April 5, 2011

The BP Wayback Machine

Snowbound Schedule

by Nate Silver

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While looking toward the future with our comprehensive slate of current content, we'd also like to recognize our rich past by drawing upon our extensive online archive of work dating back to 1997. In an effort to highlight the best of what's gone before, we'll be bringing you a weekly blast from BP's past, introducing or re-introducing you to some of the most informative and entertaining authors who have passed through our virtual halls. If you have fond recollections of a BP piece that you'd like to nominate for re-exposure to a wider audience, send us your suggestion.

As we welcome another stretch of cold-weather baseball and its attendant scheduling concerns, here's another look at Nate Silver's statistical take on the subject in a "Lies, Damned Lies" column from April 13, 2007.

Let’s face it: we live in a society that is reactive rather than proactive. In spite of years of warning to the contrary, it took a storm of epic proportions to make us recognize that New Orleans was a disaster waiting to happen. Airport security seems preoccupied with the question of what the terrorists thought of last time, rather than what they’re going to think of next. Less importantly but closer to home, it was only when the All-Star game ended in a tie that we came to recognize that such an outcome was probably inevitable until the rules of the contest were revised.

There were traces of this pattern in the reaction to last week’s snow-out in Cleveland. Note to our meteorologically-advantaged readers: it is cold in the Midwest in April. We don’t usually have to deal with snow, but for each year I’ve lived in Chicago, I’ve had an experience of arriving underdressed for a Cubs or White Sox game in April, pretending to enjoy myself for about four innings, recognizing that it wasn’t just the beer that was numbing my senses, and calling it quits around the seventh-inning stretch. Opening Day took place on the 19^th of April in 1937, the 15^th in 1957, the 10^th in 1967, the 6^th in 1987, and the 1^st this year. Something like what happened in Cleveland last week was the inevitable result of the steady march forward of baseball's calendar.

The problem isn’t entirely a matter of degrees (pun somewhat intended). April is the single month in which the weather changes the most in many North American cities. In Chicago, for example, the average high temperature is just 53 degrees on the first day of April, but has warmed to 64 degrees by the end of the month. Thus, pushing Opening Day back by two weeks in cold-weather cities would virtually eliminate the chances of playing baseball in sub-freezing conditions, and even a one-week delay would go a long way toward stemming the problem.

It would probably be possible, if baseball so desired, to have the entire two weeks of games take place in stadiums with domes, or in cities with average April high temperatures of 60 degrees or higher--25 of baseball’s 30 teams fall into this category (the exceptions are Cleveland, Detroit, Boston, and both Chicago clubs). As Joe Sheehan pointed out earlier this week, however:

It’s not as simple as scheduling first-week games in warm-weather or domed parks. Teams would, all things considered, prefer to have home dates clustered in June through August, and sticking a segment of teams with a disproportionate number of early-season home games creates problems.

Kansas City might be nicer than Cleveland in April, but it’s also the case that Kansas City in June is a lot nicer than Kansas City in April. Adding summer dates in Cleveland means that you’re taking them away from somebody else. Excluding teams that play in domed facilities, perhaps only the Rangers and Marlins experience better baseball weather in April than they do in July. Even Angelenos, for example, routinely experience game-time temperatures in the 50s for much of April; if they actually have to wear multiple layers of clothing to attend a baseball game, some of them are going to stay away. Besides, there are reasons unrelated to weather that teams would rather avoid playing home games in April. Junior is still in school in April, Mom and Dad are going to have trouble taking a day off of work, and it’s tough to for the marketing department to develop storylines early in the season. Save for Opening Day, April baseball is generally for hardcore fans.

What we’re left with, ultimately, is an optimization problem. Aggregate attendance would probably be higher if baseball avoided cold-weather cities in April, but there would be losers as well as winners; is it fair to punish the Padres or the Braves because they happen to play in a warm-weather environment? It would help to have some better sense of context. How does the seasonality of attendance patterns differ between Miami and Milwaukee, between Dallas and Detroit?

The table below analyzes attendance in each major league city from 1996 through 2006. What we’ve provided is a comparison of average per-game attendance in games played in April (and March) versus those played in the summer months of June, July, and August. A team’s home opener is excluded from the analysis, since it almost always sells out regardless of when it is played, as are games played in non-standard venues like Las Vegas, Japan, and Puerto Rico. Also provided is the average April high temperature in each city according to weather.com, and the type of facility (open-air, dome, retractable roof) that each team was playing in.

