## Player Analytics Fundamentals: Part 5 – Modeling 102

In Part 4 of the series we started talking about what should be in the analyst’s tool kit.  I advocated for linear regression to be the primary tool.  Linear regression is (relatively) easy to implement and produces equations that are (relatively) easy to understand.  I also made the point that linear regression is best suited for predicting continuous measures and used the example of predicting the number of touchdown passes thrown by a rookie QB.

But not everything we want to predict is going to be a continuous variable.  Since we are talking about predicting quarterback performance, maybe we prefer a metric that is more discrete such as whether a player becomes a starter.  Can we still use linear regression?  Maybe.

Let’s return to the example from last time.  The task was to predict professional (rookie year) success based on college level data.  We assumed that general managers can obtain data on the number of games won as a college player, whether the player graduated (or will graduate) and the player’s height.

Our initial measure of pro success was touchdown passes.  We then specified a regression model using the following equation.

But let’s say that we don’t like the TD passes metric.  Maybe we don’t like it because we think TD passes are more related to wide receiver talent than to the quality of the QB.  Rather than use TDs as our dependent variable we want to use whether a player becomes a starter.  This is also an interesting metric as it captures whether the player was selected by a coaching staff to be the primary quarterback.  This is a nice feature as the metric includes some measure of human expertise.  I’ll leave criticism to the readers as an exercise.

This leads us to the following equation:

One issue we have to address before we estimate this model is how we define the term starter.  In a statistical model we need to convert the word or category of “starter” into a number.  In this case, the easy solution is to treat players that became starters as 1’s and players that did not as 0’s.  As a second exercise – what would we do if we had three categories (did not play, reserve, starter)?

Let’s pretend we estimated the preceding model and obtained the following equation:

We can use the equation to “score” or “rate” our imaginary prospects from last time (Lewis Michaels and Manny Trips).  In terms of the input data, Lewis won 40 college games, graduated and is 5′ 10”.  Plugging Michael’s data into the equation gives us a score of .22.  The analysis that we have performed is commonly termed a linear probability model.  A simple interpretation of this result is that the expected probability of Michaels (or better said a prospect with Michaels statistics) becoming a starter is 22%.

So far so good.

Our second prospect is Manny Trips out of Stanford.  Manny won 10 games, failed to graduate and is 6’ tall.  For Manny the prediction would be -12.8%.  This is the big problem with using linear regression to predict binary (Yes/No) outcomes.  How do we interpret a negative probability?  Or a probability that is greater than 1?

So what do we do next?  I think we have two options.  We can ignore the problem.  If the goal is just to rank prospects then maybe we don’t care very much.  In this case, we just care about the relative scores not the actual prediction.  If we are just using analytics to screen QB prospects or to provide another data point then maybe our model is good enough.  The level of investment in a modeling project should be based on how the model is going to be used.  In many or most sports applications I would lean to simpler less complicated models.

Our second option is to move to a more complicated model.  There are a host of models available for categorical data.  We can use a binary logit or Probit model for the case of a binary system as above.  If the categories have a natural ordering to them (never played, reserve, starter) then we can use an ordered logit.  If there is no order to the categories, then we can use a multinomial logit.  I’m still debating on how much attention I should pay to these models.  Having a tool to deal with categorical variables can be invaluable but there is a cost.  The mathematics become more complex, estimation of the model requires specialized software and interpretation of the model becomes less intuitive.

I think I will discuss the binary logit next time.

## Player Analytics Fundamentals: Part 4 – Statistical Models

Today’s post introduces the topic of statistical modeling.  This is, maybe, the trickiest part of the series to write.  The problem is that mastering the technical side of statistical analysis usually takes years of education.  And, more critically, developing the wisdom and intuition to use statistical tools effectively and creatively takes years of practice.  The goal of this segment is to point people in the right direction, more than to provide detailed instruction.  That said – I can adjust if there is a call for more technical material.  (If you want to start from the beginning parts 1, 2 and 3 are a click away.)

Let’s start with a simple point.  The primary tool for every analytics professional (sports or otherwise) should be linear regression.  Linear regression allows the analyst to quantify the relationship between some focal variable of interest (dependent measure or DV) and a set of variables that we think drive that variable (independent variables).  In other words, regression is a tool that can produce an equation that shows how some inputs produce an outcome of interest.  In the case of player analytics, this might be a prediction of future performance based on a player’s past statistics or physical attributes.

