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May 14, 2007

Lies, Damned Lies

Tweaking the Market Size Model

by Nate Silver

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The market size model that I developed in my last series of columns triggered more reader response than just about anything I've written for Baseball Prospectus. Although I wasn't able to respond to many of those e-mails individually, they did provide a number of helpful suggestions for improving the model. That's what today's column is all about.

Almost all of the correspondence invariably fell into one of four categories:

  1. The largest batch of e-mails was from people reporting that I had mischaracterized their market. For example, Vancouver seems to be as much a Blue Jay town as it is a Mariner town, while Des Monies, Iowa belongs to the Cubs rather than the Twins (or Cardinals, or Royals, or Brewers). What I don't want to do is start assigning cities to major league teams on a case-by-case basis. The whole point of this exercise is to be systematic. However, to the extent that I can make systematic improvements that happen to dovetail with the anecdotal evidence that you guys armed me with, those reports are potentially valuable.
  2. Another theme is the increasing availability of local baseball broadcasts on television. A lot of readers wrote in to tell me that they had access to two or three or even four "local" baseball teams, not counting national broadcasts or superstations. I have therefore toned down some of the winner-take-all provisions of the media model, which may have been based on an outmoded notion of a 36-channel cable lineup.
  3. Next, there were people reporting that while I might have assigned their market to the proper team, I had not assigned a large enough fraction of it. For example, several people saw my map of Red Sox and Yankees territory, and wondered why the Red Sox hadn't been given more credit for Maine. In this case, I don't have an adjustment to make-just a response. It's important to remember that while there are few physical barriers with respect to a team's media market, the same is not true for attendance. Maine might be part of Red Sox Nation, but unless you live in the Portland area, making a day trip to Fenway Park is a bit of a tall order. Thus, while the Red Sox were given credit for only 15 percent of Maine's population in the attendance model (which is what was reflected in the Saux-Yanks map), they got credit for 63 percent of the state from a TV standpoint. These sorts of ambiguities are exactly why it was important to create separate models for attendance and TV.
  4. Finally, there were a couple of specific bells and whistles that were proposed for improving the model, one of which was to account for minor league affiliates, and the other of which was to account for traffic. I was able to incorporate adjustments for each of these parameters, as we'll discuss below.

The Minor League Adjustment

What a minor league affiliate does, in essence, is to provide a localized branding benefit to its major league parent. Since our model is already equipped to account for the influence of a team's brand, we can theoretically just extend that assumption to develop a location-specific branding bonus in areas where one of its minor league clubs is present.

This turns out to be easier to conceive than do, as the mechanics of the model require us to balance a number of different factors. The first is the length of the association between the minor league city and its major league parent. Even though the Yankees now have their Triple-A club in Scranton, it's the Phillies who probably deserve the bulk of the credit for their 18-year relationship with the Red Barons. The Indians should not get as much credit for their 13-year affair with Buffalo as the Royals do for their 39-year marriage to Omaha.

Therefore, what I did was to develop a formula that accounts for the length of the association between the major league and minor league cities, as well as how recently the relationship has ended (if it is no longer intact). Teams get partial credit for any Triple-A or Double-A presence they've had in a city within the past 25 years, though the bonus is generally very small unless the team has maintained a continuous presence in that city for a decade or more. Specifically, the branding benefit was defined by the following formula...

Branding Bonus = [((((25-(2007-LastYear))/25)^2)*(LastYear-FirstYear+1))/25] * Level + 1

…where 'FirstYear' represents the first year in which a minor league affiliate played in a particular city, and 'LastYear' the most recent season (generally 2007). 'Level' is a dummy variable that is set at 1 for a Triple-A team and 0.6 for a Double-A team; I did not worry about the lower minor league classifications. The formula is designed such that a team that has had a continuous Triple-A presence in a city for exactly 25 years gets a branding bonus of 2.0; the smallest possible bonus is 1.0 (equivalent to no bonus at all). Some specific examples:

MLB  City                Level  Tenure   Bonus
ATL  Richmond, VA        AAA  1966-2007  2.68
KCA  Omaha, NE           AAA  1969-2007  2.56
BOS  Pawtucket, RI       AAA  1973-2007  2.40
TEX  Oklahoma City, OK   AAA  1983-2007  2.00
PHI  Scranton, PA        AAA  1989-2006  1.66
LAN  Albuquerque, NM     AAA  1972-2000  1.60
CLE  Buffalo, NY         AAA  1995-2007  1.52
CIN  Chattanooga, TN     AA   1988-2007  1.48
SLN  Little Rock, AR     AA   1966-2000  1.43
LAN  Las Vegas, NV       AAA  2001-2007  1.28
COL  Tulsa, OK           AA   2003-2007  1.12
NYA  Scranton, PA        AAA  2007-2007  1.04

