Finding the Cause of Offensive Success

Which offensive statistics have the highest correlation to scoring runs?

When I watch hitters, the tool that I most frequently look for and admire is not home run power or good bat to ball ability. Instead, I look at plate discipline.

The ability of a hitter to swing at the pitch in the strike zone while laying off the pitch outside the strike zone not only gets me excited, but will carry the hitter to a long and prosperous career, right? Batting ninth for the Red Sox in Game Six of the 2013 ALCS, Xander Bogaerts took Cy Young Award candidate Max Scherzer to a full count in all three of his plate appearances, one of which ended in a double and two of which ended in a walk. Scherzer’s final pitch to Bogaerts, a beautiful 3-2 changeup on the black that would have at least drawn a swing from most hitters, was taken by Bogaerts for ball four. That pitch ended Scherzer’s night (and season), and two batters later, Shane Victorino came to the plate with the bases loaded, and, well you know the rest of the story.

Not only did Bogaerts reach base safely in each of his plate appearances, but he saw 19 pitches from Scherzer, the second highest on the team that night. While everyone loves a high batting average, Bogaerts’ successful day at the plate left little to chance. Any ball in play has a roughly 65-70 percent chance of being converted into an out (obviously this rate varies for GBs, FBs, and LDs), while each base on balls guarantees that the hitter will reach base safely.

Bogaerts’ plate discipline helped the Sox win Game 6 and advance to the World Series. But does this ability have a positive correlation to overall hitting ability over the course of an entire season? Is there a correlation between team plate discipline and total runs scored? Is plate discipline the premier offensive skill that most frequently leads to success? If not, what is?

To answer this question, I examined both PITCHf/x and traditional data from individual hitters from this season, individual hitters from the last 10 seasons (2004-2013), team batting statistics from this season and team batting statistics from the past 10 seasons. The results are below.

Part One: Single Season PITCHf/x Data for Individual Hitters

To find the correlation between individual statistics and overall batting success, I constructed a scatter plot with the statistic in question on one axis with wOBA on the other, and found the R value. For those who are unfamiliar with wOBA, the statistic values walks, hit by pitches, singles, doubles, triples, and home runs unequally by assigning a constant to each result based on the contribution each result makes towards scoring runs (i.e. home runs are valued higher than singles). The R value from the scatter plot is a decimal between 0 and 1 that shows the correlation between two sets of data, which are the statistic we are measuring and wOBA. An R value close to 1 means that there is a strong correlation between the two sets of data, while an R value close to zero means that the correlation between the sets of data is either very weak or nonexistent.

PITCHf/x data tells us specifically about the process of hitting instead of the results. The seven data points from PITCHf/x that we will be examining are O-Swing%, Z-Swing%, Swing%, O-Contact%, Z-Contact%, Contact%, and Zone%. The O in O-Swing% and O-Contact% refers to pitches outside the strike zone (digitally analyzed) while the Z in Z-Swing% and Z-Contact% refers exclusively to pitches thrown within the strike zone. The rest of the data is fairly self explanatory, as Swing% refers to the percentage of pitches that a batter swings at and Contact% refers to the percentage of the pitches swung at by a batter that he makes contact with. Zone% is the percentage of total pitches thrown to a batter that are in the strike zone.

The R values from the scatter plots showing the correlation between each PITCHf/x statistic and wOBA are found below. The sample size for these charts includes only hitters who qualified for the batting title.

StatisticR value

These figures show that the ability to lay off of pitches outside the strike zone was clearly not the best indicator of offensive success. Instead, the highest R value in this data set is Zone%. A .3882 R value may be much higher than any other category, but this number is low enough to suggest that the correlation is not extremely significant. It may seem odd that the category with the highest R value is the category that a hitter has no control over, but the strong negative correlation between Zone% and wOBA is due to pitchers consciously throwing fewer strikes to better hitters. This means that Zone% is not a skill per se, but rather a result of overall batter skill. In other words, being a good hitter leads to a low Zone%, but a low Zone% does not lead to being a good hitter since a batter has very little control over his Zone%.

