Events Unrelated to Crime
Predict Criminal Sentence Length
Nora Barry, Laura Buchanan, Evelina Bakhturina, Daniel L. Chen1
Abstract
In United States District Courts for federal criminal cases, prison sentence length
guidelines are established by the severity of the crime and the criminal history of the
defendant. In this paper, we investigate the sentence length determined by the trial
judge, relative to this sentencing guideline. Our goal is to create a prediction model of
sentencing length and include events unrelated to crime, namely weather and sports
outcomes, to determine if these unrelated events are predictive of sentencing decisions
and evaluate the importance weights of these unrelated events in explaining rulings.
We find that while several appropriate features predict sentence length, such as details
of the crime committed, other features seemingly unrelated, including daily temperature,
baseball game scores, and location of trial, are predictive as well. Unrelated events
were, surprisingly, more predictive than race, which did not predict sentencing length
relative to the guidelines. This is consistent with recent research on racial disparities in
sentencing that highlights the role of prosecutors in making charges that influence the
maximum and minimum recommended sentence. Finally, we attribute the predictive
importance of date to the 2005 U.S. Supreme Court case, United States v. Booker, after
which sentence length more frequently fell near the guideline minimum and the range of
minimum and maximum sentences became more extreme.
1
Barry: [email protected], Buchanana: [email protected], Bakhturina: [email protected]: NYU Center for
Data Science; Chen: [email protected]: Toulouse Institute for Advanced Study
Introduction
I. United States District Court
The United States District Courts (USDC) are the judicial backbone for hearing
and sentencing federal crimes in the United States.2 Federal crimes include illegal
activity committed on federal land, crimes committed by or against federal employees in
particular roles, matters involving federal government regulations (e.g., illegal
immigration, federal tax fraud, counterfeiting), or crimes against the U.S. that occur
outside of the United States, such as terrorism.3
Among federal crimes, the most
frequently heard cases involve immigration, drug trafficking, firearms, and fraud.
Most frequently, the defendant in a case enters a plea agreement with the
prosecutor, which is then approved of, or denied, by the judge.4 Otherwise, a
sentencing trial is held and the judge determines the sentence for the criminal to serve:
probation, federal prison, or both. In either situation, the judge has final say on the
criminal sentence.
There are 94 district courts in the United States. At least one district court is
located in each state or U.S. territory. States that are large or have a large population
have sub-state regional courts instead.
The United States Sentencing Commission (USSC)5,6 produces the sentencing
guidelines for federal judges to use when they make their sentencing decisions. The
judges are given a guideline range for the criminal sentence that is based upon the
severity of the crime and the defendant's criminal history. Due to these guidelines, the
2
"Court Role and Structure." United States Courts. N.p., n.d. Web. 10 May 2016.
"Types of Cases." United States Courts. N.p., n.d. Web. 10 May 2016.
4
"Plea Bargain." Wikipedia. Wikimedia Foundation, n.d. Web. 13 May 2016.
5
"United States Sentencing Commission." United States Sentencing Commission. N.p., n.d. Web. 13
May 2016.
6
"United States Sentencing Commission." Wikipedia. Wikimedia Foundation, n.d. Web. 13 May 2016.
3
largest factor determining sentence range is the criminal charges brought to the judge
by the prosecutor. For this paper, we use federal sentencing data made available by
the USDC previously curated by one of the authors.
II. Role of the Prosecutor
The primary factor determining criminal sentence in USDC cases has been found
to be, understandably, the criminal charges presented by the prosecutor and the
criminal history of the defendant. However, research suggests that features unrelated
to the case bias sentence length. In one study, the research team found that “blacks
receive sentences that are almost 10 percent longer than those of comparable whites
arrested for the same crimes.”7 This disparity can be primarily explained by the criminal
charges the prosecutors present to the court. Specifically, when the defendant is black,
the prosecutor is more likely to present a charge that carries a minimum mandatory
sentence. Many other examples of disparities based on race, sex, education, income,
etc., exist in the literature.8
III. Within Sentencing Range
Discrepancies across choice of criminal charges do not fully explain these
disparities. Judges are also known to, for example, give females a sentence nearer the
guideline minimum, or prescribe criminal sentences outside of the guideline range for
males. This motivates our decision to focus on sentence length relative to the
recommended guideline range.