This branding bonus was applied to all counties within a 35-mile radius of the minor league city, with a linear adjustment based on the distance between the county and the city. For example, a county whose geographic center is 25 miles away from the minor league city would get credit for about 30 percent (10/35) of the minor league branding bonus. This bonus was then multiplied by a team's overall influence score. For example, in Richmond, Virgina proper, the Braves get their 1.07 national influence bonus times their 2.68 localized bonus, for a total bonus of 2.87. In other words, Richmond is treated as though it's nearly three times closer to Atlanta than it is in reality.

This branding bonus only does you any good, however, if it puts the city "close" enough to the major league parent to expand the virtual borders of the market. Although Baltimore had a long association with Rochester, New York for its Triple-A affliliate (1961-2002), this probably did little good for the Orioles' major league brand; Rochester is simply too far away from Maryland. The model is able to account for these sorts of considerations organically.

Here, then, are the teams whose minor league affiliates provided them with the largest bonuses to their attendance markets:


Top Minor League Attendance Bonuses
 1. Red Sox   326,772  Pawtucket and Portland expand Boston's virtual borders.
 2. Phillies  179,348  Still getting lots of credit for Scranton; Reading helps.
 3. Orioles   149,828  Bowie protects Southern Maryland from the Nationals.
 4. A's       106,699  The River Cats help them recruit fans from Sacramento.
 5. Rangers   101,152  Oklahoma City is close enough to provide some gain.
 6. Tigers     92,292  Toledo expands their influence in Northwest Ohio.
 7. Rockies    87,316  Colorado Springs works analogously to Oklahoma City.
 8. D'Backs    73,362  …as does Tucson for the Diamondbacks.
 9. Blue Jays  59,972  Syracuse gives them a competitive position in Northern NY.
10. Braves     56,827  Richmond is still pretty far away; most of this is from Double-A.

The numbers on the TV side are a bit different. Although the Pawtucket and Portland affiliates might encourage a few more fans to drive to Red Sox games, they help less with TV since the Red Sox already dominate those areas.


Top Minor League TV Bonuses
 1. Dodgers     524,370  They steal Las Vegas from the Angels.
 2. Mets        502,361  Binghamton helps upstate, Norfolk down the seaboard.
 3. Blue Jays   303,627  Syracuse, again.
 4. Rangers     287,099  Oklahoma City, again.
 5. A's         247,865  Sacramento, again.
 6. Cubs        218,209  Des Moines doesn't help much with attendance, but does with TV.
 7. Phillies    205,143  Scranton, again.
 8. Cardinals   179,235  Enhanced penetration into Arkansas, Tennessee.
 9. Royals      133,183  Omaha and Wichita aren't big prizes, but they help.
10. Astros      105,132  Round Rock is already helping in the Austin area.

Note that all of these are net numbers. A handful of teams actually lose market share as a result of the minor league adjustment, because they get more fans poached by a competing team's affiliates than they make up with their own. The Dodgers' gain in Las Vegas, for example, is the Angels' loss, particularly as the Angels have never had their top affiliates within shouting distance of Orange County. Fresno isn't a bad place for the Giants' Triple-A affiliate, but they lose more ground in Sacramento than they make up there.

If the model is correct, then the optimal distance for a minor league affiliate seems to be in the range of 250 miles. Las Vegas is 270 miles from Los Angeles, for example; Oklahoma City is 210 miles from Dallas, and Syracuse is 245 miles from Toronto. Affiliates that are much closer than that, like the Pawtucket Red Sox, may produce gains at the box office, but probably do not do much to expand a team's media market since the team usually already "owns" the area. Conversely, affiliates that are much beyond a radius of 350-400 miles are usually too far away to provide for much synergy. It helps greatly, of course, to gain ground in a market that might be competitive between two or more clubs (Sacramento, Las Vegas, Scranton, etc), and to locate your minor league affiliates in cities with larger populations.

