.

Throwing in alot of assumptions [and using Forbes gate estimates), here's what I come up with, per three WE games lost by team:

NYY -$2.3M ($217M)
LAD -$1.6M ($115M)
NYM -$1.5M ($144M)
SDP -$1.2M ($67M)
BOS -$1.1M ($176M)
BAL -$1.1M ($47M)
CHN -$1.1M ($128M)
SEA -$1.0M ($60M)
STL -$1.0M ($92M)
HOU -$990k ($78M)
PHI -$960k ($103M)
OAK -$870k ($43M)
ANA -$850k ($72M)
CHW -$840k ($71M)
DET -$820k ($75M)
ATL -$780k ($44M)
SFG -$780k ($78M)
CLE -$760k ($52M)
WAS -$760k ($65M)
CIN -$740k ($45M)
TEX -$740k ($36M)
MIL -$690k ($61M)
ARI -$650k ($47M)
MIN -$630k ($44M)
PIT -$610k ($26M)
COL -$590k ($53M)
TOR -$520k ($52M)
KCR -$470k ($27M)
TBR -$450k ($40M)
FLA -$450k ($22M)

the numbers in parens are the 2008 gate estimates from Forbes, so some teams are losing a bit higher a percentage of their gate than others:

PIT -2.4%
BAL -2.3%
TEX -2.1%
FLA -2.1%
OAK -2.0%
...
BOS -0.6%
CHN -0.9%
PHI -0.9%
TOR -1.0%
SFG -1.0%
NYM -1.0%

Ed, how does this work during the start of the season? If each team plays a three game series to start the year we are going to have one team in each league that doesn't play for the first 3/4 days. And you cannot have interleague play the first week of the season.

I don't see these problems as insurmountable. With the lost revenue, MLB must strike a balance between maximizing short term revenue, and putting out a high quality product that will generate longer term returns. Otherwise why not have 180 regular season games, to generate revenue from the additional 18 games? Personally I would like to see a return to the 154 game season. Same with the three game series to start the season, OK one team in each league will start the season three days later. Of course the season could start with one standalone game, then move into a three game series.

I've always thought the NFL had the most interesting scheduling.

The better you do, the tougher opponents you play next season.

I din't say best, i said interestin.

Cuz this does let a team who had a lousy record last year pile up wins against a weak schedule. If they're better than they were.

I wonder how the numbers would crunch on that.

Since there are 5 teams per division, and at least one team per year has to make the playoffs. that's gives the Rays no less than 20% of a chance every season.

Since the wild card has historically come out of the Eastern Divison, that actually increases their chance.

Regarding an odd number of teams in a league: without reducing the number of games in a season or extending the season, teams get about 4 days off a month, used as travel days (and Sunday evening used as another source of travel time). Assuming the usual 3-game series, a team would lose a couple of travel days when it was its turn to sit out, leading to travel problems for a couple of series. Plus logistically it's much easier to work out a travel schedule when everyone has the same day off.

If all the teams moved to the same area, eliminating travel issues, or the number of games per week were reduced, then it could be done; otherwise, an even number of teams is needed for each pool of competing teams.