**What do we want out of baseball statistics?**

Imagine going to an arbitrary college baseball field and watching a game between two teams with which you have no familiarity. You see certain players playing and based on their single game performance you are forced to make a decision on the value that these players have in terms in winning baseball games. If you go to multiple games and collect a larger sample, you will gain more confidence in your evaluation of the players. You might even be able to see every single game. At the same time, you're liable to forget older or less dramatic events in favor of more recent or exciting ones, which will mislead your evaluation of players. Therein lies the value of statistics. They give a partial summary of the immense of data required to describe the game of baseball. The fact that television stations present statistics, at their expense, throughout baseball games demonstrates that viewers do value them.

It's important that statistics tell us the data that is beneficial to the people to whom it is being presented. Because baseball is fundamentally entertainment, it's important that statistics presented on television give information that enhanced our enjoyment of the game. I see these two enhancement as falling under two broad categories. Statistics should be evaluative and predictive.

Evaluative statistics allow judgments to be made about players. They allow the differentiation of a fundamentally bad player and a bad performance. They are enjoyable seemingly because they allow the assignment of individual responsibility to players for the fortune of the overall team. Predictive statements allow expectations to be made about the future performance of players. There is seemingly some enjoyment that is derived from both knowing a team's chances of victory and by players defying the predictions that have been established from their past performances.

In addition, for a general audience, brevity is important in evaluative and predictive statistics. The statistics should not be far removed from the atomic events that viewers can readily see. While more nuanced statistics can be more accurate and certainly have a place, it is important not to lose an audience that is not willing to invest time into deriving statistics.

**What do we get out of the baseball statistics currently seen on TV?**

During a recent spring training game between the Red Sox and Pirates, I took notes of the statistics that were presented on the screen. In this post I am limiting discussion of offensive statistics.

**I watched the game on NESN, which presented the following statistics for each plate appearance:**

- Batting average
- Home runs
- Runs batted in

From an evaluative standpoint it's important to understand how each of these statistics is computed and what it signifies.

Batting average is a player's hits divided by at bats. The concept of an 'at bat' is not entirely intuitive as it is not inclusive of plate appearances that end in a walk, hit by pitch, sacrifice, or obstruction. Thus batting average is somewhat post-hoc, it's impossible to know if a plate appearance will be an at bat until it is over. Thus, the statistics signifies the hitter's ability to get a hit, all hits being equal, in plate appearance that end it certain outcomes.

Home runs are simply a count of a player's home runs. Showing this statistic attempts to give insight into a players ability to hit for power. RBIs are a count of runs that have stored as a result of a current hit's actions, with some exclusions. These attempt to give some insight into a player's overall value to the team, as scoring runs is seen as the principle objective of the game.

All these statistics are fairly brief, but how accurate are they at describing player value. To do this, look at the common outcomes that can become of a plate appearance.

- Walk
- Single
- Double
- Triple
- Home Run
- Sacrifice
- Non-sacrifice out

It is clear to see that the statistics chosen for display on television give us some order of favorableness of plate appearance outcomes. While it is obvious that someone watching an game in progress will know that a double is better than a single, the statistics shown give no way of knowing this. Thus the choice of statistics fails in terms of evaluative ability. The situation is even more dire when consider knowledge gleaned from advanced statistics.

**What do we get out of advanced statistics?**

In

*The Book*Tom Tango et. al. gives run values for the events above. These say that for an event such as a single, across a historical summary of all times in the past where a single was hit, how much did it increase the likelihood of runs being scored in inning, weighted by the amount of runs. The computation is fairly intense but standing on its own, it provides a good benchmark of the relative values of events, as the offensive objective of baseball is run scoring.

