2018 NCAA Tournament Picks

Every year since 2010 I have used data science to predict the results of the NCAA Men’s Basketball Tournament. In this post I will describe the methodology that I used to create my picks (full bracket here). The model has Virginia, Michigan, Villanova, and Michigan State in the Final Four with Virginia defeating Villanova in the championship game:

Here are my ground rules:

• The picks should not be embarrassingly bad.
• I shall spend no more than one work day on this activity (and 30 minutes for this post). This year I spent two hours cleaning up and running my code from last year.
• I will share my code and raw data. (The data is available on Kaggle. The code is not cleaned up but here it is anyway.)

I used a combination of game-by-game results and team metrics from 2003-2017 to build the features in my model. Here is a summary:

• Team features
  • Massey ratings, obtained here.
  • My own eigenvalue centrality model, which tends to do a good job all by itself.
  • Metrics from Ken Pomeroy’s page. (These are public and are therefore fair game.)
  • Dean Oliver’s “Four Factors”, which I calculate from per-game data.
• Game features
  • Home court. (1 = home, -1 = away, 0 = neutral)
  • Year
  • (I did not have time to use site locations – the code is buggy.)

I also performed some post-processing:

• I transformed team ranks to continuous variables given a heuristic created by Jeff Sonos.
• Standard normalization.
• One hot encoding of categorical features.
• Upset generation. I found the results to be not interesting enough, so I added a post-processing function that looks for games where the win probability for the underdog (a significantly lower seed) is quite close to 0.5. In those cases the model picks the underdog instead.

The model predicts the probability one team defeats another, for all pairs of teams in the tournament. The model is implemented in Python and uses logistic regression. The model usually performs well. Let’s see how it does this year!

2017 NCAA Tournament Picks

Every year since 2010 I have used analytics to predict the results of the NCAA Men’s Basketball Tournament. I missed the boat on posting the model prior to the start of this year’s tournament. However, I did build and run a model, and I did submit picks based on the results. Here are my model’s picks – as I write this (before the Final Four) these picks are better than 88% of those submitted to ESPN.

Here are the ground rules I set for myself:

• The picks should not be embarrassingly bad.
• I shall spend no more than one work day on this activity (and 30 minutes for this post).
• I will share my code and raw data. (Here it is.)

I used a combination of game-by-game results and team metrics from 2003-2016 to build the features in my model. Here is a summary:

• Team features
  • Massey ratings which I obtained here.
  • My own eigenvalue centrality model, which tends to do a good job all by itself.
  • Metrics from Ken Pomeroy’s page. (These are public and are therefore fair game.)
  • Dean Oliver’s “Four Factors”
• Game features
  • Home court. (1 = home, -1 = away, 0 = neutral)
  • Year
  • (I had ‘day of season’ in there but pulled it. This is implicitly accounted for in some the team features above.)

I also performed some post-processing:

• I transformed team ranks to continuous variables given a heuristic created by Jeff Sonos.
• Standard normalization.
• One hot encoding of categorical features.
• Upset generation. I found the results aesthetically displeasing for bracket purposes, so I added a post-processing function that looks for games between Davids and Goliaths (i.e. I compare seeds) where David and Goliath are relatively close in strength. For those games, I go with David.

I submitted the model to the Kaggle NCAA competition, which asks for win probabilities for all possible tourney games, where submissions are scored by evaluating the log-loss of actual results and predictions. This naturally suggests logistic regression, which I used. I also built a fancy pants neural network model using Keras (which means to run my code you’ll need to get TensorFlow and Keras in addition to the usual Anaconda packages). Keras produces slightly better results in the log-loss sense. Both models predict something like 78% of past NCAA tournament games correctly.

There are a couple of obvious problems with the model:

• I did not actually train the model on past tournaments, only on regular season games. That’s just because I didn’t take the time.
• Not accounting for injuries.
• NCAA games are not purely “neutral site” games because sometimes game sites are closer to one team than another. I have code for this that I will probably use next year.
• I am splitting the difference between trying to create a good Kaggle submission and trying to create a “good” bracket. There are subtle differences between the two but I will spare you the details.

I will create a github repo for this code…sometime. For now, you can look at the code and raw data files here. The code is in ncaa.py.

2015 NFL Statistics by Player and Team

I have downloaded stats for the recently completed 2015 NFL regular season from yahoo.com, cleaned the data, and saved the data in CSV format. The files are located here. If you prefer a github repository, check here. The column headers should be self-explanatory.

