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Thursday, March 16, 2006

Quantifying Fan Interest, pt. 2

Recently, I posted a small study in which I quantified fan interest by ranking teams based on attendance relative to their city population size. It identified St. Louis as the best baseball town due to their extremely high attendance given their small city size. However, that study had a fundamental flaw. It ignored another major contributor to attendance: the performance of the team. The teams with the most die-hard, loyal fans, will tend to draw high attendance even when the team is doing poorly. Teams with more fickle fans may tend to draw reasonably well when they are winning, but will draw poorly when they struggle. The Cardinals have been a very successful franchise over the past 5 years (not to mention the past 100), so it's very reasonable to ask whether St. Louis draws high attendance because of a special group of fans, or simply because they win. To address this issue, I incorporated team performance into my analysis of attendance, with the ultimate goal of quantifying who has the best fans in baseball.

Team Performance and Attendance

To start, here is the relationship between team wins in '05 and team attendance:

As we can see, there is a positive relationship here. This regression is significant (P=0.005), but the R^2 for the this regression is 0.25, which is lower than in our model of city population size and attendance. It's not bad, but let's see if we can do better.

Looking at the points that fall off of the curve, I noticed a few things: the Giants (SF) and the Dodgers (LAN) had much higher attendance than predicted by their win totals last year. However, last year both teams were uncharacteristically bad, whereas they had both been contenders in previous years. Perhaps we're seeing a carry-over effect from prior years' success? Therefore, I also compared attendance vs. win totals over the past 2, 3, 4, etc, years. Here are the R^2's of those regressions (higher R^2 = better explanatory power = better model):

Runs Total Years R^2
05 0.2541
04-05 0.4024
03-05 0.3958
02-05 0.4030
01-05 0.4022
00-05 0.3851
99-05 0.3748

There was a dramatic boost in the explanatory power of the regression model when I provided the total wins for '04 and '05 to the model, rather than just those from 2005. This model can explain 40% of the variation in attendance, which is higher than our explanatory power using city population size. There was also very slight increase when I included win totals dating back to '02. While essentially equivalent to the '04-'05 data, I decided to use the '02-'05 data going forward a) in order to achieve the best possible fit to the model, and b) because one city behaved very differently depending on which value I used (discussed below). Furthermore, it seems like four years is a good figure that captures the typical perceptions/memory of a baseball fan. For example, Cincinnati has not had a winning season since 2000, and most people (myself, a lifelong fan, included...unfortunately) do not think of them as a winning franchise. Seattle, on the other hand, has suffered through two consecutive miserable seasons, and yet I still think of them as a competitive franchise due to their outstanding run from '00 to '03.

Here is the scatterplot of the '02-'05 win totals vs. attendance:

Note the tighter fit than in the '05-only graph. Also note that it is a nice, linear fit, indicating that an extra win for a good team is worth just about the same as a win for a poor team.

Combining the two variables to measure fan loyalty

There was little correlation between win totals and city population levels (r=0.30, R^2 = 0.09, regression non-significant), so I conducted a multiple regression analysis using both Log(City Population) and '02-'05 Win Totals as predictors of Attendance. Both were significant effects, and the resultant regression equation was:

Attendance = -4,196,660 + 667,280.3*log(City Population) + 8290.499*('02-'05 Wins).

The R^2, 0.60, indicates that this model explains 60% of all variation in attendance last year. This value is up from 0.34 for the city population model alone, and 0.40 for the win totals model alone.

Interestingly, the model predicts an increase of ~8300 fans annually for each win over the past five years. Therefore, improving a team by 10 wins should result in only about ~83,000 more fans attending in a given year. Do that 4 years in a row (for the Reds, this would mean posting about an overall 0.500 record these past 4 years), however, and you're up to 322,000 fans per year. At ~$25/fan, that's $8,300,000--just shy of Adam Dunn's average salary these next two years.

To take it a step further, the predicted attendance difference between teams that post four consecutive 90-win seasons (e.g. the Cardinals) and four consecutive 70-win seasons (e.g. the Reds) is a staggering 663,240 fans, or roughly (at ~$25/person) $16,500,000. It pays to win, especially if you can do so long term.