To make this more concrete, let’s say we want to do an analysis of rookie quarterback performance (we’ve been talking a bit about QB metrics so far in the series).  Selecting QBs involves significant uncertainty.  The transition from the college game to the pro game requires the QB to be able to deal with more complex offensive systems, more sophisticated defenses and more talented opposing players.  The task of the general manager is to identify prospects that can successfully make the transition.

Data and statistical analysis can potentially play a part in this type of decision.  The starting point would be the idea that observable data on college prospects can help predict rookie year performance.  As a starting point let’s assume that general managers can obtain data on the number of games won as a college player, whether the player graduated (or will graduate) and the player’s height.  (We just might be foreshadowing a famous set of rules for drafting quarterbacks).

The other key decision for a statistical analysis of rookie QB performance versus college career and physical data is a performance metric.  We could use the NFL passer rating formula that we have been discussing.  Or we could use something else.  For example, maybe the number of TD passes thrown as a rookie.  This metric is interesting as it captures something about playing time and ability to create scores.

Touchdowns are  also a metric that “fits” linear regression.  Linear regression is best suited to the analysis of quantitative variables that vary continuously.  The number of touchdowns we observe in data will range from zero to whatever the is the rookie TD record.  In contrast, other metrics such as whether the player becomes a starter or a pro bowler are categorical variables.  There are other techniques that are better for analyzing categorical variables.  (if you are a stats jockey and are objecting to the last couple of statements please see the note below).

The purpose of regression analysis is to create an equation of the following form:

This equation says that TD passes are a function of college wins, graduation and height.  The βs are the weights that are determined by the linear regression analysis.  Specifically, linear regression determines the βs that best fits the data.  This is the important point.  The weights or βs are determined from the data.  To illustrate how the equation works lets imagine that we estimated the regression model and obtained the following equation.

This equation says that we can predict rookie TD passes by plugging in each player’s data related to college wins, graduation and height.  It also says that a history of winning is positively related to TDs and graduation also is a positive.  The coefficient for height is zero.  This indicates that height is not a predictor of rookie TDs (I’m making these number up – height probably matters).  One benefit of developing a model is that we let the data speak.  Our “expert” judgment might be that height matters for quarterbacks.  The regression results can help identify decision biases if the coefficients don’t match the experts predictions.  I am neglecting the issue of significance for now – just to keep the focus on intuition.

Let’s say we have two prospects.  Lewis Michaels out of the University of Illinois who won 40 college games (hypothetical and unrealistic), graduated (in engineering) and is 5’10” (a Flutiesque prospect).  Our second prospect is Manny Trips out of Duke.  Manny won 10 games, failed to graduate and is 6’ tall.  Michaels would seem to be the better prospect based on the available data.  The statistical model allows us to predict how much better.

We make our predictions by simply plugging our player level data into the equation.  We would predict Lewis would throw 10 TDs in his rookie year (1+.1*40+5*1+0*70).  For Manny the prediction would be 2 TDs.  For now, I am just making up the coefficients (βs).  In a later entry I will estimate the model using some data on actual NFL rookie QB performance.

Regression has its shortcomings and many analysts love to object to regression analyses.  But for the most part, linear regression is a solid tool for analyzing patterns in data.  It’s also relatively easy to implement.  We can run regressions in Excel!  We shouldn’t underestimate how important it is to be able to do our analyses in standard tools like Excel.

I will extend our tool kit in a future entry.  I briefly mentioned categorical variables such as whether or not a player is a starter.  For these types of Yes/No (starter or not a starter) there is a tool called logistic regression that should be in our repertoire.

*One reason this note is tricky is that I’m trying to get the right balance and tone.  I can already hear the objections.  Lets save these for now.  For example, readers do not need to alert me to the fact that TDs are censored at zero.  Or that there is a mass point at zero because many rookies don’t play.  Or that TDs are counted in discrete units so maybe a Poisson model is more appropriate.  You get the idea.  There are many ways to object to any statistical model.  The real question isn’t whether a model is perfect.  The real question should be whether the model provides value.

## Player Analytics Fundamentals: Part 3 – Metrics, Experts and Models

Last time I introduced the topic of player “metrics.” (If you want to get caught up you can start with Part 1 and Part 2 of the series.)  As I noted, determining the right metric is perhaps the most important task in player analytics.  It’s almost too obvious of a point to make – but the starting point for any analytics project should be deciding what to measure or manage.  It’s a non-trivial task because while the end goal (profit, wins) might be obvious, how this goal relates to an individual player (or strategy) may not be.