There are other reasons to select a minor league affiliate apart from its direct influence on the major league brand, but a fair number of affiliate placements seem pretty illogical, and you can sometimes identify multi-team 'trades' that would seem to benefit all clubs involved. For example:

   White Sox:  Charlotte    --> Indianapolis
   Pirates:    Indianapolis --> Buffalo
   Indians:    Buffalo      --> Columbus
   Nationals:  Columbus     -->  Charlotte

The Travel Time Adjustment

What the attendance model is really attempting to estimate is the utility function for millions of individual fans. Say you'd like to go to a Yankees game. Are you willing to endure a half-hour commute to do so? An hour-long commute? A two-hour commute? The as-the-crow-flies distance between two cities can provide some rough estimate of the commute time, but we could do a bit better by accounting for prevailing traffic patterns.

Unfortunately, there is no centralized resource that provides the transit times between any two given cities. (Well, there's MapQuest, but that data isn't available in analysis-friendly form.) We can come to some reasonable approximations, however, using the Census Bureau's data on average commute times in the 233 largest counties in the United States. The average commute to work originating from Queens County, New York, for example, takes 41.7 minutes, as compared with 21.1 minutes in Milwaukee County, Wisconsin.

I translated the average commute times (ACTs) into miles per hour by using the following formula:

AVERAGE MPH: (17.5 / ACT) * 60

Although the transformation between ACT and MPH is not quite as straightforward as the formula makes it out to be, we generally wind up with intuitive results. The shortest average commute times in the country are on the order of 17.5 minutes; the formula assumes that this translates into a typical freeway speed of 60 miles per hour. By comparison, the formula returns an average commute of 50 MPH in Milwaukee, 40 MPH in Houston, and 25 MPH in New York.

Of course, if you're considering making the trip from Albany to New York to see a Yankees game, you do not have to deal with New York City traffic the entire way; most of the time, you're having an easy go of things on the Thruway. The traffic adjustment, therefore, was applied only to the last 20 miles of the trip into the major league city. In addition, a traffic adjustment was made for the first 20 miles of the outbound trip from the county of origin, based on the origin county's average commute time (if the Census Bureau did not provide an average commute time for the origin county, I assumed it to be equal to 90 percent of the average statewide commute time). All travel in between the city centers is assumed to take place at the 60 MPH freeway speed. The average MPH from various places into Yankee Stadium, then, works out to the following:

   Bergen County, NJ        25.7 MPH
   Suffolk County, NY       35.2 MPH
   Philadelphia County, PA  46.4 MPH
   Albany County, NY        53.9 MPH
   Los Angeles County, CA   59.5 MPH

The model assumes that 50 MPH represents the "break-even" commute speed; anything faster than that results in a bonus, and anything slower than that, a penalty. Note that the travel time adjustment impacts the attendance market only; it has no effect on a team's media market.

As you'd anticipate, the travel time adjustment tends to operate as a great equalizer, harming the clubs in the largest cities:


Teams Most Hurt by Travel Time Adjustment
  1. Mets       1,938,730
  2. Yankees      900,686
  3. Dodgers      884,948
  4. Angels       684,489
  5. Orioles      614,032
  6. Nats         489,364
  7. Phillies     459,925
  8. Cubs         393,753
  9. White Sox    372,505
 10. Giants       283,213

It's interesting that the Mets seem to be so much more impacted by New York traffic than the Yankees, but this is for a couple of different reasons. First, commuting into Queens is more cumbersome than commuting into the Bronx for the vast majority of the team's potential audiences. Secondly, the Yankees have a stronger influence rating, which helps provide a buffer against the traffic problems; you might go out of your way to see a game at Yankee Stadium, but probably not one at Shea.


Teams Most Helped by Travel Time Adjustment
  1. Reds        512,531
  2. Indians     386,545
  3. Cardinals   261,990
  4. Brewers     239,277
  5. Braves      178,551
  6. Tigers      176,309
  7. Padres      129,380
  8. Twins        88,708
  9. Royals       87,504
 10. Rockies      19,396

The Midwest generally has advantageous traffic patterns, both because it presents the driver with few geographic obstacles, and because it is not growing terribly quickly, meaning that there's been plenty of time for the supply of freeways to catch up with the demand. This puts markets like Columbus and Indianapolis and Louisville more in play than they would be otherwise.