7
Rehavi, M. Marit, and Sonja B. Starr. "Racial Disparity in Federal Criminal Sentences." Journal of
Political Economy 122.6 (2014): 1320-354. Web.
8
Mustard, David B. "Racial, Ethnic and Gender Disparities in Sentencing: Evidence from the US Federal
Courts." SSRN Electronic Journal SSRN Journal (n.d.): n. pag. Web.
For the USDC, the Federal Sentencing Commission writes recommended
sentence minimum and maximum terms to help ensure that convicts who committed
similar crimes are charged with similar sentences. As can be seen in the lookup table in
Figure 1, the severity of the crime and the criminal history of the convict are used to
determine the appropriate sentence range. The judge then determines or approves a
sentence length, frequently, but not necessarily within this range.
In the paper, we look past the recommended sentencing range and predict the
sentence length within this range. Knowing that discrepancies in sentence length exist,
and that the sources of these discrepancies have not been fully uncovered, we
investigate a new set of features that may bias sentence length.
In particular, we
explore whether characteristics of events that co-occur with sentencing decisions
predict, and potentially bias, those outcomes. The event types we chose to examine
are weather and sports.
First, we consider the difference in conditions when sentence length falls below
or above the midpoint of the sentence guideline range to uncover the feasibility of
prediction in this setting. We then move to investigating sentence length percentile
relative to the sentence guideline range. This standardization allows us to look at where
within a guideline range a sentence falls. The interpretation of this percentile measure
is described in Table 1 below. We perform regression to predict this percentile.
Figure 1. Federal Sentencing Lookup Table
< 0%
0% - 50%
50% - 100%
> 100%
sentence length below
guideline minimum
(rare)
sentence length between
guideline minimum and
guidline midpoint
sentence length between
guideline midpoint and
guideline maximum
sentence length above
guideline maximum
(rare)
Table 1. Interpretation of Range Percentile Measure
Data Description
I. United States District Court Data
The United States District Court Federal Sentencing data was made available by
the Office of Research and Data in the United States Sentencing Commission. This
data spanned federal court cases from 1992–2013. There are 35 features in this data,
characterizing the defendant and crime. We keep 15 of these features due to their
interpretability. Dummy variables were created as needed for features including race,
location and citizenship. This brought us to a total of 253 features.
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Date: continuous time variable
Sentencing Month
Sentencing Year
Trial: 1 if a trial occurred
Sex: 1 if the defendant is male
Citizen: categorical variable denoting U.S. citizenship status
Drug Crime: 1 if the crime involved drugs
Crime Type: categorical variable denoting the crime type
Race: categorical variable denoting the race of the defendant
State: categorical variable denoting the state in which the crime occurred
District: categorical variable denoting the district in which the crime occurred
Probation Office: categorical variable denoting the probation office in which the
pre-sentencing report is prepared
NumCounts: the number of counts of conviction
Education: categorical variable denoting the education level of the defendant
Pre/Post Booker: 1 if the trial occurs before the United States v. Booker trial
(explained further in the Discussion section)
We also utilized some of the court-defined sentencing features such as Guideline
Minimum and Maximum sentence length, Court Recommendation, Gun Min I & II, Gun
Max I & II, Normed Range, Court Minimum and Court Maximum in our baseline model,
but ultimately dropped them when building our final model. These features are
explained further in the appendix.
In our baseline model, our target variable was a binary indicator {-1,1} we
computed denoting whether a sentence length fell below or above the midpoint of the
sentence range. After, our target variable was sentence length percentile relative to the
range. We compute the value using standard normalization.
As our target variable was defined with the minimum and maximum sentence range,
we dropped the minimum and maximum sentence range features when fitting our model
to prevent data leakage.