However, before I get too deep into metric development, I want to take a small detour and talk briefly about statistical models.  We won’t get to modeling in this entry – the goal is to motivate the need for statistical models!  If we are doing player analytics we need some type of tool kit to move us from mere opinion to fact based arguments.

To illustrate what I mean by “opinion” lets consider the example of rating quarterbacks.  In the previous entry, I presented the Passer Rating Formula used to rate NFL quarterbacks.  As a quick refresher let’s look at this beast one more time.The formula includes completion percentage (accuracy), yards per attempt (magnitude), touchdowns (ultimate success) and interceptions (failures).  Let’s pretend for a second that the formula only contained touchdowns and interceptions (just to make it simple).  The question then becomes how much should we weight touchdowns per attempt relative to interceptions per attempt?  The actual formula is hopelessly complex in some ways – we have fractional weights and statistics in different units – so let’s take a step back from the actual formula.

Imagine we have two experts proposing Passer Rating statistics that are based on touchdowns and interceptions only.  One expert might say that touchdowns per attempt are twice as important as interceptions.  We will label this “expert” created formula as ePR1 for expert 1 Passer rating.  The formula would be:

Maybe this judgment would be accompanied by some logic along the lines of “touchdowns are twice as important because the opposing team doesn’t always score as the result of an interception.”

However, the second expert suggests that the touchdowns and interceptions should be weighted equally.  Maybe the logic of the second expert is that interceptions have both direct negative consequences (loss of possession) and also negative psychological effects (loss of momentum), and should therefore be weighted more heavily.  The formula for expert 2 can be written as:

I suspect that many readers (or a high percentage of a few readers) are objecting to developing metrics using this approach.  The approach probably seems arbitrary.  It is.  I’ve intentionally presented things in a manner that highlights the subjective nature of the process.  I’ve reduced things down to just 2 stats and I’ve chosen very simple weights.  But the reality is that this is the basic process through which novices tend to develop “new” or “advanced” statistics.  In fact, it is still very much a standard practice.  The decision maker or supporting analysts gather multiple pieces of information and then use a system of weights to determine a final “grade” or evaluation.

The question then becomes which formula do we use?  Both formulas include multiple pieces of data and are based on a combination of logic and experience.  I am ignoring (for the moment) a critical element of this topic – the issue of decision biases.  In subsequent entries, I’m going to advocate for an approach that is based on data and statistical models.  Next time, we will start to talk more about statistical tools.

## Player Analytics Fundamentals: Part 2 – Performance Metrics

I want to start the series with the topic of “Metric Development.”  I’m going to use the term “metric” but I could have just as easily used words like stats, measures or KPIs.  Metrics are the key to sports and other analytics functions since we need to be sure that we have the right performance standards in place before we try and optimize.  Let me say that one more time – METRIC DEVELOPMENT IS THE KEY.

The history of sports statistics has focused on so called “box score” statistics such as hits, runs or RBIs in baseball.  These simple statistics have utility but also significant limitations.  For example, in baseball a key statistic is batting average.  Batting average is intuitively useful as it shows a player’s ability to get on base and to move other runners forward.  However, batting average is also limited as it neglects the difference between types of hits.  In a batting average calculation, a double or home run is of no greater value than a single.  It also neglects the value of walks.

These short-comings motivated the development of statistics like OBPS (on base plus slugging).  Measures like OBPS that are constructed from multiple statistics are appealing because they begin to capture the multiple contributions made by a player.  On the downside these types of constructed statistics often have an arbitrary nature in terms of how component statistics are weighted.

The complexity of player contributions and the “arbitrary nature” of how simple statistics are weighted is illustrated by the formula for the NFL quarterback ratings.

This equation combines completion percentage (COMP/ATT), yards per attempt (YARDS/ATT), touchdown rate (TD/ATT) and interception rate (INT/ATT) to arrive at a single statistic for a quarterback.  On the plus side the metric includes data related to “accuracy” (completion percentage) to “scale” (yards per), to “conversion” (TDs), and to “failures” (interceptions).  We can debate if this is a sufficiently complete look at QBs (should we include sacks?) but it does cover multiple aspects of passing performance.   However, a common reaction to the formula is a question about where the weights come from.  Why is completion rate multiplied by 5 and touchdown rates multiplied by 20?