You will find seven CSV files, which you can open in Excel or Google Sheets:

• QB: quarterback data.
• RB: running backs.
• WR: wide receivers.
• TE: tight ends.
• K: kickers. I have broken out attempted and made field goals by distance into separate columns for convenience.
• DEF: defensive stats by team.
• ST: special teams stats by team.

Enjoy!

2016 NCAA Tournament Picks

Every year since 2010 I have used analytics to make my NCAA picks. Here is a link to the picks made by my model [PDF]: the projected Final Four is Villanova, Duke, North Carolina, and Virginia with Villanova defeating North Carolina in the final. (I think my model likes Virginia too much, by the way.)

Here’s how these selections were made. First, the ground rules I set for myself:

• The picks should not be embarrassingly bad.
• I shall spend no more than on this activity (and 30 minutes for this post).
• I will share my code and raw data.

Okay: the model. The model combines two concepts:

1. A “win probability” model developed by Joel Sokol in 2010 as described on Net Prophet.
2. An eigenvalue centrality model based on this post on BioPhysEngr Blog.

The win probability model accounts for margin of victory and serves as preprocessing for step 2. I added a couple of other features to make the model more accurate:

• Home-court advantage is considered: 2.5 points which was a rough estimate I made a few years ago and presumably is still reasonable.
• The win probability is scaled by an adjustment factor which has been selected for best results (see below).
• Recency is considered: more recent victories are weighted more strongly.

The eigenvalue centrality model requires game-by-game results. I pulled four years of game results for all divisions from masseyratings.com (holla!) and saved them as CSV. You can get all the data here. It sounds complicated, but it’s not (otherwise I wouldn’t do it) – the model requires less than 200 lines of Python, also available here. (The code is poor quality.)

How do I know these picks aren’t crap? I don’t. The future is uncertain. But, I did a little bit of backtesting. I trained the model using different “win probability” and “recency” parameters on the 2013-2015 seasons, selecting the combination of parameters that correctly predicted the highest percentage of NCAA tournament games during those seasons, getting approximately 68% of those games right. I don’t know if that’s good, but it seems to be better than applying either the eigenvalue centrality model or the win probability model separately.

In general, picks produced by my models rank in the upper quartile in pools that I enter. I hope that’s the case this year too.

2014 NFL Statistics by Player and Team in Excel

I have downloaded stats for the recently completed 2014 NFL regular season from yahoo.com, cleaned the data, and saved in Excel and CSV formats. The files are located here. The column headers should be self-explanatory.

The Excel workbook has seven worksheets:

• QB: quarterback data.
• RB: running backs.
• WR: wide receivers.
• TE: tight ends.
• K: kickers. I have broken out attempted and made field goals by distance into separate columns for convenience.
• DEF: defensive stats by team.
• ST: special teams stats by team.

The same folder also has separate CSV files for each position, which may be more helpful if you are a coder.

Predicting the 2014-2015 NBA Season

Over the weekend I created a model in Excel to predict the 2014-2015 NBA season. The model simulates the full 82-game schedule, using player Win Shares from the 2013-2014 season to estimate the strength of each team, accounting for roster changes. This model is not perfect, or even particularly sophisticated, but it is interesting. Here are the model’s predictions as of 10/15/2014, with projected playoff teams in bold.

Eastern	W	L	PCT	GB	Home	Road
Cleveland	61	21	0.744	0	31-10	30-12
Toronto	57	25	0.695	4	30-11	27-14
Chicago	49	33	0.598	12	26-15	23-18
Washington	44	38	0.537	17	24-17	21-20
New York	44	38	0.537	17	23-18	21-20
Miami	42	40	0.512	19	22-19	20-21
Detroit	42	40	0.512	19	22-19	20-21
Charlotte	41	41	0.500	20	22-19	19-22
Atlanta	41	41	0.500	20	22-19	19-22
Indiana	37	45	0.451	24	20-21	17-24
Boston	30	52	0.366	31	16-25	14-27
Brooklyn	26	56	0.317	35	14-27	11-30
Orlando	25	57	0.305	36	14-27	12-29
Milwaukee	24	58	0.293	37	14-27	11-30
Philadelphia	14	68	0.171	47	8-33	6-35

Western	W	L	PCT	GB	Home	Road
LA Clippers	57	25	0.695	0	30-11	27-14
San Antonio	57	25	0.695	0	30-11	27-14
Oklahoma City	54	28	0.646	3	29-14	26-15
Phoenix	53	29	0.646	4	28-13	25-16
Golden State	53	29	0.646	4	28-13	25-16
Portland	49	33	0.598	8	26-15	23-18
Houston	47	35	0.573	10	25-16	22-19
Dallas	47	36	0.566	10	24-17	22-19
Memphis	41	41	0.500	16	22-19	19-22
Denver	40	42	0.488	17	21-20	19-22
Minnesota	37	45	0.451	20	20-21	17-24
Sacramento	32	50	0.390	25	17-24	15-26
LA Lakers	31	51	0.378	26	17-24	14-27
New Orleans	27	55	0.329	30	15-26	12-29
Utah	25	58	0.301	33	14-27	11-30

You can download my full spreadsheet here. It’s complicated but not impossible to follow. It does not exactly match the results presented above because I have a messier version that accounts for recent injuries, e.g. Kevin Durant.