II. Weather Data
In order to properly account for the weather in each district on a given day, we
used a dataset originating from the NOAA (National Oceanic and Atmospheric
Administration) database. This dataset consists of daily weather for 96 cities from
1992–2013. It includes over 90 features that depict various aspects of the weather
conditions for each day. However, many of these features contain missing values, or
are merely translations of other features. For this reason, we chose to include only the
features below. We also feel these features capture the aspects of weather that are
necessary in exploring a potential relation between weather and judge decisions.
Table 2. Weather Data Features
III. Sports Data
Sports data available to us included data from MLB (Major League Baseball),
NBA (National Basketball Association), NFL (National Football League), NHL (National
Hockey League), and college football (CFB) for the years in which we had U.S. District
Court Data.
For the four professional leagues (MLB/NBA/NFL/NHL), there was an instance of
each team in each game played (i.e. each game had two instances). While the features
available were not identical across sports they were generally similar, and included
information such as team name, field played on, score, and betting over/under.
For the CFB data, there was one instance per game. Unlike the professional
sports data, the CFB data is not as complete.
This is understandable due to the
organization of college football competitions. Teams typically play schools of the same
size, budget, and quality of facilities.9 Due to this, some games played by smaller
schools are not recorded. However, the games played by the Division I schools, the
schools with the most developed football programs and likely the greatest regional
following, are well represented. This data included team name, field played on, score,
and so on.
For each of the five sports datasets, we created two dataframes. The first
dataframe includes information about the each team per game on the same day as the
trial. We assumed that the judge would not know the result of the game before the end
of the workday. For this dataframe, we included the date, team name, whether a game
occurred, and whether the game would be played at the home stadium, or away.
District was also needed, but added later.
Date
Team
Game Y/N
Home/Away
District
Table 3. Features in Day-Of Sports Dataframe
The second desired dataframe represents the results of each game.
The
assumption is that if the outcome of a game were to affect the outcome of a trial, it
would only be influenced by games played the day before.10 Because we were
concerned with the game the day before, our second dataframe listed the date one day
after the date that the game was played. We then included the team name, whether the
game occurred, whether the game would be played at the home stadium or away, the
points scored by the team, the points scored by the opposing team, the score margin
9
"College Football." Wikipedia. Wikimedia Foundation, n.d. Web. 13 May 2016.
A more sophisticated approach would be to taper off the weighting of game importance for several days
following each game. We did not take this approach here.
10
(difference between team’s scores), and whether the team won or lost. Again, district
was included later.
Date + 1
Team
Game Y/N
Home/Away
Points Scored
Points Allowed
Score Margin
Win/Loss
Table 4. Features in Day-Prior Sports Dataframe
There were several challenges when pre-processing the sports data so that they
could be organized into these dataframes. For example, for the score margin was not
included in all data, and was calculated in these cases. The CFB data was organized
differently from the professional sports data, so each instance of a game had to be split
between the results per game per team.
A lookup table between the team names and the district that would presumably
be interested in that team was curated manually. For the lookup table to remain useful,
several simplifying assumptions had to be made. In the first pass, each team was
paired with the district where their home stadium was located. This meant that major
cities such as Los Angeles, which is located in the Central California District Court
district, were represented several times in the lookup table.11
New York City was
challenging in that Brooklyn falls under the Eastern New York District Court, and the
rest of New York City falls under the Southern New York District Court. In the majority
of cases, New York City teams were represented by both districts, unless Brooklyn had
its own team.
After each team was paired with its “hometown” district, we induced spatial
spread in the professional sports data. First, in states that have several districts but
11
Consider MLB (Los Angeles Dodgers/ Los Angeles Angels of Anaheim), NBA (Los Angeles Clippers/
Los Angeles Lakers), and NHL (Los Angeles Kings/ Anaheim Ducks)
District
only one team, the team was paired with all districts in that state. If a state had several
districts and several teams, fandom maps based on Facebook likes12 were used to
determine the more popular team in the ambiguous districts in that state.