Is it a great statistic?  One way to evaluate is via a quick check of the historical record.  Does the historical ranking jive with our intuition?  Here is a link to historical rankings.

Every sport has examples of these kinds of “multi-attribute” constructed statistics.  Basketball has player efficiency metrics that involve weighting a player’s good events (points, rebounds, steals) and negative outcomes (turnovers, fouls, etc…).  The OBPS metric involves an implicit assumption that “on base percentage” and “slugging” are of equal value.

One area I want to explore is how we should construct these types of performance metrics.  This is a discussion that involves some philosophy and some statistics.  We will take this piece by piece and also show a couple of applications along the way.

## Player Analytics Fundamentals: Part 1

Each Spring I teach courses on Sports Analytics.  These courses include both Marketing Analytics and On-Field Analytics.  The “Blog” has tended to focus on the Marketing of Fan side.  Moving forward, I think the balance is going to change a bit.  My plan is to re-balance the blog to include more of the on-field topics.

Last year I published a series of posts related to the fundamentals of sports analytics.  This material is relevant to both the marketing and the team performance sides of sports analytics.  This series featured comments on organizational design and decision theory.

This series is going to be a bit different than the team and player “analytics” that we see on the web.  Rather than present specific studies, I am going to begin with some fundamental principles and talk about a “general” approach to player analytics.  There is a lot of material on the web related to very specific sports analytics questions.  Analytics can be applied to baseball, football, soccer and every other sport.  And within each of these games there are countless questions to be addressed.

Rather than contribute to the littered landscape, I want to talk about how I approach sports analytics questions.  In some ways, this series is the blue print I use for thinking about sports analytics in the classroom.  My starting point is that I want to provide skills and insights that can be applied to any sport.  So we start with the fundamentals and we think a lot about how to structure problems.  I want to supply grounded general principles that can be applied to any player analytics problem.

So what’s the plan?  At a high level, sports analytics are about prediction.  We will start with a discussion about what we should be predicting.  This is a surprisingly complex issue.  From there we will talk a little bit about different statistical models.  This won’t be too bad, because I’m a firm believer in using the simplest possible models.  The second half of the series will focus on different types of prediction problems.  These will range from predicting booms and busts, to a look at how to do “comparables” in a better fashion.  In terms of the data, I think it will be a mix of football and the other kind of football.

## Analytics, Trump, Clinton and the Polls: Sports Analytics Series Part 5.1

Recent presidential elections (especially 2008 and 2012) have featured heavy use of analytics by candidates and pundits.  The Obama campaigns were credited with using micro targeting and advanced analytics to win elections. Analysts like Nate Silver were hailed as statistical gurus who could use polling data to predict outcomes.  In the lead up to this year’s contest we heard a lot about the Clinton campaign’s analytical advantages and the election forecasters became regular parts of election coverage.

Then Tuesday night happened.  The polls were wrong (by a little) and the advanced micro targeting techniques didn’t pay off (enough).

Why did the analytics fail?

First the polls and the election forecasts (I’ll get to the value of analytics next week). As background, commentators tend to not truly understand polls.  This creates confusion because commentators frequently over- and misinterpret what polls are saying.  For example, whenever “margin of error” is mentioned they tend to get things wrong.  A poll’s margin of error is based on sample size.  The common journalist’s error is that when you are talking about a collection of polls the sample size is much larger than an individual poll with a margin of error of 3% or 4%.  When looking at an average of many polls the “margin of error” is much smaller because the “poll of polls” has a much larger sample size.  This is a key point because when we think about the combined polls it is even more clear that something went wrong in 2016.

Diagnosing what went wrong is complicated by two factors.  First, it should be noted that because every pollster does things differently we can’t make blanket statements or talk in absolutes.  Second, diagnosing the problem requires a deep understanding of the statistics and assumptions involved in polling.

In the 2016 election my suspicion is that a two things went wrong.  As a starting point – we need to realize that polls include strong implicit assumptions about the nature of the underlying population and about voter passion (rather than preference).  When these assumptions don’t hold the polls will systematically fail.

First, most polls start with assumptions about the nature of the electorate.  In particular, there are assumptions about the base levels of Democrats, Republicans and Independents in the population.  Very often the difference between polls relates to these assumptions (LA Times versus ABC News).