The Best Baseball Towns

Back to our original question of identifying the best baseball towns, here are the residuals from this analysis, which are simply differences, in terms of number of people, between actual attendance and the attendance predicted by the multiple regression equation:

City Residual
STL 795,733
LAN 581,203
BAL 548,046
SD 477,634
WAS 448,168
SF 423,609
SEA 409,486
NYA 361,515
CHN 309,963
MIL 303,398
DET 246,358
LAA 199,818
CIN 14,751
BOS 4,706
KC -24,986
PIT -58,457
COL -60,019
TEX -67,720
PHI -73,973
NYN -76,210
HOU -165,077
CLE -221,142
ATL -252,879
ARI -412,846
TB -464,567
FLO -486,400
OAK -565,156
MIN -646,616
CHA -663,018
TOR -885,321

[Note that the residuals on the left are represented graphically on the right. The horizontal axis in the graph is just random scatter that I included to make the team names more legible.]

So where are the greatest baseball fans of all? Despite their superb performance over the past few years, St. Louis was the king of baseball towns last year, with almost 800,000 more fans than would be expected for a city of that size and a team that successful. The Dodgers, Orioles, Padres, and Washington Nationals round out the top five franchises in terms of loyalty. It will be interesting to see if the Nationals maintain this level of interest moving forward into their second year.

The worst fan base was that of the Toronto Bluejays, who have been a moderately successful team in an enormous city, and drew almost 900,000 fewer fans than expected. They were followed by the Chicago White Sox, the Minnesota Twins, the Oakland Athletics, and the Florida Marlins. All of these teams have reputations as solid franchises that don't have the fan bases they deserve. The White Sox, having just won their first World Series since 1908, should expect better times ahead. However, the Twins and A's are woefully underattended given their superb record these past years, and the Twins (at least) were candidates for contraction some years ago. The Marlins have been one of the strangest franchises in baseball since they joined the National League, fluctuating from positively horrid to World series champions several times. They are currently fighting for a new stadium South Florida, but it would not be surprising to see them move elsewhere at some point if that effort does not prove tractable. Clearly they deserve better attendance.

I mentioned above that one team behaved rather differently if one used the '04-'05 win data instead of the '02-'05 win data. The team was the Seattle Mariners, who went from superb (4 consecutive 90+ win seasons, including the unbelievable 116-win '01 season) to horrible (63 & 69 wins in '04 and '05) very recently. If one only uses the last two years' wins, Seattle would boast the best fans in baseball. The 4-year data, however, indicates that Seattle Fans are still good, but are apparently still riding the wave of their past success. Nevertheless, one has to wonder how much longer they will tolerate their teams' woes.

How did the Reds do? The Reds have the 2nd-smallest attendance residual (absolute value), indicating that our fans are almost exactly average. We drew 14,751 more fans last year than expected (182 more per home game) for a city our size (Cinci is small) and a team this bad (5 consecutive losing seasons). It's actually pretty good news. We're not Minnesota or Tampa Bay. If the team starts winning, there's reason to expect that attendance will increase in a manner consistent with our team's performance. Here's hoping the momentum that started his offseason with Castellini and Krivsky will carry over into good decisions about the ballclub and a terrific increase in performance over the next 4 years.

Future directions

I have plans to continue this work in a few directions:
  1. The R^2 of 0.60 is decent, but I would like to see if I can increase it further still. I can think of a several other factors that might result an attendance boost: a new stadium, postseason appearances, changes in ownership/front office/management, the signing of a big free agent, etc. The beauty of the regression models is that we can assign actual attendance values to each of these items.
  2. I would also like to partition out the 4-year win totals into separate effects for each season; how valuable was a win in '05 compared to a win in '02?
  3. Finally, I'm interested to see how fan loyalty has changed over the years in different cities. One way to do this would be to plot attendance residuals of teams over time -- say in '05, '00, '95, '90, '85, etc. I would expect to see fan loyalty change over time. This'll require a fair bit of work, but I think it would be fascinating.
Stay tuned to this blog in the coming months for more work on this front, among other things. Thanks for reading. -j