The Cavs, Spurs, and Clips are the favorites to win the title in this model (a previous version of this model also had the Thunder in this class, but Kevin Durant is now injured). Comparing these estimates to over-unders in Vegas, the biggest differences are Brooklyn (lower), Indiana (higher), Memphis (lower), Minnesota (higher), New Orleans (lower), Phoenix (higher). If you take the time to read through the methodology at the end of this post, you may be able to see why some of these differences exist. Some are probably reasonable, others may not be.

How It Works

Many of the ingredients for this model were presented in my previous three posts, where I compiled game-by-game results for the 2013-2014 season, built a simple model to predict rookie performance, and tracked roster changes. Now the task is pretty simple: estimate the strength of each team, figure out how unpredictable games are, and then simulate the season using the strengths, accounting for uncertainty. At the end I discuss weaknesses of this model, which if you are a glass-half-full type of person also suggest areas for improvement.

Step 1: Estimate the strength of each team. Team strengths are estimated by adding up the 2013-2014 Win Shares for the top twelve players on each NBA team. In my last post I gave a spreadsheet with Win Shares for all 2013-2014 NBA players based on data from basketball-reference.com. I made three adjustments to this data for the purposes of this analysis:

• Added rookies. I estimated projected 2014-2015 Win Shares for rookies using the logarithmic curve given in this post.
• Accounted for injuries to good players. Kobe Bryant, Derrick Rose, Rajon Rondo, and a couple of other high profile players were injured in 2013-2014. I replaced their Win Share total with the average of the past three seasons, including the season they were injured. Is this reasonable? I don’t know.
• Trimmed to 12. I manually trimmed rosters so that only the 12 players with the highest Win Shares remained.

Adding Win Shares gives an overall “strength rating” for each team.

Step 2: Estimate the unpredictability of game results. Most of the time, a good team will beat a bad team. Most of the time. Can we quantify this more precisely? Sure. From a previous post, I determined that home court advantage is approximately 2.6 points per game. We also found that although the difference in total season wins is a predictor of who will win in a matchup between two teams, it is a rather weak predictor. in other words, bad teams beat good teams quite often, especially at home. For our prediction model we make another simple assumption: every team’s performance over the course of the season varies according to a normal distribution, with the mean of this distribution corresponding to their overall team strength.

Normal distributions are defined by two parameters: mean and standard deviation. If I know what the normal distribution looks like then I can estimate the probability of the home team winning in a matchup: take the difference of their team strengths, then calculate the cdf of the distribution at –2.6 (the home court advantage). But what is the standard deviation? I can estimate it by “replaying” all of the games in the previous season. If I guess a value for the standard deviation, I can calculate win probabilities for all games. If I add up the win probabilities, for say, Boston, then this should sum to Boston’s win total for the season (sadly, 25). So if I want to estimate the standard deviation, all I have to do is minimize the sum of deviations from estimated and actual 2013-2014 win totals. I can do this using Excel’s Solver: it’s a nonlinear minimization problem involving only one variable (the standard deviation).

It turns out that the resulting estimate does a very good job of matching 2013-2014 results:

• The estimated win totals for all teams were within 2 wins of their actual values.
• The estimated home winning percentage matches the actual value quite closely!

Step 3: Determine win totals for the 2014-2015 season. I obtained the 2014-2015 schedule for $5 from nbastuffer.com. Using this schedule, I calculated win probabilities for each game using the team strengths in Step 1 and the standard deviation in Step 2. If I add up the totals for each team, I get their estimated win totals. Voila! Since the prediction is created by looking at each game on the schedule, we also get home and away records, in conference records, and so on. It’s also easy to update the estimate during the season as games are played, players are traded or injured, and so on.