The problem with assumptions about party affiliation in an election like 2016, is that the underlying coalitions of the two parties are in transition.  When I grew up the conventional wisdom was that the Republicans were the wealthy, the suburban professionals, and the free trading capitalists while the democrats were the party of the working man and unions.  Obviously these coalitions have changed.  My conjecture is that pollsters didn’t sufficiently re-balance.  In the current environment it might make sense to place greater emphasis on demographics (race and income) when designing sampling segments.

The other issue is that more attention needs to be paid towards avidity / engagement/ passion (choose your own marketing buzz word).  Polls often differentiate between likely and registered voters.  This may have been insufficient in this election. If Clinton’s likely voters were 80% likely to show up and Trumps were 95% likely then having a small percentage lead in a preference poll isn’t going to hold up in an election.

The story of the 2016 election should be something every analytics professional understands.  From the polling side the lesson is that we need to understand and question the underlying assumptions of our model and data.  As the world changes do our assumptions still hold?  Is our data still measuring what we hope it does?  Is a single dependent measure (preference versus avidity in this case) enough?

## Moving towards Modeling & Lessons from Other Arenas: Sports Analytics Series Part 5

The material in this series is derived from a combination of my experiences in sports applications and my experiences in customer analysis and database marketing.  In many respects, the development of an analytics function is similar across categories and contexts.  For instance, a key issue in any analytics function is the designing and creation of an appropriate data structure.  Creating or acquiring the right kinds of analytics capabilities (statistical skills) is also a common need across industries.

A need to understand managerial decision making styles is also common across categories.  It’s necessary to understand both the level of interest in using analytics and also the “technical level” of the decision makers.  Less experienced data scientists and statistician have a tendency to use too complicated of methods.  This can be a killer.  If the models are too complex they won’t be understood and then they won’t be used.  Linear regression with perhaps a few extensions (fixed effects, linear probability models) are usually the way to go.    Because sports organizations have less history in terms of using analytics the issue of balancing complexity can be especially challenging.

A key distinction between many sports and marketing applications is the number of variables versus the number of observations.  This is an important point of distinction between sports and non-sports industries and it is also an important issue for when we shift to discussing modeling in a couple of weeks.  When I use the term variables I am referencing individual elements of data.  For example, an element of data could be many different things such as a player’s weight or the number of shots taken or the minutes played.  We might also break variables into the categories of dependent variables (things to explain) versus independent variables (things to explain with).  When I use the term observations I am talking about “units of analysis” like players or games.

In many (most) business contexts we have many observations.  A large company may have millions of customer accounts.  There may, however, be relatively few explanatory variables.  The firm may have only transaction history variables and limited demographics.  Even in sports marketing a team interested in modeling season ticket retention may only have information such as the number of tickets previously purchased, prices paid and a few other data points.  In this same example the team may have tens of thousands of season ticket holders.  If we think of this “information” as a database we would have a row for every customer account (several thousand rows) and perhaps ten or twenty columns of variables related to each customer (past purchases and marketing activities).

One trend is that the number of explanatory variables is expanding in just about every category. In marketing applications we have much more purchase detail and often expanded demographics and psychographics.  However, the ratio of observations to columns usually still favors the observations.

In sports we (increasingly) face a very different data environment.  Especially, in player selection tasks like drafting or free agent signings.  The issue in player selection applications is that there are relatively few player level observations.  In particular, when we drill down into specific positions we often find ourselves having only tens or hundreds or player histories (depending on far back we want to go with the data).  In contrast, we may have an enormous number of variables per player.

We have historically had many different types of “box score” type stats but now we have entered into the era of player tracking and biometrics.  Now we can generate player stats related to second-by-second movement or even detailed physiological data.  In sports ranging from MMA to soccer to basketball the amount of variables has exploded.

A big question as we move forward into more modeling oriented topics is how do we deal with this situation?

## Decision Biases: Sports Analytics Series Part 4

One way to look at on-field analytics is that it is a search for decision biases.  Very often, sports analytics takes the perspective of challenging the conventional wisdom.  This can take the form of identifying key statistics for evaluating players.  For example, one (too) simple conclusion from “Moneyball” would be that people in baseball did not adequately value the value of being walked and on-base percentage.  The success of the A’s (again – way oversimplifying) was based on finding flaws in the conventional wisdom.