Other Adjustments and Revised Results

In addition to the minor league and travel time adjustments, I made the following tweaks based on user feedback:

  • The out-of-state competition penalties were cut in half; that is, they were reduced to a 25 percent penalty for the attendance model and a 50 percent penalty for the TV model. Naturally, this provided the most benefit to teams such as the Cardinals, who are close to a state boundary.
  • The requirement that teams have at least a 50 percent natural claim on a county's TV market before getting credit for it was dropped. Instead, the "dominance exponent" for TV audience was increased from 2.0 to 2.5. This allows teams to compete more organically for their share of the TV audience.
  • The Nationals are no longer given credit for Virginia or Maryland as "home" states.
  • Tijuana, Mexico was included in the model, to the benefit of the Padres.
  • Although out-of-state penalties were reduced, out-of-country penalties were increased. In particular, out-of-country destinations in Canada and Mexico are now assigned a 100 percent penalty on their mileage, plus an additional 25-mile "border crossing" penalty.

The cumulative result of all these fixes was as follows:


Team  Attendance   Rank     Rel         TV/Media      Rank     Rel
ARI    3,803,042    21       63         5,504,149      26       56
ATL    5,508,612    14       92        16,066,685       3      162
BAL    5,745,887    12       96         9,537,244      16       96
BOS    7,085,546     8      118        11,330,286       8      114
CHA    7,485,869     7      125        10,186,762      11      103
CHN    7,741,244     6      129        12,025,789       7      121
CIN    3,697,207    22       62         9,961,279      13      100
CLE    3,983,090    20       66         8,132,574      21       82
COL    2,868,147    27       48         4,570,488      30       46
DET    5,419,662    15       90         9,562,464      15       96
FLO    4,226,982    18       70         6,166,678      24       62
HOU    5,012,076    16       84        10,204,092      10      103
KCA    1,941,956    30       32         4,597,099      29       46
LAA   11,149,730     4      186        13,286,360       5      134
LAN   11,869,232     3      198        14,630,751       4      148
MIL    2,648,677    29       44         5,779,013      25       58
MIN    3,034,112    25       51         5,502,151      27       55
NYA   18,310,500     1      305        24,167,393       1      244
NYN   14,437,748     2      241        17,509,149       2      177
OAK    6,218,957    10      104         9,111,470      18       92
PHI    8,028,349     5      134        12,284,832       6      124
PIT    2,749,402    28       46         5,470,016      28       55
SDN    4,197,822    19       70         7,340,168      23       74
SEA    3,425,763    23       57         8,168,161      20       82
SFN    5,860,148    11       98         9,512,707      17       96
SLN    3,134,013    24       52         9,082,314      19       92
TBA    2,999,411    26       50         7,378,965      22       74
TEX    4,976,888    17       83         9,652,074      14       97
TOR    6,835,975     9      114        10,597,278       9      107
WAS    5,521,128    13       92        10,100,942      12      102
TOT  179,917,176                      297,419,333

In general, the relative ranking of the teams was not altered very much, but there are a handful of material exceptions:

  • Angels. Relative TV share reduced to 134 from 155. Losing Las Vegas to the Dodgers harms them, as does providing for more competition with the Padres in Orange County.
  • Braves. Relative TV share reduced to 162 from 176. They actually gained a little bit of TV audience, but since the Braves were already doing so well in that department, other teams gained more as we liberalized out-of-state and competition rules.
  • Brewers. Relative TV share increased to 58 from 44. They're picking up a few more TV households in Northeast Illinois; I'm not 100 percent sure I like this result.
  • Giants. Relative TV share reduced to 96 from 109, as they lose influence in Sacramento to the A's.
  • Indians. Relative TV share increased to 82 from 65. They're picking up more out-of-state TV audience in Pennsylvania and Michigan.
  • Mariners. Relative TV share reduced to 82 from 92 after losing some credit for British Columbia.
  • Nationals. Relative attendance share reduced to 92 from 101; relative TV share reduced to 102 from 116. Removing the protections they had on Maryland and Virginia harms them significantly, as does their lack of synergy with their minor league affiliates.
  • Orioles. Relative attendance share increased to 96 from 90; relative TV share increased to 96 from 79. This is the flip side of the Nationals' case.
  • Padres. Relative attendance share increased to 70 from 59; relative TV share increased to 74 from 53. This is mostly Tijuana, but they also get to compete more directly with the Angels and the Dodgers for their media market.
  • Pirates. Relative TV share increased to 55 from 40. Still not doing well, but additional out-of-state audience in Ohio and New York helps them some.
  • White Sox. Relative TV share increased to 103 from 92. Eliminating the winner-take-all provisions of the TV model helps prevent the Cubs from shutting them out.

Later this week, we'll do some homework for the Florida Marlins, and answer the question: if you build it, will they come?

Nate Silver is an author of Baseball Prospectus. 
Click here to see Nate's other articles. You can contact Nate by clicking here

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