Why this model stinks. The biggest virtue of this model is that it was easy to build. I can think of at least ten potential shortcomings with this model:

1. Win Shares are probably not the best metric for individual and team strength.
2. It assumes that individual performance for 2014-2015 will be the same as 2013-2014. Paul Pierce isn’t getting any younger.
3. It does not account for predictable changes in playing time from season-to-season.
4. 2014-2015 win shares are not normalized to account for players leaving and entering the league.
5. 2014-2015 win shares do not account for positive and negative synergies between players.
6. There is no reason to believe that the standard deviation calculated in Step 2 should be the same for all teams.
7. I have not given any justification for using a normal distribution at all!
8. The vagaries of the NBA schedule are not accounted for. For example, teams play worse in their second consecutive road game.
9. Several teams, including the Philadelphia 76ers, will tank games.
10. Injuries were handled in an arbitrary and inconsistent fashion.

It will be interesting to see how this model performs, in spite of its shortcomings.

NBA Rosters and Team Changes: 2013-2014

I have downloaded statistics for all NBA players from basketball-reference.com, and accounted for roster changes (as of Sunday, October 5).

• Click here to download a CSV file with 2013-2014 NBA rosters.
• Click here to download an XLSX file with 2013-2014 NBA rosters.

The Tm2013 column is a three-letter abbreviation for the player’s 2013-2014 team. For players that played on two or more teams, the entry represents the team for which the player played the most minutes. The Tm2014 is the player’s current NBA team (as of Sunday, October 5) according to nba.com. Rookies are not included in this spreadsheet.

If you’ve read my previous two posts, you may have guessed that I am leading up to a prediction of the upcoming 2014-2015 NBA season. You’d be correct – I will post my model and predictions tomorrow.

In the meantime, you can actually use the spreadsheet above to create a very crude prediction. The last column in this spreadsheet is “win shares”. If you create a pivot table based on Tm2014 and Win Shares, you get the sum of player win shares for current rosters – a crude measure of team strength. Here is what that table looks like:

Team	Sum of WS
CLE	60.7
SAS	59.4
TOR	58.6
LAC	58
IND	56.6
OKC	54.1
GSW	53.8
PHO	52.6
POR	50.8
DAL	48.6
HOU	47.9
WAS	46.8
NYK	44.3
DET	43.9
MEM	43.5
MIA	40.8
CHI	40.4
ATL	38.9
DEN	36.9
MIN	34.3
SAC	32.6
CHA	32.1
NOP	31
LAL	26.9
BRK	26.1
BOS	25.9
UTA	23.8
ORL	23.1
MIL	21.3
PHI	7.2

I can think of at least five weaknesses in this “pivot table model”. Can you?

Predicting NBA Rookie Performance By Draft Position

Nate Silver (and others) have tracked how NBA draft position relates to total career performance, see for example this article. But what about first-year performance?

I pulled two sets of data from basketball-reference.com to answer this question:

• Rookie season Win Shares for all players from 2003 – 2014.
• Draft positions by year from 2004-2014.

I then merged them using Power Query and then created a pivot table to calculate the average number of rookie season “win shares” by draft position. You can download my Excel workbook here. Here is what I found:

The first pick in the draft averages nearly five Win Shares in his rookie season, and while the pattern is irregular, win shares decrease as we get deeper into the draft (duh). (The blip at the end is due to Isaiah Thomas, drafted by the Kings who promptly screwed up by letting him go.) I have drawn a logarithmic trendline which fits the data not-to-shabbily: R^2 of 0.7397. Obviously we could do much better if we considered additional factors related to the player (such as their college performance) and team (the strength of teammates playing the same position, who will compete with the rookie for playing time). Here are the averages for the first 30 draft positions:

Draft POSITION	Win Shares
1	4.96
2	2.69
3	2.96
4	4.14
5	2.23
6	1.84
7	3.36
8	1.68
9	2.59
10	1.52
11	0.84
12	1.51
13	1.48
14	1.36
15	1.64
16	1.19
17	2.37
18	1.02
19	0.71
20	1.09
21	1.74
22	2.14
23	1.54
24	2.29
25	0.98
26	1.23
27	1.08
28	0.40
29	0.54
30	0.94
31	0.79

NBA Game Results: 2013-2014

The NBA preseason is in full swing! For those of you who like to fool around with data, I have prepared a CSV file with game-by-game results for the 2013-2014 season. The data was downloaded from basketball-reference.com using Power Query and cleaned up (see below).

• Click here to download NBA 2013-2014 game results in CSV format.
• Click here to download NBA 2013-2014 game results in XSLX format.

