Brace yourself for a rare feeling, because its time to be proud to be a Royals fan. On the field, the Royals beating up on the Cardinals and chasing the White Sox in a captivating race for fourth place in the AL Central. Off the field, despite poor raw attendance figures, fans are supporting the Royals at the K quite well relative to their AL Central rivals, especially considering market size.
I bring this up, because, as many of you know, I'm spending the summer in Cleveland (city of, even, no suburbs, though I'm literally right on the border of Cleveland and Shaker Heights), where the current drive-time sports radio topic is the Indians and spotty attendance at Jacob's Field.
Consider the per-game attendance figures for the AL Central:
-Detroit: 34,785 per game (40-29)
-ChiSox: 32,133 (29-37)
-Minnesota: 27,969 (34-34)
-Cleveland: 23,550 (41-28)
-Kansas City: 19,017 (29-42)
As alluded to last week, in Nate Silver's study of market size at BP, the Royals ranked dead last in baseball in terms of "attendance sphere" size, i.e. the total population pool which could be expected to randomly attend a game. Here's Silver's explanation:
1. The distance in miles between each county and each major league ballpark was determined using the Haversine formula. Before you ask, I was able to identify the exact geographic coordinates of each major league stadium.
2. This raw distance was adjusted for out-of-state commuters. When I was running some gut-checks of the model, I found that many of the counter-intuitive results involved travel across state lines. The Indians were getting too much credit for southern Michigan, for example. Therefore, each team was assigned to its home state(s); the Royals were given both Kansas and Missouri, and the Nationals were given both Virginia and Maryland in addition to the District. The Blue Jays were assigned to the "state" of Canada. A 10 percent penalty was applied to an out-of-state commuter in a state without a home team; for example, a fan in South Carolina is assigned a 10 percent mileage penalty with respect to his distance to Turner Field. If the commuter comes from a state that does have a home team, a much harsher 50 percent mileage penalty is applied. For example, a fan in Western Massachusetts has a 50 percent penalty assigned to all teams but the Red Sox. I provided for a grace period of 10 miles before any penalties were applied, so that immediate border cities (such as Covington, Kentucky for the Reds) were not affected.
3. The raw distance was further adjusted based on a team's influence, by dividing the mileage by a team's relative influence rating. What this does, effectively, is to expand a team's geographic radius if it has a stronger brand. For example, the Red Sox get to draw attendance from a radius of 252 miles rather than the standard 200, while the Devil Rays are confined to 158 miles.
4. A team's 'Claim Percentage' for a given county is assigned based on the following formula (my apologies if this is starting to sound like Win Shares):
Claim Percentage = ((200 - Adjusted Distance) / 200) ^ 2.41
The "200" number you see in the formula corresponds to a maximum radius of 200 miles from which a team might draw attendance. The 2.41 exponent was chosen because it means that a fan 50 miles away from the ballpark is worth about half as much as fan right next door to the ballpark. Both of these constants are arbitrary, since I am not aware of any empirical research that relates distance from the ballpark to the likelihood of attendance at a baseball game. However, I believe my choices produce results that are fairly intuitive, as reflected in this chart:
Adjusted Distance Claim Percentage
0 100.0%
1 98.8%
5 94.1%
10 88.4%
25 72.5%
50 50.0%
75 32.2%
100 18.8%
150 3.5%
200 0.0%
5. The Claim Percentage is multiplied by the county's population to produce a raw attendance estimate.
- The raw attendance estimate is adjusted for dominance. Typically, baseball allegiance in any given area involves a tipping point of one kind or another; the more popular team or teams tend to crowd out all others, since fans of a secondary team will find that they can't find their team's games on TV, will have nobody to talk about the team with at the water cooler, and so forth. The mathematics of the dominance adjustment are a bit convoluted, but the basic idea is to reassign fans from one team to another by squaring the raw attendance estimates. So a team with a natural 3:2 advantage based on geography alone instead winds up at a 9:4 advantage.
- Finally, we check to see whether the raw attendance estimates between all teams in any given county add up to more than 150 percent of that county's population. If so, the estimates are prorated downward to the 150 percent cap. Effectively, this means that in a market with two identical clubs, each team is assigned a maximum of 75 percent of its potential fan base. Once again, the selection of this constant is somewhat arbitrary.
Once again, here are the per-game attendance figures for the AL Central, with win-loss and Attendance Market Size listed:
-Detroit: 34,785 per game; 40-29 record; 5.2 M. Attendance Market
-ChiSox: 32,133; 29-37; 7.3 M.
-Minnesota: 27,969; 34-34; 3.0 M.
-Cleveland: 23,550; 41-28; 3.8 M.
-Kansas City: 19,017; 29-42; 1.9 M.
The Royals have the smallest population base, in terms of potential ticket buyers, in the game, and its not particularly close. The next smallest markets are Milwaukee (2.43 M.) and Pittsburgh (2.48 M.). The Royals own the only base under 2.0 million, and are one of only five teams with a market base under 3.0 million.
Which is a long way of saying 19,017 is not bad, potentially even pretty derned good. Of course, still nowhere near the loyalty and dedication demonstrated by the "best fans in baseball", to say nothing of our obvious intelligence gap, but, thats another matter.
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Ohh, tonight's game? Yea. Its the Self-Appointed Team Effort Inspector (2-2, 8.54 ERA) against, well... is it still Kip Wells?