Additionally, bat to ball skills (contact rates) seem to be much more significant than plate discipline (swing rates) in almost all circumstances. The single area where plate discipline outweighs contact percentage is in pitches outside the strike zone, though the difference is slight and cannot be used to draw any large conclusions. As a whole, since the correlations are so slight, this data set is not very useful for finding the cause of offensive success.

The lack of a correlation could be due to a small sample size, but it also could be a result of looking at the wrong statistics. While the PITCHf/x data examines hitting at its most basic level, it seems that parallels are difficult to reach because of the lack of consistency within baseball players. For example, Adam Jones is notorious for chasing pitches outside the strike zone, but he is still one of the better hitters in the league. Contrarily, Marco Scutaro had the lowest O-Swing% in the league in 2013, but he did not provide as much value to his club as Jones. There is not one approach that works for all hitters, thus it is very difficult to determine which basic hitting skills lead to offensive success. Perhaps better correlations can be found through result based data as opposed to process based data.

Part Two: Ten Year Data for Individual Hitters

The next set of data examines hitters from the past ten years in mostly different categories. O-Swing%, the only carryover from the PITCHf/x data, is joined by several new data points that I think may have a significant correlation to wOBA. The notable omission from this list is batting average, but its R value was low enough in the single season comparison (I did not include this but in 2013 R = .7001) that it seemed useless to chart it again when other values such as OBP and SLG were clearly higher. I am focused on finding inefficiencies within these statistics and since using batting average as a premier metric has already been refuted in the sabermetric community it seems unnecessary to prove that again.

StatisticR value
LD+ + K/BB+.4257
OBP*1.8 + SLG.9953

The first six statistics are fairly common, LD stands for line drive, GB for ground ball, FB for fly ball, OBP for on-base percentage and SLG for slugging percentage. The last two, however, are new.

I was initially surprised at the lack of correlation between LD% and wOBA and BB/K and wOBA, so I combined them into one statistic to see if batters that exhibit both skills are likely to succeed. Since the data are on different scales, the easiest way to combine them is by making them into a plus or minus statistic. If you are familiar with sabermetrics, you may have heard of statistics such as ERA- and wRC+ that compare the statistic for each player to the league average, which is scaled to 100. That is exactly what I did here with both LD% and K/BB rate. Upon adding the numbers together, 200 became the new league average and I compared the new statistic, LD%+ + BB/K+ with wOBA, but unfortunately it did not have a significant correlation.

The other new statistic is OBP*1.8 + SLG. After recently rereading Moneyball (which I highly recommend to anyone interested in baseball and/or business), I was inspired to find the correlation between the combination of OBP and SLG. The Athletics front office originally calculated that one point of OBP was worth three points of SLG, but it is common knowledge that the number has been reduced to 1.8. Using this constant to value OBP and SLG in conjunction with one another I was not surprised that the equation had an extremely high R value of .9953 when compared to the wOBA of each player.

Even when not used in conjunction with one another OBP and SLG have the highest R values by a significant margin. BB/K is next (omitting LD+ + K/BB+), followed by GB/FB (inverse relation, meaning hitting fly balls is ideal), O-Swing%, and finally LD%. The value of a low O-Swing% has almost doubled with the larger, more accurate sample size but it remains lower than initially expected.

I was also surprised that the correlation between LD% and wOBA is low since LDs have the highest chance of any batted ball to fall for a hit. This low correlation may be a result of line drives being likely to turn into singles whereas a batter often must hit a fly ball to record an extra base hit.

Part Three: Team Data

Perhaps one could object to the study thus far and say that the goal of batting is not to record a high wOBA, but rather to help the team score runs. This is a valid objection and will be examined in the following set of data. If the correlation between wOBA and total team runs scored is not strong we can essentially discount the entirety of the study thus far.

The charts below show the R values for each statistic when compared to total team runs scored. The first chart represents team values in 2013 and the second chart represents team values from 2004-2013.

StatisticR value
OBP*1.8 + SLG.9478
ISO + OBP.9107

StatisticR value
OBP*1.8 + SLG.9799
ISO + OBP.9395

The R value for wOBA (.9449 for 2013 and .9809 for 2004-2013) is higher than any other individual statistic that does not require an additional formula to reach. This is significant because it tells us that the comparisons we made using wOBA as a guide were accurate and justified for gauging what statistics correlate best with scoring runs.

