fri, 12-apr-2013, 19:00

Next month I’ll be attending a game at Wrigley Field and my brother and I had some discussion about the best strategy for us to meet up somewhere in Chicago after the game. Knowing how long a game could be, and how many people are likely to be crowding the train platforms is useful information that can be inferred from the game data that http://www.retrosheet.org/ collects and distributes.

It’s also a good excuse to fiddle around the the IPython Notebook, pandas and the rest of the Python scientific computing stack.

I downloaded the game log data from http://www.retrosheet.org/gamelogs/index.html using this bash one-liner:

```for i in `seq 1871 2012`; \
do  wget http://www.retrosheet.org/gamelogs/gl\${i}.zip ; \
unzip gl\${i}.zip; \
rm gl\${i}.zip; \
done
```

# Game Length

Game length in minutes is in column 19. Let’s read it and analyze it with Pandas.

```import pandas as pd
import matplotlib.pyplot as plt
import datetime

def fix_df(input_df, cols):
""" Pulls out the columns from cols, labels them and returns
a new DataFrame """
df = pd.DataFrame(index=range(len(input_df)))
for k, v in cols.items():
df[v] = input_df[k]

return df

cols = {0:'dt_str', 2:'day_of_week', 3:'visiting_team',
6:'home_team', 9:'visitor_score', 10:'home_score',
11:'game_outs', 12:'day_night', 13:'complete',
16:'park_id', 17:'attendance', 18:'game_time_min'}
raw_gamelogs = []
for i in range(1871, 2013):
fn = "GL{0}.TXT".format(i)
raw_gamelog = pd.concat(raw_gamelogs, ignore_index=True)
gamelog = fix_df(raw_gamelog, cols)
gamelog['dte'] = gamelog.apply(
lambda x: datetime.datetime.strptime(str(x['dt_str']), '%Y%m%d').date(),
axis=1)
gamelog.ix[0:5, 1:] # .head() but without the dt_str col
```
dow vis hme vis hme outs day park att time dte
0 Thu CL1 FW1 0 2 54 D FOR01 200 120 1871-05-04
1 Fri BS1 WS3 20 18 54 D WAS01 5000 145 1871-05-05
2 Sat CL1 RC1 12 4 54 D RCK01 1000 140 1871-05-06
3 Mon CL1 CH1 12 14 54 D CHI01 5000 150 1871-05-08
4 Tue BS1 TRO 9 5 54 D TRO01 3250 145 1871-05-09
5 Thu CH1 CL1 18 10 48 D CLE01 2500 120 1871-05-11

(Note that I’ve abbreviated the column names so they fit)

The data looks reasonable, although I don’t know quite what to make of the team names from back in 1871. Now I’ll take a look at the game time data for the whole data set:

```times = gamelog['game_time_min']
times.describe()
```
```count    162259.000000
mean        153.886145
std          74.850459
min          21.000000
25%         131.000000
50%         152.000000
75%         173.000000
max       16000.000000
```

The statistics look reasonable, except that it’s unlikley that there was a completed game in 21 minutes, or that a game took 11 days, so we have some outliers in the data. Let’s see if something else in the data might help us filter out these records.

First the games longer than 24 hours:

```print(gamelog[gamelog.game_time_min > 60 * 24][['visiting_team',
'home_team', 'game_outs', 'game_time_min']])
print("Removing all NaN game_outs: {0}".format(
len(gamelog[np.isnan(gamelog.game_outs)])))
print("Max date removed: {0}".format(
max(gamelog[np.isnan(gamelog.game_outs)].dte)))
```
```      visiting_team home_team  game_outs  game_time_min
26664           PHA       WS1        NaN          12963
26679           PHA       WS1        NaN           4137
26685           WS1       PHA        NaN          16000
26707           NYA       PHA        NaN          15115
26716           CLE       CHA        NaN           3478
26717           DET       SLA        NaN           1800
26787           PHA       NYA        NaN           3000
26801           PHA       NYA        NaN           6000
26880           CHA       WS1        NaN           2528
26914           SLA       WS1        NaN           2245
26921           SLA       WS1        NaN           1845
26929           CLE       WS1        NaN           3215
Removing all NaN game_outs: 37890
Max date removed: 1915-10-03
```