- Walk .323
- Single .475
- Double .776
- Triple 1.070
- Home Run 1.397
- Sacrifice -.20
- Any out* -.299

**These include sacrifices, so we know that all non-sacrifice outs is lower. I don't have information for non-sacrifice outs readily available.*The Book

*provides a much more detailed breakdown of events and their run values.*

If we accept that baseball is fairly static over time, we have good way of, within a reasonable bound, assigning value to the events that can occur during a plate appearance. Tango defines wOBA to be sum the outcomes of a players' plate weighted by their run values divided by the number of plate appearances. wOBA is designed to correlate with the runs created from events and it is shown to generally be stable year to year. Thus wOBA seems to match both the evaluative and predictive criteria.

Thus it seems reasonable to replace the batting average, homerun, RBI cobination with wOBA, as the former clearly misrepresents the relative values of events. But wOBA fails the brevity criterion. While the weights for each event do have a logical basis, explaining and calculating them briefly is largely impractical and presenting them without explanation gives them the appearance of 'magic numbers'. While those who bring a posses a knowledge of advanced statistics would be overjoyed to see wOBA on television over the grossly misrepresentative trio seen today, the alienation of those whose do not would be highly unreasonable.

**Where is the middle ground?**

I feel as though in a situation such as this, where two ultimately harmful options exist, the best course of action is to do no harm. Presenting batting average, home runs, and RBIs is harmful in that it presents a false perception of a player's value. Presenting wOBA is harmful in even though it assignments values for properly, it is far enough removed from the atomic events of the game that it is hard to understand.

The solution may be not to assign value at all, but merely show the outcome of every plate appearance of a player and allow the user to assign value based on their perception of the game. While a traditional, uninformed viewer is still likely to undervalue walks, they are still likely to give it more than the negligible value that it is presented as having in the current statistical trio. The problem is a concise representation of the out come of every plate appearance, where a full season may be in excess of 600 for an everyday player.

An idea I've thought about is representing a player's season with a box the size of the typical batting statistics display, but having varyingly colored regions based on plate appearance outcome. Hits, for example, could all be some shade of blue with varying intensity for hit type. These regions would be overlaid with the percentage of total plate appearances. Thus instead of talking about a .257 hitter or having a .400 wOBA, people would talk about 33% hitters, 10% walkers, or 12% doublers. In high definition, this sort of visual-based system could be feasible, though standard definition might be a stretch. The other significant issue is resistance to any sort of change. Batting average, home runs, and RBIs are insufficient and deceptive and furthermore they

*are*statistics in the same way that wOBA is. Percentages of plate appearance outcomes are arguably even easier to understand than batting average, but they are unfamiliar and nontraditional; they don't sound like what baseball statistics have always sounded like.

Baseball has changed over time, but an element of tradition and conservatism runs through its psyche. Though since the 80s new ways and more complicated ways of looking at baseball have emerged and gained considerable traction, they remain fringe elements largely isolated from television broadcasts of baseball and likely always will be. It would take a daring broadcaster to break from tradition, but should one try, the best approach might be to break even different ground: rather present differently processed statistics, presents stats in their most raw unprocessed forms.

*Sidebar: OBP + SLG*

*On base percentage (OBP) and slugging (SLG), are two relatively simple measures that, when combined and adjusted by a linear factor, come close to approximating wOBA. On base percentage is simple taking all plate appearances that result in getting on base and dividing them by total plate appearances. Slugging is essentially batting average, but with singles having a weight of 1, doubles 2, triples 3, and home runs 4. Clearly this is both easier to understand than wOBA and more accurate than the batting average, home run, RBI trio.*

*Fundamentally it's distasteful to both groups. Its weightings, and thus the value judgment that it makes on players, are less accurate than that of wOBA. Plus when presented in its added form, two unlike things are being combined, giving it somewhat of the appearance of a magic number.*

*OBP and SLG do have some representation in mainstream television broadcasting. But they are never in the forefront, possibly mentioned or shown when a single player is being discussed in great detail. Perhaps one day OBP and SLG will be shown as a peer with batting average. This is of course not ideal, as walks will still be undervalued (they adjust only two of the three stats while a single hit adjusts all three). Nevertheless, showing them does lessen the extent of the incorrect value judgment that statistics on television currently provide.*