Average Attendance

Team          April    Summer   Difference Temp Type
Milwaukee     19,991   30,442   10,450     54   Retractable
(Miller)
New York (A)  34,700   44,418   9,718      60   Open
Chicago (A)   17,246   26,681   9,434      59   Open
Detroit       16,156   25,039   8,882      59   Open
Milwaukee     13,423   22,089   8,667      54   Open
(County)
Houston       21,762   29,734   7,972      79   Retractable
(Minute Maid)
Chicago (N)   29,165   36,851   7,686      59   Open
Philadelphia  20,654   28,201   7,547      62   Open
New York (N)  26,833   33,913   7,080      60   Open
St. Louis     32,865   39,806   6,941      66   Open
Oakland       16,691   23,495   6,804      66   Open
Seattle (Saf) 33,350   40,119   6,769      58   Retractable
Pittsburgh    17,188   23,954   6,766      62   Open
Cincinnati    21,515   27,593   6,078      65   Open
Atlanta       31,498   37,487   5,989      73   Open
Washington    26,374   31,850   5,476      66   Open
Baltimore     34,561   39,305   4,744      68   Open
Kansas City   16,130   20,799   4,669      67   Open
Minnesota     17,228   21,897   4,668      57   Dome
Cleveland     31,129   35,708   4,579      57   Open
Toronto       22,620   27,090   4,470      52   Retractable
San Francisco 30,174   34,610   4,436      64   Open
Texas         30,202   34,285   4,083      76   Open
Houston (Ast) 32,149   35,548   3,399      79   Dome
Los Angeles   38,119   41,472   3,352      73   Open
Seattle (King)31,932   35,096   3,164      58   Dome
Anaheim       29,559   32,699   3,140      73   Open
Boston        30,029   32,873   2,844      56   Open
Montreal      10,238   12,630   2,392      51   Dome
Arizona       32,786   34,826   2,040      83   Retractable
Colorado      36,378   38,120   1,742      61   Open
San Diego     30,531   31,257     726      69   Open
Florida       18,407   19,043     636      79   Open
Tampa Bay     17,569   18,187     618      81   Dome

We immediately see some relationship between temperature and attendance patterns. The three teams with the smallest difference between April and Summer attendance are San Diego, Florida, and Tampa Bay, while the largest differences belong to teams in cold-weather Milwaukee, Chicago, and New York. There are a few exceptions here and there-–the Astros haven’t drawn very well in April, and some cold-weather teams like Boston exhibit small differences in attendance because they’re playing near capacity. But in general the pattern fits the conventional wisdom: all teams have a few more empty seats in April, but cold-weather teams suffer more than most.

We can summarize these results by breaking the teams into different quartiles based on average April temperatures. For purposes of this analysis, we’ll exclude any teams that play in domes or retractable facilities–-we’ll revisit that issue in a moment. In addition, we’ll exclude any seasons in which the team played to 90 percent or greater of its stadium’s listed capacity. When a team has a great amount of excess demand for its tickets, it’s going to be hard to discern any meaningful patterns in its attendance data. The Cubs, for example, could probably sell out Wrigley Field two or three times over for a July series against the Cardinals; they are now trying to economize on this phenomenon by means of a tiered pricing scheme in which April tickets are discounted while summer tickets are sold at premium prices, which will be reflected in their revenue figures but not in their attendance.

Temperature             April         Summer         Difference
Cold (<60 degrees)     18,307         27,092         8,785
Cool (60-64)           24,516         31,730         7,214
Temperate (65-68)      24,142         30,009         5,867
Warm (69+)             29,208         32,235         3,027

These results confirm the pattern that we described before, and suggest that somewhere between one-half and three-quarters of the shortfall in April attendance is the direct result of suboptimal weather; the rest is the result of systemic factors.

Does having a dome solve the problem? Yes and no. Below is the attendance breakdown based on the facility classification; again, we have excluded any seasons in which the team sold out 90 percent or more of its tickets.

Facility         April         Summer         Difference
Open-Air         24,610         30,540         5,930
Retractable      26,215         31,600         5,385
Dome             17,295         20,623         3,328

There is a predictable difference between domed and open-air facilities; in fact, domed stadiums exhibit attendance patterns that are very similar to warm-weather facilities, regardless of their location. On the other hand, retractable roof stadiums play as much like open-air facilities as they do domes. Fans generally do not like watching a baseball game with a roof on top of their heads. By my count, there have been 109 seasons in which a team played its entire home schedule under a roof; in only 13 of those seasons (12%) did the team finish in the top five in its league in attendance. Retractable roofs, then, can limit the damage from a bad-weather day, but they cannot eliminate it entirely. Fans are more likely to turn out if they expect the roof to be open, particularly in cities that have short summers, like Milwaukee.

