The Value of Simplicity

In The Wages of Wins we present measures of performance for both NBA players and NFL quarterbacks.  In presenting these measures we noted our objectives.  We wished to have metrics that were accurate and simple.  Obviously accuracy is important.  Performance measures are meant to tell us how individual players impact team outcomes, so it makes sense to construct metrics that connect what a player does to wins. 

But why is simplicity important?

One issue is Occam’s Razor, which can be expressed as “when you have two competing theories which make exactly the same predictions, the one that is simpler is the better.”

Occam’s Razor is certainly one of the guiding principles we employ in developing our models.  And for those who are interested, a discussion of the history behind this idea can be found HERE.

Beyond Occam’s Razor is the issue of accessibility.  If two measures provide similar evaluations of player performance, the simple measure is likely to be most accessible to the largest number of fans. 

To illustrate this point, let’s review what we said in the book about performance measures in baseball.   

How should one measure the value of a hitter’s production in baseball?  Alan Schwarz in The Numbers Game detailed the history of performance metrics in baseball.  This history begins with batting average – or hits divided by at-bats.  This measure has been around since the 19th century.  Batting average is a very simple measure, but since it treats all hits the same, people suspected pretty early on that this was not the most accurate metric.  And simple regression analysis confirms this suspicion.  Batting average only explains 70% of the variation in the runs a team scores. 

Slugging percentage and on-base percentage also are fairly simple to calculate.  And people like Dick Cramer, Pete Palmer, and Allen Barra have found that multiplying slugging average and on-base percentage together produced a measure highly correlated with runs scored.  In fact, 91% of runs scored could be explained by multiplying slugging average and on-base percentage.  More commonly, though, people just add together slugging percentage and on-base percentage, which give you OPS.  OPS explains 90% of the variation in a team’s runs scored. 

Pete Palmer also developed a measure called linear weights.  This metric involves regressing a team’s runs scored on singles, doubles, triples, home runs, and a collection of additional statistics like walks, outs, and stolen bases.  Obviously this is quite a bit more complicated than OPS, both to uncover the value of the various statistics and employing these values in measuring the productivity of a batter.  All that effort, though, allows one to explain 94% of the variation in runs scored.

In the Wages of Wins all this analysis was detailed.  Additionally, we discuss the correlation between each measure.  Specifically, we found that there is a 97% correlation between a ranking of hitters based on OPS and another ranking based on a linear weights model.

Okay, OPS and linear weights are telling basically the same story.  What’s the point?  OPS is a simple measure while linear weight is more complex.  People might tend to believe a more complex measure is more valuable.  And the linear weights model does produce a bit more accuracy. But it also imposes a cost.  Most people do not understand – or care to understand (perhaps rightfully so) – regression analysis.  And without regression analysis, you cannot know the relative value of all the elements that go into linear weights.  It turns out, though, that you can have roughly the same ranking of players with OPS. 

For some, the cost of understanding and calculating linear weights is quite small.  So the added benefits outweigh the costs and these people turn to linear weights.  Actually, these people probably turn to even more complex measures developed in the twenty years since Pete Palmer first introduced this model.

For most fans, I suspect, the costs imposed by linear weights outweigh the benefits.  And hence OPS, which is now reported by most on-line sports websites, is the preferred measure to evaluate hitters.

Given the story of OPS and linear weights, let’s turn to the measures we introduce for basketball and football. 

Let’s start with football. In an earlier post, QB Score was explained as follows: 

We were able to estimate the relative value of Yard Gained – which includes rushing and passing yards – Plays – which includes passing attempts, sacks, and rushing attempts – and Turnovers – which includes interceptions and fumbles.  Our research indicates that one play – in terms of wins and points – is worth about three times the value of a single yard.   A turnover is worth about 50 yards.  Now these values – 3 and 50 – are not exact.  But it is close enough to give you a quick estimate of a quarterback’s effectiveness.  Given this, QB Score – which is both less complex and more accurate than the NFL’s quarterback rating system — is calculated as follows: 

QB Score = Yards  – 3 X Plays – 50 X Turnovers

One could also calculate the number of Net Points a quarterback’s stats produce as well as the quarterback’s Wins Produced.  But the rankings from QB Score, Net Points, and Wins Produced would be virtually identical.  Even when one turns to the Football Outsiders metrics of VOA and PAR one finds very similar results.  Again, some fans do not mind complexity and in fact seem to seek it out.  For them, VOA and PAR are their best bets. But for most fans, QB Score is the easiest to compute and gives essentially the same evaluation.  And relative to the NFL’s quarterback rating system – perhaps the most complicated statistic ever developed – QB Score is certainly an improvement in both accuracy and completeness.

A similar story can be told about Win Score.  In an earlier post I offered this explanation: 

Now let’s turn to basketball.  Again the methodology is the same.  Determine the relative value of each statistic.  Our research indicates that the relative value of a point, rebound, steal, turnover, and field goal attempt – in absolute terms – is equal.  Assists, blocked shots, free throw attempts, and personal fouls – again in absolute terms – are each worth less than a point, a rebound, etc…  To keep it simple, one can argue that each of these latter stats is worth ½ a point, rebound, etc…  Now the ½ value is not exact, but using ½ keeps it simple and we find one gains very little using the exact relative value.  In other words, player rankings do not change very much when you use the exact values.   So given this argument, one can measure performance with this simple calculation, which we call Win Score.

Points + Rebounds + Steals + ½*Assists + ½*Blocked Shots  Field Goal Attempts – Turnovers –  ½*Free Throw Attempts –  ½*Personal Fouls 

It is important to note that Win Score is not the same as Wins Produced.  And Win Score is a bit more complicated than QB Score.  This is because players at different positions in the NBA offer different levels of production.  For example, big men tend to get many rebounds, guards tend to get more assists. So to compare players at different positions one has to weight Win Score by the appropriate position average.  If you are looking at a center or power forward, you should know that the average big man posts a per-minute Win Score of 0.22.  If you are looking at a small forward, the per-minute mark is 0.15.  For guards, Win Score per-minute is 0.13.  So per 40 minutes, an average big man should have a Win Score of about 9, an average small forward should be at about 6, while guards are average if they post a 5 in Win Score. 

I would emphasize, Wins Produced provides an even better evaluation of performance.  But if your looking at a box score you probably don’t want to calculate each player’s Wins Produced (I know I don’t).  No, as I did during the NBA Finals, one can learn quite a bit about the relative value of performers in each game by just noting each player’s Win Score.

In essence, QB Score and Win Score should be thought of along the same lines of OPS.  Are these the absolutely most accurate measures of performance?  No, but each are quite accurate and highly correlated with more sophisticated and complicated metrics.  Plus these metrics are simple.  And at the end of the day, paraphrasing Occam’s Razor, the simple answer is often the best answer. 

– DJ

Comments are closed.