Finally,
Boston teams were assigned to all New England districts, assuming homogeneity of
fandom. If a district had no team and no obvious way to induce spread, it was not
assigned any team (e.g., Guam, Puerto Rico, Montana, etc.). Due to the number of
CFB teams, and assumptions about college football fan followings, we did not feel that
spreading data outside of the district the school is located in was appropriate or desired.
We choose not to use the betting over/under information included in the
professional sports data, though that would be an interesting area of research worth
pursuing.13
In the college football data, we choose not to include team ranking or
whether the game was a special championship. An interesting future research aim
would be to give a heavier weight to championship games and bowls, presuming that
the lead up and results of the games would be more impactful on the community of fans
invested in the game.
Similarly, this information could be incorporated into the
professional sports data.
IV. Data Merge
i. Weather
12
e.g., Person, and Barry Petchesky. "Here's Facebook's 2015 MLB Fandom Map." Regressing. N.p., 01
Apr. 2015. Web. 13 May 2016.
13
In principal, three types of fans can be envisioned. An extremely avid fan follows the odds and
experiences anticipatory utility even before a game. An avid fan follows the odds and experiences utility
only in the event of a surprise. A normal fan does not follow the odds and merely responds to the actual
sports outcomes. Distinguishing these types of fans would be interesting, and we proceed here with the
assumption that judges are normal fans.
To combine the weather data with district courts data, we merge on date and
location. First, we create a datetime feature from the “year”, “month”, and “day” features
in the weather data. Second, we alter the location features of both datasets to prepare
for the merge.
The features “city” and “courthouse” correspond to the location in the weather
and district courts datasets, respectively. However, we found that the city names differ
between the USDC and weather datasets. In other words, we found many courthouses
for which there was no corresponding weather data. To avoid dropping criminal cases
that do not have corresponding weather data, we created our own metadata to link
courthouses in the district data to the nearest city in the weather data. Through this, we
were able to precisely merge the two datasets without loss of information. The schema
of this merge includes all district court features, along with weather features 0-4 in the
weather table above.
ii. Sports
To merge the sports data with the previously merged district court and weather
data, we first dropped team name; we were interested to see if hometeam games
affected the judges’ sentence, rather than particular teams. For each of the sports
dataframes described above, we merge over date and district.
Each sport is
represented separately. If no sports data was available for any day-district combination,
the sports data fields were filled with zeros.
Methods & Results
I. Binary Baseline Model
To explore if sentencing length prediction is a feasible prediction setting, we
started with a binary classification problem in place of regression. We created our
target variable using the “rangePT” feature, which depicts where within the sentencing
guidelines the judges’ final sentencing decision falls.
For example, rangePT = 1
encodes that the judge’s sentencing length is equal to the guideline minimum, while
rangePT = 2 encodes that the judges’ sentence falls on the lower half of the range, and
so on. The table below depicts how we transformed this feature in detail.
Table 5. Baseline Target Variable Summary
In order to apply models such as support vector machine (SVM) and Logistic
Regression for our baseline model, we project the rangePT variable into the set {-1,1}
based on where the sentencing decision falls (below or above the median).
For
consistency, we drop the cases where either the sentencing length is equal to the
median (rangePT = 3) or there is no guideline range to begin with (rangePT = 6).14
We fit both an SVM and Logistic Regression model for this classification.
Because of the large number of features in our dataset, SVM failed to run on standard
14
These are dropped because there is no sense of being above or below median for these cases.
computers. As a result, we began to consider other options for larger-scale model
building such as Spark.15
Spark was able to run an SVM baseline model. However,
our Logistic Regression model enabled us to both extract the important features (an
attribute unsupported by Spark) and see the accuracy we are able to achieve in this
setting. The figures below show a visual of accuracy of our model and the top 10%
most important features learned by the model.
Figure 2. ROC/AUC Represent Accuracy of Logistic Regression
As we can see in the ROC graph, our logistic regression model achieves a very
high AUC accuracy (.93). However, this classification problem is very different from our
goal prediction problem, regression on sentence length percentile with range.
Regardless, it is reassuring to see that accurate predictions are possible in this setting.
