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June 26, 2001

Aim For The Head

Fan Satisfaction

by Keith Woolner

This week's question comes from J.A., who asks:

Does anybody ever plug in attendance figures to the great statistical slicer-and-dicer in the sky? Specifically, what percentage of fans who attend the actual game have ever witnessed the home team win? I bet it's different from the percentage predicted by simple win-loss record.

I was trying to think of some things that affect attendance:

  • overall popularity of the franchise (more people have seen Yankees home games than any other club, I bet); this would tend to increase Home Victories Witnessed (HVW)
  • strength of the opponent; in non-perpetually-sold-out stadiums, this would decrease HVW
  • home-team playoff contention; this would increase HVW
  • day of the week; no idea whether home teams play better in front of Sunday-afternoon crowds as opposed to on Tuesday nights
I bet 60% of fans in all the ballparks over all the years have witnessed the home team win, even if only 53% of games have ended with the home team victorious.

Thanks for the question, J.A..

I love this kind of question. While it might not be deeply meaningful or provide profound sabermetric insight, it shows a novel way to think about the game. At the same time, you might discover something unexpected, and heck, it's just fun.

Let's extend J.A.'s idea in a couple of ways. First, there's his original question: what percentage of fans get to see the home team win? Though it's presumptuous to assume that all fans root for the home team, let's describe fans who see the home team win the game they attend as "satisfied fans." What factors will influence the percentage of satisfied fans?

Given that there's a bit of a home-team advantage in baseball (though not as large as in some other sports), we'd expect that slightly over half the attendees across all games were "satisfied," i.e., saw the home team win. On the other hand, if visiting teams that draw well on the road are also those that win more often on the road, this would tend to push the percentage of satisfied fans down.

Another factor that may influence the observed percentages is the time of year. Attendance tends to rise in the summer months as the weather gets better and kids get out of school. Therefore, teams that start the year on a hot streak may have a lower percentage of satisfied fans than a team with a comparable record who happened to win more during the summer months.

There's the intangible angle: are there teams that tend to play better (and win more often) in front of large home crowds than small home crowds? Do they tap into the energy that a supportive crowd cheering for them provides? If so, the synergies between large crowds and team performance should drive up the rate of satisfaction.

Enough speculation. Let's get to the numbers. To investigate this further, let's define two metrics that aren't part of our usual arsenal:

HW_ATT%: The percentage of fans who saw the home team the game they attended, aka "satisfied fans"

H_ATT/WIN: The ratio of HW_ATT% to Home Winning Percentage. Values less than 1.0 indicate that fewer fans saw the team win than you'd expect from their winning percentage. Values greater than 1.0 indicate that more fans saw the team win that you'd expect from their winning percentage.

Here are the results through games of June 24:

TM     G    W    L       H_ATT      HW_ATT  WIN%  HW_ATT% H_ATT/WIN

PHI   32   21   11     619,195     374,151  .656     .604      .921
SDN   38   14   24   1,107,747     386,158  .368     .349      .946
NYN   38   18   20   1,308,830     587,912  .474     .449      .948
ATL   34   18   16   1,142,171     584,678  .529     .512      .967
ANA   33   20   13     825,774     485,883  .606     .588      .971
ARI   38   22   16   1,228,720     691,659  .579     .563      .972
CLE   35   20   15   1,341,924     746,612  .571     .556      .974
MIN   38   25   13     844,678     541,655  .658     .641      .975
FLO   36   22   14     568,808     339,812  .611     .597      .978
SEA   37   27   10   1,509,889   1,081,961  .730     .717      .982
CHA   36   22   14     776,169     465,923  .611     .600      .982
KCA   39   16   23     811,894     327,545  .410     .403      .983
BAL   41   20   21   1,464,873     706,720  .488     .482      .989
HOU   37   18   19   1,245,726     600,976  .486     .482      .992
COL   41   22   19   1,696,205     904,666  .537     .533      .994
SFN   39   25   14   1,572,095   1,002,297  .641     .638      .995
MIL   34   20   14   1,154,771     676,693  .588     .586      .996
LAN   40   25   15   1,354,494     844,477  .625     .623      .998
CHN   35   23   12   1,136,667     745,431  .657     .656      .998
BOS   39   23   16   1,258,672     742,353  .590     .590     1.000
CIN   34    8   26     824,647     196,776  .235     .239     1.014
SLN   40   26   14   1,559,857   1,030,770  .650     .661     1.017
TBA   40   14   26     624,074     222,837  .350     .357     1.020
DET   38   19   19     808,486     412,694  .500     .510     1.021
TOR   38   18   20     790,900     385,812  .474     .488     1.030
PIT   34   15   19   1,073,286     488,711  .441     .455     1.032
NYA   36   21   15   1,382,871     839,156  .583     .607     1.040
OAK   37   18   19     943,947     479,191  .486     .508     1.043
TEX   34   13   21   1,258,664     503,646  .382     .400     1.047
MON   34   14   20     300,085     154,007  .412     .513     1.246