There’s no value for game_outs, so there isn’t data for how long the game actually was. We remove 37,890 records by eliminating this data, but these are all games from prior to the 1916 season, so it seems reasonable:

```gamelog = gamelog[pd.notnull(gamelog.game_outs)]
gamelog.game_time_min.describe()
```
```count    156639.000000
mean        154.808975
std          32.534916
min          21.000000
25%         133.000000
50%         154.000000
75%         174.000000
max        1150.000000
```

What about the really short games?

```gamelog[gamelog.game_time_min < 60][[
'dte', 'game_time_min', 'game_outs']].tail()
```
```               dte  game_time_min  game_outs
79976   1948-07-02             24         54
80138   1948-07-22             59         30
80982   1949-05-29             21         42
113455  1971-07-30             48         27
123502  1976-09-10             57         30
```

Many of these aren’t nine inning games because there are less than 51 outs (8 innings for a home team, 9 for the visitor in a home team win ✕ 3 innings = 51). At the moment, I’m interested in looking at how long a game is likely to be, rather than the pattern of game length over time, so we can leave these records in the data.

Now we filter the data to just the games played since 2000.

```twenty_first = gamelog[gamelog['dte'] > datetime.date(1999, 12, 31)]
times_21 = twenty_first['game_time_min']
times_21.describe()
```
```count    31580.000000
mean       175.084421
std         26.621124
min         79.000000
25%        157.000000
50%        172.000000
75%        189.000000
max        413.000000
```

The average game length between 2000 and 2012 is 175 minutes, or just under three hours. And three quarters of all the games played are under three hours and ten minutes.

Here’s the code to look at the distribution of these times. The top plot shows a histogram (the count of the games in each bin) and a density estimation of the same data.

The second plot is a cumulative density plot, which makes it easier to see what percentage of games are played within a certain time.

```from scipy import stats
# Calculate a kernel density function
density = stats.kde.gaussian_kde(times_21)
x = range(90, 300)
rc('grid', linestyle='-', alpha=0.25)
fig, axes = plt.subplots(ncols=1, nrows=2, figsize=(8, 6))

# First plot (histogram / density)
ax = axes[0]
ax2 = ax.twinx()
h = ax.hist(times_21, bins=50, facecolor="lightgrey", histtype="stepfilled")
d = ax2.plot(x, density(x))
ax2.set_ylabel("Density")
ax.set_ylabel("Count")
plt.title("Distribution of MLB game times, 2000-2012")
ax.grid(True)
ax.set_xlim(90, 300)
ax.set_xticks(range(90, 301, 15))

# Second plot (cumulative histogram)
ax1 = axes[1]
n, bins, patches = ax1.hist(times_21, bins=50, normed=True, cumulative=True,
facecolor="lightgrey", histtype="stepfilled")
y = n / float(n[-1]) # Convert counts to percentage of total
y = np.concatenate(([0], y))
bins = bins - ((bins[1] - bins[0]) / 2.0) # Center curve on bars
ax1.plot(bins, y, color="blue")
ax1.set_ylabel("Cumulative percentage")
ax1.set_xlabel("Game time (minutes)")
ax1.grid(True)
ax1.set_xlim(90, 300)
ax1.set_xticks(range(90, 301, 15))
ax1.set_yticks(np.array(range(0, 101, 10)) / 100.0)
plt.savefig('game_time.png', dpi=87.5)
plt.savefig('game_time.svg')
plt.savefig('game_time.pdf')
```

The two plots show what the descriptive statistics did: 70% of games are under three hours but it’s not uncommon for games to last three hours and fifteen minutes. Beyond that, it’s pretty uncommon.

# Change in game times in the last 100 years

Now let’s look at how game times have changed over the years. First we eliminate all the games that weren’t complete in 51 or 54 innings to standardize the “game” were’re evaluating.

```nine_innings = gamelog[gamelog.game_outs.isin([51, 54])]
nine_innings['year'] = nine_innings.apply(lambda x: x['dte'].year, axis=1)
nine_groupby_year = nine_innings.groupby('year')
mean_time_by_year = nine_groupby_year['game_time_min'].aggregate(np.mean)
fig = plt.figure()
p = mean_time_by_year.plot(figsize=(8, 4))
p.set_xlim(1915, 2015)
p.set_xlabel('Year')
p.set_ylabel('Game Time (minutes)')
p.set_title('Average MLB nine-inning game time since 1915')
p.set_xticks(range(1915, 2016, 10))
plt.savefig('game_time_by_year.png', dpi=87.5)
plt.savefig('game_time_by_year.svg')
plt.savefig('game_time_by_year.pdf')
```

That shows a pretty clear upward trend interrupted by a slight decline between 1960 and 1975 (when offense was down across baseball). Since the mid-90s, game times have hovered around 2:50, so maybe MLB’s efforts at increasing the pace of the game have at least stopped what had been an almost continual rise in game times.