15
"Apache Spark™ - Lightning-Fast Cluster Computing." Apache Spark™ - Lightning-Fast Cluster
Computing. N.p., n.d. Web. 13 May 2016.
Figure 3. Top 10% Most Important Features in Logistic Regression Model
The most valuable information that we gain from this model is the analysis of the
top 10% most important features learned by the logistic regression model. All features
listed are from the USDC dataset, and they encode different aspects of the sentencing
decision process. For example, the top two features are “Guideline Min” and “Guideline
Max,” which define the sentencing range. This is to be expected. The higher is the
guideline
minimum,
the
more
likely
the
sentence
was
above
the
median
recommendation. The higher is the guideline maximum, the more likely the sentence
was below the median. In this setting, the features that are defined by the severity of
the crime will undoubtedly be more important in predicting sentencing length than the
weather and sports features. While obvious in retrospect, this initial analysis helped us
determine that sentence length percentile within range can be an appropriate target
variable.
II. Features of Interest & Optimized Model
For our final model (predicting where sentencing length falls relative to the
guideline range), we compared Random Forest, Linear Regression and Gradient
Boosting models. For Random Forest and Gradient Boosting, we used 100 estimators,
which were then averaged to produce a final prediction. Although we would have liked
to use more estimators, we were limited by the extensive runtime for fitting these
models. In the end, we found Random Forest to be the most accurate in terms of mean
squared error. The figure below shows the MSE for each of the three models attempted
with default parameter values and 100 estimators:
Figure 4. Comparison of Models in Mean Squared Error.
We found that our Random Forest performed the best, and we utilized parameter
tuning to choose the best model from this hypothesis space. We were then able to tune
the model hyperparameters and increase the number of estimators to 250 to further
improve accuracy.
The hyperparameters we tuned include min_samples_leaf (the
minimum number of samples in newly created leaves) and max_features (the number of
features to consider when looking for the best split), which both help control overfitting.
The optimal hyperparameters we found were min_samples_leaf = 9 and max_features
= 0.6 (60% of features used in each node split). Once we fit our final, optimized model,
we were able to extract the most important features shown below.
Unlike our logistic regression baseline model, with Random Forest, we cannot tell
whether these features have a negative or positive importance in our model, i.e., if they
are negatively or positively correlated with our sentencing percentile target variable.
Therefore, we compute the correlation between these features and our target variable,
and color the bar graph accordingly to aid the reader in interpretation.
Figure 5. Top 10% Most Important Features in Random Forest Model
Discussion
I. Model Performance
Our baseline model predicted whether a criminal sentence falls above or below
the sentencing guideline midpoint. It performed robustly with very high AUC of ROC.
Unsurprisingly, we saw that the guideline minimum and maximum were the most
predictive features.
Other features in the top 10% most predictive were all features
from the USDC dataset. Our final model had modest ability in predicting a continuous
value. After tuning hyperparameters, we have a total mean square error of 2,941, less
error then we encountered with any other model tested.
II. Important Features
i. Court Case Information
The most important feature from the USDC data found to predict the percentile
within the range of sentence guideline was the number of previous criminal charges.
The sentence length and number of counts are positively correlated, as we would
expect. This indicates that the judge is taking in particular information about the crime
into consideration when determining the sentence length. Number of prior convictions
could suggest the likelihood for the defendant to be a repeat offender, and therefore, the
presumption would be that society would benefit from that defendant being imprisoned
longer.
A set of additional predictive features was whether the crime involved firearms,
arson, or drugs. Again, this is a reassuring sign that the judge is using case specific
information in their decision.
ii. Unrelated Defendant Information
We did not see that the race of the defendant was an important feature in our
predictive model, as suggested in previous research.
However, we do find
characteristics of the defendant that should not influence sentence length did enter the
top 10% most predictive features, such as sex and education level.
