This document summarizes how the author used big data and statistical modeling to improve their fantasy baseball performance. They downloaded play-by-play data to build regression models predicting home run performance based on long-term and short-term stats. The long-term model showed players' 162-game skill strongly predicted home runs. The short-term model found 15-game streaks modestly predicted performance but were less important. This analysis helped the author win 4 of 5 fantasy leagues by picking up struggling hitters and relying more on proven skills over hot streaks.

1. How I Used Big Data to Dominate My Fantasy Baseball Leagues – And What You Can
Get From It With Zero Stats Expertise
I started playing fantasy baseball over a decade ago, but I was never all that successful. I
had research to do, classes to take and then classes to teach. Working 50 or more hours a
week and juggling the various jobs of graduate school didn’t leave much time to adjust my
lineups every day. On the other hand, I had developed some big data skills while working
on my dissertation. Last year I decided it was time to turn the tables.
This is the story of how I used big data to go from one championship with my first 30
fantasy baseball teams to winning four of my five leagues last year. It wasn’t because I got
lucky on draft day. My teams that finished in the 99th percentile of ESPN’s leagues turned
over half the original rosters. Once I finished my dissertation I decided to celebrate by
doing a little side project to help figure out which players to add and drop in the middle of a
season.
My goal was a little different than a professional general manager or even someone playing
daily fantasy sports on a professional basis. I already knew that the day-to-day
performance of baseball players was highly volatile. A large bankroll to afford hundreds of
entries today was more valuable for daily fantasy sports than my skill set. I just finished
graduate school, so I didn’t exactly have that kind of bankroll! (I also realized DFS would be
highly vulnerable to insider trading because knowing others’ roster choices was extremely
valuable, and months later the industry fell under heavy scrutiny for this behavior.)
I posted a lot of this on my blog after last season – it probably helped me get my current
internship with Baseball Prospectus – but I wanted to revise that posting for a broader
audience that may not be as familiar with statistics. You won’t need any special information
to use my strategy to help you win your fantasy leagues this year. I designed my study to
help people without advanced stats training make good decisions quickly by testing
whether ESPN and Yahoo’s default “player rater” was the most useful information.
The short answer is no for hitters and yes for pitchers. ESPN defaults to giving one
aggregate metric of player value and their ranking compared to other players over the last
15 days. For Yahoo it’s the last two weeks. Inexperienced fantasy baseball owners rely
solely on this heuristic to make decisions. In 2016 ESPN redesigned their app to shove
these ratings in your face and make it harder to get the full range of data that ESPN
provides. This is fine for pitchers, who tend to be streaky when it comes to allowing home
runs. However, a hitter’s hot streak isn’t very sustainable. Switching from the 15 day player
rater to the 30 day or full season player rater for hitters let me win four of my five leagues
while spending less than 10 minutes a day on fantasy baseball.
Our Eyes Can Deceive Us
Baseball is notorious for streaky home run hitters. Lucas Duda hit three home runs in his
first 41 games last year. He hit six in his next 7 games, then went another 35 games with
only one home run. Duda eventually hit 27 home runs. Daniel Murphy hit five home runs

2. before the All Star break last year then homered in six straight playoff games. As humans,
we tend to remember these hot and cold streaks. We’re not very good at comparing Duda’s
hot and cold 27 home run season to Curtis Granderson’s more consistent 26 home run
season.
Home runs are rare events. Most players do not hit a home run in a particular game. The
number of home runs a player hits in a season does not follow a bell curve. Many players
would hit 12-15 homers over a full season, while Chris Davis hit 47 last year. Abnormal
distributions are actually pretty common when we are counting how often a person or
organization does something. How many books have you read this year? How many
employees have you hired? Some people or organizations will be unusually active and
stretch the distribution. Most of my dissertation focused on statistical models for counts
(like the volume of news coverage after a media event) and rare events (how often was a
particular phrase used online in a particular 15 minute window). I had the perfect skills to
create a regression model for hitting home runs.
Building a Big Data Model
At the beginning of a fantasy baseball season it is fine to look at a player’s performance
over the last season or last few seasons to make initial evaluations for the current season.
However, baseball players fluctuate from these projections during the season. ESPN and
Yahoo player raters try to assign one number to these fluctuations. How much should we
worry about those ebbs and flows? To find out, I needed to get play-by-play information on
a daily basis. I went to Retrosheet, which provides this information for free, and
downloaded the 2010-14 play-by-play databases (remember I did all the stats a year ago).
The first thing I needed to do with this data was create some measure of how good a
particular player was at hitting home runs, driving in runs, and so on over a particular
period of time. I had to create my own kind of player rater. To keep this posting a
manageable length, I will just focus on home runs, because they are the play with the
largest impact. I started by counting the number of home runs a player hit over a certain
number of games. This helped me evaluate players like Nelson Cruz or Troy Tulowitzki,
who can be very productive when healthy but because injuries have limited their playing
time.
As any baseball fan knows, it is much easier to hit home runs in certain ballparks than
others. So the next thing I did was calculate how many home runs (and singles, strikeouts,
etc.) occurred at a particular park in a particular year. All pitcher hitting was excluded, to
make the National and American League stats directly comparable. I divided the number of
home runs, singles and so on by the number of plate appearances to create a metric for an
average player’s expected performance when they played in that stadium. Then I matched a
players’ actual performance to the expected performance. This is more detailed than just
looking at which team someone plays for. A player who plays half their games in San
Francisco (a notoriously difficult park for home runs) also visits Colorado and Arizona
(home run havens).