Examples of “challenges” to conventional wisdom are common in analyses of on-field decision making.  For example, in past decades the conventional wisdom was that it is a good idea to use a sacrifice bunt to move players into scoring position or that it is almost always a good idea to punt on fourth down.  I should note that even the term conventional wisdom is problematic as there have likely always been long-term disagreements about the right strategies to use at different points in a game.  Now, however, we are increasingly in a position to use data to determine the right or optimal strategies.

As we discussed last time, humans tend to be good at overall or holistic judgments while models are good at precise but narrow evaluations.  When the recommendations implied by the data or model are at odds with how decisions are made, there is often an opportunity for improvement.  Using data to find types of undervalued players or to find beneficial tactics represents an effort to correct human decision making biases.

This is an important point.  Analytics will almost never outperform human judgment when it comes to individuals.  What analytics are useful for is helping human decision makers self-correct.  When the model yields different insights than the person it’s time to drill down and determine why.  Maybe it’s a shortcoming of the model or maybe it’s a bias on the part of the general manager.

The term bias has a negative connotation.  But it shouldn’t for this discussion.  For this discussion a bias should just be viewed as a tendency to systematically make decisions based on less than perfect information.

The academic literature has investigated many types of biases.  Wikipedia provides a list of a large number of biases that might lead to decision errors.  This list even includes the sports inspired “hot-hand fallacy” which is described as a “belief that a person who has experienced success with a random event has a greater chance of further success in additional attempts.”  From a sports analytics perspective the question might be asked is whether the hot-hand is a real thing or just a belief. The analyst might be interested in developing a statistical test to assess whether a player on a hot streak is more likely to be successful on his next attempt.  This model would have implications for whether a coach should “feed” the hot hand.

Academic work has also looked at the impact of factors like sunk costs on player decisions.  The idea behind “sunk costs” is that if costs have already been incurred then those costs should not impact current or future decision making.  In the case of player decisions “sunk costs” might be factors like salary or when the player was drafted.  Ideally, a team would use the players with the highest expected performance.  A tendency towards playing individuals based on the past would represent a bias.

Other academic work has investigated the idea of “status” bias.  In this case the notion is that referees might call a game differently depending on the players involved.  It’s probably obvious that this is the case.  Going old school for a moment, even the most fervent Bulls fans of the 90’s would have to admit that Craig Ehlo wouldn’t get the same calls as Michael Jordan.

In these cases, it is possible (though tricky) to look for biases in human decision making.  In the case of sunk costs investigators have used statistical models to examine the link between when a player was drafted and the decision to play an athlete (controlling for player performance).  If such a bias exists, then the analysis might be used to inform general managers of this trait.

In the case of advantageous calls for high profile players, an analysis might lead to a different type of conclusion. If such a bias exists, then perhaps leagues should invest more heavily in using technology to monitor and correct referee’s decisions.

• People suffer from a variety of decision biases. These biases are often the result of decision making heuristics or rules of thumbs.
• One use of statistical models is to help identify decision making biases.
• The identification of widespread biases is potentially of great value as these biases can help identify imperfections in the market for players or improved game strategies.

## A Quick Example of the Limitations of Analytics: Sports Analytics Series Part 3.1

In Part 3 we started to talk about the complementary role of human decision makers and models.  Before we get to the next topic – Decision Biases – I wanted to take a moment to present an example that helps illustrate the points being made in the last entry.

I’m going to make the point using an intentionally nontraditional example.  Part of the reason I’m using this example is that I think it’s worthwhile to think about what might be “questionable” in terms of the analysis.  So rather than look at some well-studied relationships in contexts like NFL quarterbacks or NBA players, I’m going to develop a model of Fullback performance in Major League Soccer.

To keep this simple, I’m going to try and figure out the relationship between a player’s Plus-Minus statistic and a few key performance variables.  I’m not going to provide a critique of Plus-Minus but I encourage everyone to think about the value of such a statistic in soccer in general and for the Fullback position in particular.  This is an important exercise for thinking about combining statistical analysis and human insight.  What is the right bottom line metric for a defensive player in a team sport?

The specific analysis is a simple regression model that quantifies the relationship between Plus-Minus and the following performance measures:

• % of Defensive Ground Duels Won
• % of Defensive Aerial Duels Won
• Tackling Success Rate (%)
• % of Successful Passes in the Opponents ½

This is obviously a very limited set of statistics.  One thing to think about is that if I am creating this statistical model with even multiple years of data, I probably don’t have very many observations.  This is a common problem.  In any league there are usually about 30 teams and maybe 5 players at any position.  We can potentially capture massive amounts of data but maybe we only have 150 observations a year.  Note that in the case of MLS fullbacks we have less than that.  This is important because it means that in sports contexts we need to have parsimonious models.  We can’t throw all of our data into the models because we don’t have enough observations.