The next observation to make is that O-Swing% is much more significant in the team totals than in the individual totals. Baseball, after all, is a team game and the goal is for one team to score more runs than the other team. The increase of the R value for a low O-Swing% seems to be either overlooked by most individual statistics, or perhaps laying off of pitches outside the zone boosts the performance of other players by driving up pitch counts of opposing pitchers. Laying off of pitches outside the zone certainly leads to walks which has a positive correlation to scoring runs, but if all of the contribution comes from walks then it would seem that individual O-Swing% would have the same correlation to wOBA that O-Swing% has to team runs. Since wOBA and team runs to not correlate perfectly there is certainly a chance for error if the constant for walks in the formula in wOBA does not value their contribution highly enough.

The remainder of the gap could be a result of a general rise in R values from the individual to the team data. It is unclear what causes this consistent rise of R values, but it is worth noting that there are far fewer data points for the team totals (30) than individual totals. Despite having fewer data points, the team totals contain more total data since the information is not limited to hitters who qualified for the batting title.

This list is more expansive and includes statistics we have not yet examined such as AVG, ISO (Isolated Power), and a new formula, ISO + OBP. ISO is the simple formula of SLG - AVG and is designed to isolate (hence the name) the extra base power of hitters from their ability to hit singles. By adding ISO to OBP, we create a rudimentary version of wOBA that values on-base ability and extra base hits (XBHs).

Of the three triple slash numbers (AVG/OBP/SLG), batting average shows the lowest correlation to offensive success. It is odd, therefore, that valuation of players and teams is often done by simply ranking batting average. The goal of baseball is not to hit for a high average, it is to score runs, and the low R value for AVG shows that a different and more accurate valuation tactic should be used for hitters, ideally wOBA.

Lessons Learned

What can we take away from this data? Is there a larger lesson to be learned? My initial focus was on plate discipline and the effect of O-Swing% on both wOBA and team runs, but low correlations led me to a different conclusion: extra base power is severely undervalued. I was shocked when I saw the extremely high R values for SLG in both the individual and team data. SLG is a fairly rudimentary statistic, using the simple formula of total bases divided by at bats, but is evidently very useful.

SLG often has a poor reputation for its relative imprecision which seems to be undeserved. For example, three singles are certainly better than one triple and two outs, but SLG measures them equally (SLG = 1.000 in each case). The other two statistics in the triple slash line, AVG and OBP, contain similar flaws such as a home run being counted the same as a single (AVG and OBP = 1.000).

If we examine this notion of valuing SLG in its’ practical context, we can see that it indeed makes sense. To score a run and barring the unlikely, a team will need one of the following groupings of events to occur before recording three outs (assuming outs made on the bases, stolen bases, sacrifice bunts, sacrifice flys, or obstruction calls do not occur).

1. Any combination of four batters to reach base safely.
2. Three batters to reach base safely, the last of which records a hit and one of which records a hit that allows the lead runner to advance at least two bases.
3. Two XBHs.
4. A batter to reach base safely followed by an XBH or an XBH followed by at least a single (if the XBH is a double this assumes the runner can go from first to home on the double or second to home on the single)
5. Home run

Without an XBH, a minimum of three hitters must reach base safely to score one run. Contrarily, assuming a team is not filled with slow runners, a team can expect to score at least one run by only two hitters reaching base safely if one reaches on an XBH. If three XBHs occur in the same inning, the team will be assured of scoring at least two runs. If three singles occur in an inning, it is possible that the team will fail to score even a single run.

The modern game seems to discount the extra base hit for unknown reasons, instead focusing almost exclusively AVG, home runs, and RBIs. Home runs clearly have a significant impact, but what about doubles? Does anyone know who led the league in doubles? How about total extra base hits? Since the goal is to score runs, we ought to focus on the statistics that correlate most significantly to scoring runs, specifically SLG.

I encourage the reader to take away a new appreciation of SLG in baseball and its’ high correlation to scoring runs. Traditional measures of offensive success fail to appreciate the value of SLG, so just as Billy Beane and the Athletics did in Moneyball, let’s recognize and take advantage of a market inefficiency.

The next time you’re thinking to yourself about whether Adam Dunn's .219 AVG means that he is a poor hitter, look at his .442 SLG and think again.