          587  518  32,536,119  17,551,162  .531     .539     1.015

Overall, the home team wins about 53% of the time, while a slightly higher percentage of fans actually see the team win. Naturally, the percentage of satisfied fans varies from team to team, as good teams tend to win a higher percentage of their home games, and thus would have higher percentages of satisfied fans even if attendance for every game was identical.

The only real outlier in the table above are the Montreal Expos, who have treated more than half their fans to wins, despite having lost nearly 60% of their home games. However, the sabermetician's favorite excuse, "sample size" can probably be invoked here as well. With relatively small numbers of fans attending each game, a single well-attended series coinciding with a sweep can skew the totals much more easily than a team who sells out every game.

It's not too surprising that the teams on each end of the list are also two of the three teams with the lowest home attendance totals, while conversely, no team that has drawn 1.5 million people at home so far is more than 2% away from the expected value of 1.00.

For completeness, here's the counterpart to the table above--each team's road "satisfaction" figures--keeping in mind that "satisfaction" still refers to the team indicated winning, that is, the percentage of fans on the road who saw the team win (i.e., beat the home team). Maybe this is better termed "dissatisfaction" or "anti-satisfaction," since we're talking about spoiling the fans' chance to see the home team win.

TEA    G    W    L       V_ATT      VW_ATT  WIN% VW_ATT_% V_ATT/WIN

OAK   37   17   20     993,582     371,876  .459     .374      .815
BOS   34   20   14   1,092,419     550,395  .588     .504      .857
COL   34   15   19     979,705     395,675  .441     .404      .915
MIN   35   18   17   1,019,766     484,040  .514     .475      .923
BAL   33   14   19     875,334     345,878  .424     .395      .931
CHN   38   20   18   1,326,714     651,287  .526     .491      .933
LAN   34   13   21   1,114,489     397,494  .382     .357      .933
PIT   38   10   28   1,003,414     247,752  .263     .247      .938
SDN   37   21   16   1,182,414     630,895  .568     .534      .940
DET   33   13   20     948,023     355,159  .394     .375      .951
SEA   37   28    9   1,080,639     779,563  .757     .721      .953
ANA   40   16   24   1,202,043     459,410  .400     .382      .955
CHA   36   14   22     981,359     364,906  .389     .372      .956
TBA   34    8   26     897,844     203,426  .235     .227      .963
NYN   38   15   23   1,083,080     413,077  .395     .381      .966
CLE   37   24   13   1,014,949     640,261  .649     .631      .973
SLN   35   14   21   1,201,258     470,790  .400     .392      .980
MIL   38   18   20   1,106,068     515,152  .474     .466      .983
ARI   37   24   13   1,137,336     728,398  .649     .640      .987
PHI   41   21   20   1,004,479     508,138  .512     .506      .988
HOU   36   20   16     967,214     533,804  .556     .552      .993
TEX   39   15   24   1,146,149     448,654  .385     .391     1.018
FLO   38   17   21     976,922     446,894  .447     .457     1.023
SFN   36   15   21   1,191,869     515,413  .417     .432     1.038
ATL   40   22   18   1,199,351     689,257  .550     .575     1.045
NYA   37   20   17   1,272,956     721,427  .541     .567     1.048
KCA   35   12   23     905,791     327,254  .343     .361     1.054
CIN   40   20   20   1,465,236     781,907  .500     .534     1.067
MON   42   16   26   1,244,366     508,503  .381     .409     1.073
TOR   36   18   18     921,350     498,272  .500     .541     1.082

          518  587  32,536,119  14,984,957  .469     .461     0.982

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

Related Content:  Fans,  Win Percentage,  The Who,  Game 1,  Yankees Fans,  Team

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The Week in Quotes: Ju... (06/25)
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Aim For The Head: Walk... (07/12)
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The Daily Prospectus: ... (06/27)

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