The format is simple:

• Date = When the game was played
• Visitor = three letter abbreviation of the visiting team
• VisitorPts = visiting team score
• VisitorSeasonWins = number of wins by the visiting team for the entire season
• Home = TLA of home team
• HomePts = home team score
• HomeSeasonWins = number of wins by the home team for the entire season
• WinMargin = HomeSeasonWins – VisitorSeasonWins
• Margin = HomePts – VistorPts

I include the number of wins for each team in the files because I wanted to see how often good teams beat bad teams. The diagram below plots the difference in total wins for teams against the margin of victory. I have used the trendline feature in Excel to verify that while (by definition) good teams beat bad ones frequently, the variability is quite high. Notice the R^2 value.

The intercept for the trendline is 2.5967, which represents the home court advantage in points. In a future post I hope to use this data to make some predictions about the upcoming NBA season.

Enjoy!

Fantasy Football Ratings 2014

I have prepared fantasy football ratings for the 2014 NFL season based on the data from last year’s season. I hope you will find them useful! You can download the ratings here.

These ratings are reasonable but flawed. The strengths of the ratings are:

• They are based on player performance from the 2013 season, using a somewhat standard fantasy scoring system. (6 points for touchdowns, -2 for turnovers, 1 point per 25 passing yards, 1 point per 10 passing yards, and reasonable scoring for kickers.)
• The ratings are comparable across positions because the rating means the expected number of fantasy points that a player will score compared to a “replacement level” player for that position. I call this “Fantasy Points Over Replacement”: FPOR.
• Touchdowns are a key contributor fantasy performance, but they are fickle: they often vary dramatically between players of the same overall skill level, and even between seasons for the same player. In a previous post I showed that passing and rushing touchdowns are lognormally distributed against the yards per attempt. I have accounted for this phenomenon in the rankings. Loosely speaking, this means that a player that scored an unexpectedly high number of touchdowns on 2013 will be projected to score fewer in 2014.
• The ratings do a rough correction for minor injuries. Players that play in 10 or more games in a season are rated according to the number of points they score per game. Therefore a player who missed, say, two games in 2013 due to injury is not disadvantaged compared to one that did not.

There are several weaknesses:

• I have data for several previous seasons but do not use it. This would stabilize the ratings, and we could probably account for maturation / aging of players from season-to-season.
• Rookies are not rated.
• We do not account for team changes. This factor is often very important as a backup for one team may end up as a starter for another, dramatically affecting fantasy performance. (I actually have a pretty good heuristic for accounting for this, but I have not implemented it in Python…only SAS and I no longer have access to a SAS license.)
• Players who missed a large portion of the 2013 season are essentially penalized for 2014, even if they are expected to return fully.
• I have not rated defense/special teams.

You may want to adjust the rankings accordingly. Here are the top 25 rated players (again, the full ratings are here):

Name	Position	RawPts	AdjPts	FPOR
LeSean McCoy	RB	278.6	199.3125	85.96875
Jamaal Charles	RB	308	194	80.65625
Josh Gordon	WR	218.6	176.3571429	71.57142857
Matt Forte	RB	261.3	177.46875	64.125
Calvin Johnson	WR	219.2	157.7142857	52.92857143
DeMarco Murray	RB	205.1	155.4642857	42.12053571
Reggie Bush	RB	185.2	153.4285714	40.08482143
Jimmy Graham	TE	217.5	113.90625	35.90625
Antonio Brown	WR	197.9	140.53125	35.74553571
Knowshon Moreno	RB	236.6	148.6875	35.34375
Adrian Peterson	RB	203.7	147.5357143	34.19196429
Marshawn Lynch	RB	239.3	145.59375	32.25
Le’Veon Bell	RB	171.9	142.9615385	29.61778846
Demaryius Thomas	WR	227	134.0625	29.27678571
A.J. Green	WR	208.6	133.6875	28.90178571
Eddie Lacy	RB	207.5	141.5	28.15625
Andre Johnson	WR	170.7	131.90625	27.12053571
Alshon Jeffery	WR	182.1	131.34375	26.55803571
Peyton Manning	QB	519.98	172.48125	22.18125
Stephen Gostkowski	K	176	176	22
Drew Brees	QB	435.68	172.2	21.9
Ryan Mathews	RB	184.4	133.5	20.15625
DeSean Jackson	WR	187.2	124.875	20.08928571
Pierre Garcon	WR	162.6	124.3125	19.52678571
Jordy Nelson	WR	179.4	123.1875	18.40178571

FPOR is the adjusted, cross-position score described earlier. RawPts is simply 2013 fantasy points. AdjPts are the points once touchdowns have been “corrected” and injuries accounted for.

We will see how the ratings work out! If I have time I will post a retrospective once the season is done.