We can examine these results a bit more precisely by means of a regression analysis. In particular, that regression analysis reveals the following:

1. In an open-air facility, each drop of one degree in average April temperature results in a decline of 313 fans in per-game April attendance.
2. In a retractable-roof facility, each drop of one degree in average April temperature results in a decline of 121 fans in per-game April attendance.
3. In a domed facility, each drop of one degree in average April temperature results in a decline of 22 fans in per-game April attendance.

The first two figures are highly statistically significant; the latter one is not. We can use the results of the regression analysis to estimate the average loss in attendance and gate receipts that each team can expect to suffer as a result of playing a series in April rather than during the summer. Projected financial losses assume a three-game series, and an average of $40 in marginal revenue per fan per game (accounting for both ticket prices and concessions revenues).

Team          Temp         Type         Loss         Series
Boston         56         Open         8,955       $1,074,624
Cleveland      57         Open         8,642       $1,037,028
Chicago (A)    59         Open         8,015         $961,836
Detroit        59         Open         8,015         $961,836
Chicago (N)    59         Open         8,015         $961,836
New York (A)   60         Open         7,702         $924,240
New York (N)   60         Open         7,702         $924,240
Colorado       61         Open         7,389         $886,644
Philadelphia   62         Open         7,075         $849,048
Pittsburgh     62         Open         7,075         $849,048
Toronto        52         Retract      6,799         $815,928
Milwaukee      54         Retract      6,558         $786,936
San Francisco  64         Open         6,449         $773,856
Cincinnati     65         Open         6,136         $736,260
Seattle (Saf.) 58         Retract      6,075         $728,952
St. Louis      66         Open         5,822         $698,664
Oakland        66         Open         5,822         $698,664
Washington     66         Open         5,822         $698,664
Kansas City    67         Open         5,509         $661,068
Baltimore      68         Open         5,196         $623,472
San Diego      69         Open         4,882         $585,876
Atlanta        73         Open         3,629         $435,492
Dodgers)       73         Open         3,629         $435,492
Anaheim        73         Open         3,629         $435,492
Houston        79         Retract      3,538         $424,536
Minnesota      57         Dome         3,489         $418,668
Arizona        83         Retract      3,055         $366,552
Tampa Bay      81         Dome         2,954         $354,444
Texas          76         Open         2,689         $322,704
Florida        79         Open         1,749         $209,916

These numbers hint at one potential solution to the optimization problem; teams could barter series dates in exchange for fees. For example, a summer series is worth about $500,000 more to the White Sox than it is to the Twins. Thus, the White Sox could have paid the Twins about that sum of money to swap the home series they played against them last weekend for one of the Twins’ home series during the summer. Such a proposal might be good economics; however, it is probably bad business–-baseball does not need to create more mechanisms by which a small-market team might wind up alienating its fans.

Fortunately, there is a more natural solution in play that would allow baseball to increase the size of the pie without penalizing warm-weather teams. The calendar impacts attendance in more than one way; although summer games draw better than April games, so too do weekend series draw better than weekday series. In particular, the average attendance for Friday, Saturday, and Sunday games played since 1996 is 32,491, as compared to 26,590 fans per weekday game. Conveniently, the difference of about 6,000 fans per game almost exactly mirrors that of April versus summer dates.

The optimal solution would allow cold-weather teams to trade out of April games as liberally as possible, but they would do so at a price of giving up weekend series for weekday series. The Indians, for example, could have traded out their ill-fated weekend series against the Mariners for the weekday games in Seattle scheduled between September 25 and 27.

Such exchanges might be more easily conceived of than actually executed. The baseball schedule is operating under a large number of parameters and constraints. Baseball prefers not to have the White Sox and Cubs playing at home at the same time, for example, and there are travel restrictions embodied in the CBA to contend with. The fact is that baseball does a tremendous job with its scheduling overall, and already makes some effort to avoid having cold-weather teams play at home in April. Among those teams represented in all 11 years of our sample data, those with the largest number of April home dates were the Mariners (dome), Rangers (warm), and Marlins (warm), while those with the fewest were the Indians, Red Sox, and Tigers.

Still, baseball is probably leaving some money on the table with its current scheduling philosophy, and there are some non-zero-sum losses that result when games must be canceled and rescheduled. There is no need for panic over what happened in Cleveland last week, but there may be opportunities for improvements that find favor with fans, owners, and players alike.

Nate Silver is an author of Baseball Prospectus. 
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