3. My first measure of “home run skill” was the actual number of home runs hit minus the
expected number of home runs for an average player taking the same plate appearances in
those ballparks. A player who does “as expected” would get a 0. The lowest value over a full
season of 162 starts was 23 home runs below expected. The highest value was 36.775.
Unlike other metrics, this carries skill over from year-to-year. I also measured skill over
other time periods. If we look at a player’s last fifteen starts, home run skill ranges from -
2.589 to 8.268, because fifteen games isn’t as much time for Chris Davis to differentiate
himself from Ben Revere.
Standardized Skill
Player raters on ESPN and Yahoo do not give raw counts. These sites are sophisticated
enough to know that home runs are rarer than runs scored. That’s why players are
measured in how many standard deviations they are away from the mean on a particular
statistic. Measuring skill in standard deviations also lets them but performance over the
last 15 days and over the same season on the same scale. This is a very wise move, and
something I need to do for myself. Thankfully it is very easy to standardize variables. This
has one important side effect: really hot players will be further away from the mean over
short time periods like 15 games, but over 162 games we will see some regression to the
mean.
Choosing Regression Models
Choosing the best form of regression for looking at home runs is more difficult than it
would appear. [As a warning, the following two paragraphs will refer to regression models
that were not taught in the required statistics classes in my PhD program. I give a technical
explanation for how I did the best I could with freely available information, but someone
looking to make decisions on a professional basis would want to invest in better data.]
Basic ordinary least squares regression could work, but it is unlikely to be the best option.
Like I explained earlier, the number of home runs someone hits in a game does not follow a
normal bell curve distribution. The most common outcome is someone hitting zero home
runs. Negative binomial regressions seem ideally suited to this kind of rare outcome. I used
them throughout my dissertation. Unfortunately, none of the negative binomial regressions
I have tried so far have converged successfully, for any hitting outcome. (Negative binomial
regression models are notorious for this.) I also tried zero-inflated negative binomial
regression, a complex two-stage process that assumes certain parks will enable or suppress
home runs and then looks at players’ skill, but they also failed to converge.
As a result, the best model that actually converges on some kind of prediction equation is a
Poisson model. Poisson models are designed for counting things that are specific units and
don’t quite have a bell curve distribution because a few people have unusually large counts.
Home runs hit in a season is a perfect example. The number of languages someone speaks
is another good example. Poisson would make a lot of sense for hits per game, but wasn’t
my first choice for looking at home runs. I felt confident enough to use these results to use
them in my fantasy leagues, but I’m not sure I’d use them if I was a real life general