It is important to
further investigate whether these features truly influence the judge, as it would be unjust
if they led to bias.
iii. Time as an Important Feature
The most predictive feature in our Random Forest model was the date of the
sentencing decision. To the best of our knowledge, this can be linked to the 2005
United States Supreme Court decision referred to as United States v. Booker.16 This
court decision determined that only prior convictions, facts admitted by the defendant,
and facts proved to the jury beyond reasonable doubt could be used to extend the
criminal sentence longer than the mandatory maximum. In other words, it introduced
situations in which a judge could prescribe a sentence outside the sentencing range.
We believe that this formal decision on opportunities to vary sentence length
encouraged judges to change the way they made this determination. Interesting, while
the U.S v. Booker case questioned the judge’s right to increase the sentence length
past the maximum guideline sentence, we saw an overall decrease in the length of
16
"United States v Booker." Wikipedia. Wikimedia Foundation, n.d. Web. 13 May 2016.
sentence term relative to guideline range.
Additionally, the range of minimum and
maximum sentences becomes more extreme.
Figure 6. Trends in Sentencing Pre and Post US v. Booker
Figure 7. Trends in Sentencing Yang, 2013
iv. Sports as an Important Feature
In our final model, we found that several sports features, all related the final
scores of Major League Baseball Games, do in fact predict criminal sentence length. In
future work, it would be important determine whether sporting events significantly bias a
judge’s decision. If these sports features are truly predictive of the judges sentencing
decisions, it’s worth noting that they are due to games that happened the prior day, not
games that are going to happen.
v. Weather & Location as Important Features
We found many weather features appear in our top 10% most predictive
features.
Temperature minimum and maximum were our 2nd and 3rd most predictive
features, and were positively correlated with sentence length. Additionally, we found
that location of the courthouse (in particular, courthouses in Arizona, California, and
Texas) were predictive of sentence length.
Because these are all states in the
southern part of the United States, we believe determining why weather and location
are co-appearing in the top predictive features would be an interesting area of future
research.
Moreover, we found that USDC cases in the three states mentioned above
account for a significant proportion of all USDC cases in the US, displayed in Figure 8
below. In the Appendix, we show the crime breakdowns of these states. Being from
these states sharing a border with Mexico could possibly increase the likelihood of
being heard in a federal criminal court.
Figure 8. Proportion of USDC Cases in Arizona, California, and Texas
Conclusions
A justice system reasonably aspires to be consistent in the application of law
across cases and to account for the particulars of a case. Our goal was to create a
prediction model of criminal sentence lengths that accounts for non-judicial factors such
as weather and sports events among the feature set. The feature weights offer a
natural metric to evaluate the importance of these features unrelated to crime relative to
case-specific factors. Using a Random Forest, we found several expected crime related
features appearing within the top 10% most important features. However, we also
found defendant characteristics (unrelated to the crime), sport game outcomes,
weather, and location features all predictive of sentence length as well, and these
features were, surprisingly, more predictive than the defendant’s race. Further
investigating this predictive ability would be of interest to those studying the criminal
justice system.
Finally, date appears as the most predictive feature in determining sentence
length. We suspect that judges revised their method of determining sentence length
after United States v. Booker. Following this case, sentence length more frequently falls
near the guideline minimum, while the range of minimum and maximum sentences
becomes more extreme.
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Appendix
Feature Description:
•
•
•
•
•
•
Gun Min I & Gun Min II: two features representing the mandatory minimum
sentence (according to different calculations)
Gun Max I & Gun Max II: two features representing the mandatory maximum
sentence (according to different calculations)
Guideline Minimum and Guideline Maximum: two features representing the
guideline minimum and maximum sentence length
Court Recommendation: the recommended sentence length according to a
court-defined formula
Court Minimum and Court Maximum: the court-defined minimum and
maximum sentence length (used in the formula for Court Recommendation
Normed Range: normalized sentencing range
Crime Breakdown by Location: The figures below display the breakdown of crime types in the
U.S. as a whole, Arizona, Texas and California. Through these graphs we hoped to determine
whether or not the distribution of crime type in Arizona, Texas and California caused them to
become important features in our final model. Unfortunately, it is difficult to make a definite
conclusion.