The table below lists the regression output.  Basically, the output is saying that % Successful passes in the opponent’s half is the only statistic that is significantly and positively correlated with a Fullback’s Plus-Minus statistic.

 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > |t| Intercept 1 -1.66764 0.41380 -4.03 <.0001 % Defensive Ground Duels Won 1 -0.00433 0.00314 -1.38 0.1692 % Def Aerial Duels Won 1 -0.00088542 0.00182 -0.49 0.6263 Tackling Success Percentage 1 0.39149 0.25846 1.51 0.1305 % Successful Passes in Opponents 1/2 1 0.02319 0.00480 4.83 <.0001

The more statistically oriented reader might be asking the question of how well does this model actually fit the data.  What is the R-Square?  It is small.  The preceding model explains about 5% of the variation in Fullback’s Plus-Minus statistics.

And that is the important point.  The model does its job in that it tells us there is a significant relationship between passing skill and goal differential.  But it is far from a complete picture.  The decision maker needs to understand what the model shows.  However, the decision maker also needs to understand what the model doesn’t reveal.   This model (and the vast majority of other models) is inherently limited.  Like I said last time – the model is a decision support tool / not something that makes the decision.

Admittedly I didn’t try to find a model that fits the data really well.  But I can tell you that in my experience in sports and really any context that involves predicting or explaining individual human behavior, the models usually only explain a small fraction of variance in performance data.

## Questioning the Value of Analytics: Sports Analytics Series Part 3

Continuing the discussion about organizational issues and challenges, a fundamental issue is understanding and balancing the relative strengths and weaknesses of human decision makers and mathematical models.  This is an important discussion because before diving into specific questions related to predicting player performance it’s worthwhile to first think about how modeling and statistics should fit into an overall structure for decision making.  The short answer is that analytics should serve as a complement to human insight.

The “value” of analytics in sports has been the topic of debate.  A high profile example of this occurred between Charles Barkley and Daryl Morey.  Barkley has gone on record questioning the value of analytics.

“Analytics don’t work at all. It’s just some crap that people who were really smart made up to try to get in the game because they had no talent. Because they had no talent to be able to play, so smart guys wanted to fit in, so they made up a term called analytics.  Analytics don’t work.”

The quote reflects an extreme perspective and it is legitimate to question whether Charles Barkley has the background to assess the value of analytics (or maybe he does, who knows?).  But, I do think that Barkley’s opinion does have significant merit.

In much of the popular press surrounding books like Moneyball or The Extra 2% analytics often seem like a magic bullet.  The reality is that statistical models are better viewed as decision support aids.  Note that I am talking about the press rather than then books.

The fundamental issue is that models and statistics are incomplete.  They don’t tell the whole story.  A lot of analytics revolves around summarizing performance into statistics and then predicting how performance will evolve. Defining a player based on a single number is efficient but it can only capture a slice of the person’s strengths and weaknesses.  Predicting how human performance will evolve over time is a tenuous proposition.

What statistics and models are good at is quantifying objective relationships in the data.  For example, if we were interested in building a model of how quarterback performance translates from college to professional football we could estimate the mathematical relationship between touchdown passes at the college level and touchdown passes at the pro level.  A regression model would give us the numerical patterns in the data but such a model would likely have little predictive power since many other factors come in to play.

The question is whether the insights generated from analytics or the incremental forecasting power actually translate into something meaningful.  They can.  But the effects may be subtle and they may play out over years.  And remember we are not even considering the financial side of things.  If the best predictive models improve player evaluations by a couple of percent maybe it translates to your catcher having a 5% higher on base percentage or your quarterback having a passer rating that is 1 or 2 points higher.  These things matter.  But are they dwarfed by being able to throw 10 or 20 million more into signing a key player?

If the key to winning a championship is having a couple of superstars.  Then maybe analytics don’t matter much.  What matters is being able to manage the salary cap and attract the talent.  But maybe the goal is to make the playoffs in a resource or salary cap constrained environment.  Then maybe spending efficiently and generating a couple of extra is the objective.  In this case analytics can be a difference maker.