# Attendance

I’ll be seeing a game at Wrigley Field, so let’s examine attendance at Wrigley.

Attendance is field 17, “Park ID” is field 16, but we can probably use Home team (field 6) = “CHN” for seasons after 1914 when it opened.

```twenty_first[twenty_first['home_team'] == 'CHN']['attendance'].describe()
```
```count     1053.000000
mean     37326.561254
std       5544.121773
min          0.000000
25%      36797.000000
50%      38938.000000
75%      40163.000000
max      55000.000000
```

We see the minimum is zero, which may indicate bad or missing data. Let’s look at all the games at Wrigley with less than 10,000 fans:

```twenty_first[(twenty_first.home_team == 'CHN') &
(twenty_first.attendance < 10000)][[
'dte', 'visiting_team', 'home_team', 'visitor_score',
'home_score', 'game_outs', 'day_night', 'attendance',
'game_time_min']]
```
dte vis hme vis hme outs day att game_time
172776 2000-06-01 ATL CHN 3 5 51 D 5267 160
173897 2000-08-25 LAN CHN 5 3 54 D 0 189
174645 2001-04-18 PHI CHN 3 4 51 D 0 159
176290 2001-08-20 MIL CHN 4 7 51 D 0 180
177218 2002-04-28 LAN CHN 5 4 54 D 0 196
177521 2002-05-21 PIT CHN 12 1 54 N 0 158
178910 2002-09-02 MIL CHN 4 2 54 D 0 193
181695 2003-09-27 PIT CHN 2 4 51 D 0 169
183806 2004-09-10 FLO CHN 7 0 54 D 0 146
184265 2005-04-13 SDN CHN 8 3 54 D 0 148
188186 2006-08-03 ARI CHN 10 2 54 D 0 197

Looks like the zeros are just missing data because these games have relevant data for the other fields and it’s impossible to believe that not a single person was in the stands. We’ll get rid of them for the attendance analysis.

Now we’ll filter the games so we’re only looking at day games played at Wrigley where the attendance value is above zero, and group the data by day of the week.

```groupby_dow = twenty_first[(twenty_first['home_team'] == 'CHN') &
(twenty_first['day_night'] == 'D') &
(twenty_first['attendance'] > 0)].groupby('day_of_week')
```
```groupby_dow['attendance'].aggregate(np.mean).order()
```
```day_of_week
Tue            34492.428571
Wed            35312.265957
Thu            35684.737864
Mon            37938.757576
Fri            38066.060976
Sun            38583.833333
Sat            39737.428571
Name: attendance
```

And plot it:

```filtered = twenty_first[(twenty_first['home_team'] == 'CHN') &
(twenty_first['day_night'] == 'D') &
(twenty_first['attendance'] > 0)]
dows = {'Sun':0, 'Mon':1, 'Tue':2, 'Wed':3, 'Thu':4, 'Fri':5, 'Sat':6}
filtered['dow'] = filtered.apply(lambda x: dows[x['day_of_week']], axis=1)
filtered['attendance'] = filtered['attendance'] / 1000.0
fig = plt.figure()
d = filtered.boxplot(column='attendance', by='dow', figsize=(8, 4))
plt.suptitle('')
d.set_xlabel('Day of the week')
d.set_ylabel('Attendance (thousands)')
d.set_title('Wrigley Field attendance by day of the week, 2000-2012')
labels = ['Sun', 'Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat']
l = d.set_xticklabels(labels)
d.set_ylim(15, 45)
plt.savefig('attendance.png', dpi=87.5)
plt.savefig('attendance.svg') # lines don't show up?
plt.savefig('attendance.pdf')
```

There’s a pretty clear pattern here, with increasing attendance from Tuesday through Monday, and larger variances in attendance during the week.

It’s a bit surprising that Monday games are as popular as Saturday games, especially since we’re only looking at day games. On any given Monday when the Cubs are at home, there’s a good chance that there will be fourty thousand people not showing up to work!

tags: baseball  python
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