4. manager. Teams should have better proprietary data – all of my work here is based on
publicly available information.
Regression Model 1: A Baseline of Long Term Skill
To start off, let’s see if a player’s long-term track record predicts whether they are more
likely to hit a home run today. If players who hit more home runs over a 162 game season
are not more likely to hit more home runs today, then hitting a home run today would be
almost completely random. The outcome is the number of home runs a player hits in a
particular game. To make sure I am comparing apples to apples, I am limiting this to
players who start. Because fantasy baseball rewards home runs per game and not per plate
appearance, I did not include any other controls for plate appearances per game.
In the regression model I only use one independent variable: home run skill based on a
player’s last 162 starts. If a player had yet to start 162 games before the game in question,
they are excluded from the regression model. This is a very strict limitation. My database
has 206,008 position player starts over five seasons but only 105,484 valid observations
for the first regression model. One reason for this is I used the entire 2010 season is used as
seed data to establish players’ track record to predict performances starting in 2011. The
other reason is some players are not good enough to get 162 major league starts. Every
player was used to calculate expected performance, but only players good enough to stay in
the majors will be in my regression model. This means the players who are actually in my
analysis are slightly above the average MLB player. Remember, we’re trying to figure out if
the long term data that exists is better than short term hot streaks..
. poisson hr_pg hr162 if under162gs!=1
Iteration 0: log likelihood = -37885.596
Iteration 1: log likelihood = -37885.596
Poisson regression Number of obs = 105484
LR chi2(1) = 1893.60
Prob > chi2 = 0.0000
Log likelihood = -37885.596 Pseudo R2 = 0.0244
-----------------------------------------------------------------------------
hr_pg | Coef. Std. Err. z P>|z| [95% Conf.Interval]
-------------+---------------------------------------------------------------
hr162 | .3843963 .0087115 44.12 0.000 .367322 .4014706
_cons | -2.238728 .0097242 -230.22 0.000 -2.257787 -2.219669
------------------------------------------------------------------------------
These results fit our expectations. A player who is one standard deviation better at hitting
home runs over his prior 162 starts will hit e ^ 0.3843983 = 1.46872 times as many home
runs in the current game, as compared to the average player hitting in those ballparks.
Since Poisson is an exponential regression model, the top home run hitters would be
expected to hit more than twice the home runs in any game. Don’t get too excited though.
The very large and negative coefficient tells us that hitting home runs is still rare. One way
to examine this is with Stata’s “margins” command, which allows us to predict the number

5. of home runs someone hits per game at different levels of skill. For illustration I chose -2
standard deviations of skill, -1, 0, +1, +2 and +3.
* Standard errors for each estimate range from .001 to .008, so a 95 percent confidence
interval would not be visible in this graph.
Based on this regression model, a player with average skill at hitting home runs would hit
.106 homers per game they start. If we do a little back of the envelope math and assume
four plate appearances per start, that translates to one home run per every 37.735 plate
appearances. Home runs are pretty rare, even for hitters who do an average job at hitting
home runs. Well above average power is extremely valuable and scarce – something to
remember for next year’s drafts. A player with +2 standard deviations of home run hitting
skill, based on their track record over 162 games, would hit 0.2299 home runs per game
they start. It’s more than double what the average power hitter would accomplish.
Regression Model 2: Adding Short Term Hot Streaks
Now let’s add a measure of short-term success hitting home runs. I chose 15 starts, because
I was playing on ESPN leagues that default to showing player ratings over the last 15
games. In the interests of time, I will skip the regression model with short-term streaks as
the only independent variable. One potential problem is a home run a player hit yesterday
would show up in my short term and long term variables. To correct for this I created a
slightly different long term variable: home run hitting skill in the previous 16-162 starts.
This way short term and long term skill are mutually exclusive.
. poisson hr_pg hr15 hr162_b if under162gs!=1
Iteration 0: log likelihood = -37884.932
Iteration 1: log likelihood = -37884.932
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
-2 1 0 1 2 3
HR Skill (162 GS)
Predicted # of Home Runs Hit Today,
By Long Term HR Skill Only

6. Poisson regression Number of obs = 105484
LR chi2(2) = 1894.93
Prob > chi2 = 0.0000
Log likelihood = -37884.932 Pseudo R2 = 0.0244
------------------------------------------------------------------------------
hr_pg | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
hr15 | .0716725 .0090748 7.90 0.000 .0538863 .0894587
hr162_b | .3473053 .0095419 36.40 0.000 .3286035 .3660071
_cons | -2.244009 .0097878 -229.27 0.000 -2.263193 -2.224825
------------------------------------------------------------------------------
If streaks like Daniel Murphy’s record in last year’s playoffs were completely random and
have no carry over, we would expect to see a coefficient of 0 for the home runs in the last
15 starts variable. The value is greater than zero. This means there is some short-term
effect that carried over from game to game. However, it’s not very big. Here is a graph
based on a margins command for home run skill over the past 15 starts:
I might be able to publish this finding as evidence of a “hot hand” in baseball. It is
significant at the p < 0.001 level. However, I read these results as a warning against picking
up the hot hand in fantasy baseball. Long-term track records of hitting home runs are much
more important. If I drop an established home run hitter on a cold streak for a random guy
suddenly hitting homers, the move will probably backfire. I won one of my leagues by
scooping up veteran hitters on cold streaks, taking advantage of other fantasy owners’
impatience.
I’d only rely on short-term measures if a hitter’s opportunities suddenly change (via trades
/ injuries / road trips) or if there are no hitters with a solid long-term track record
available. When top prospects like Alex Bregman get promoted, it’s often a roll of the dice
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
-2 1 0 1 2 3
HR Skill (15 GS)
Predicted # of Home Runs Hit Today,
By Short Term HR Skill

