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May 14, 2007
Lies, Damned Lies
Tweaking the Market Size Model
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:
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 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:
Later this week, we'll do some homework for the Florida Marlins, and answer the question: if you build it, will they come?