7. whether they will help your team. My statistical model can’t help, but it can tell you which
players to drop. Without getting in to all the details, the 30 day player rater is considerably
better than the 15 day rater, but it’s still relatively bad compared to season long
performance.
Regression Model 3: Adding Pitchers
Pitchers present different opportunities. A pitcher who suddenly starts performing badly
may be experiencing an undiagnosed injury or fatigue. Pitchers who start performing
better may have overcome these physical ailments or made meaningful mechanical
changes. Short-term fluctuations may matter more for pitchers than they do for hitters.
To make sure I’m building off the work I already did, I am going to pose a slightly different
question. After we factor in a hitter’s ability to hit home runs, will they hit more home runs
when facing pitchers who are particularly bad at limiting home runs? Again, does the short
term matter more than the long term?
Obviously, 15 and 162 game thresholds are not ideal for establishing pitcher skill. I used
100 plate appearances as the short-term cutoff and 400 as the long-term cutoff. 100 may be
a bit much for a short-term cutoff but it’s a nice round number. Each starting pitcher is
tracked individually. Requiring 162 starts for a hitter is much more restrictive. There were
only 2952 plate appearances where a qualified starting pitcher with 400 batters faced went
against a non-qualified hitter.
Tracking relievers is much harder. Most will not reach 400 batters faced in a season – and
many won’t even reach 100. In typical fantasy baseball leagues the closer is the only
reliever with significant value. Opportunities to save games matter more than greatness.
We wouldn’t drop hot or cold relievers unless the team says they are removing a closer
from his position. To simplify things I aggregated all relievers for a particular team and
treated each bullpen as a composite pitcher. Then I ran separate analyses to see if the
results changed for at-bats versus starters versus relievers. The differences were minor, so
I won’t make distinctions here. (It’s mainly an issue of relievers needing slightly better skill
at avoiding home runs or they get demoted.)
Home run “skill” for pitchers is measured as home runs allowed. Just like batter skill, I
constructed this measure by comparing a pitcher’s performance to the average pitcher
working at a particular ballpark. Since this is home runs allowed, low numbers are good for
the pitcher. In a regression model, a positive coefficient means batters hit more home runs
against a pitcher who has been susceptible to giving up home runs, even after controlling
for the hitter’s skill.
. poisson hr_pg hr15 hr162_b p_hr100 p_hr400_b if under162gs!=1
Iteration 0: log likelihood = -36971.257
Iteration 1: log likelihood = -36971.257
Poisson regression Number of obs = 102,892

8. LR chi2(4) = 2122.62
Prob > chi2 = 0.0000
Log likelihood = -36971.257 Pseudo R2 = 0.0279
------------------------------------------------------------------------------
hr_pg | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
hr15 | .0698402 .0091523 7.63 0.000 .051902 .0877785
hr162_b | .3461104 .0096322 35.93 0.000 .3272316 .3649892
p_hr100 | .1869119 .011318 16.51 0.000 .1647291 .2090947
p_hr400_b | .0026707 .0111019 0.24 0.810 -.0190887 .02443
_cons | -2.250443 .0099851 -225.38 0.000 -2.270013 -2.230872
One of the first things to note is that the importance of a hitter’s skill in getting home runs
doesn’t really change after controlling for whether the pitcher tends to serve up long balls
or keep them in the ballpark. When evaluating hitters, think about their track record and
the park they are playing in. Don’t worry as much about the reputation of the opposing
pitcher if someone with bona fide power is sitting on the waiver wire!
When evaluating pitchers, I would focus overwhelmingly on whether a pitcher has done
well in the last 30 days. From 2010-14 pitchers most didn’t have consistent skill in avoiding
home runs. They had meaningful ebbs and flows. It’s hard to know what exactly causes this
based solely on box scores. I suspect pitchers’ performance has more serious ups and
downs because of the physical strain of pitching. A pitcher who gets tired may make more
mistakes or lose velocity. Pitchers may need more than a month of spring training to fully
warm up but then stay warm. Detailed data on changing velocity and release points could
solve this question. In the short term, if you are a fantasy baseball player looking for an
edge, play the hot hand with pitching and be wary of it with hitting.