How Does a Batter Contribute to Their Team?

For as long as baseball has been around, there have been discussions about what makes a good player, and most specifically, which statistics contribute to the team's overall success.  Many people will say that the ability to play small ball contributes to a team's success.  Others will say that it's all about team speed and running the bases.  Still others will say it's all about power hitting.  Most, however, will say that it's a combination of all of the above.

So what do statistics say about this?

To determine whether small ball or big ball contributes more to a team's success when it comes to runs, I took a sample of nearly 1,000 teams from 1975 to 2012 (with strike-shortened seasons 1981, 1994, and 1995 excluded).  From this, I determined the total of the team's stolen bases and the team's home runs.  Stolen bases are a hallmark of small ball.  Small ball involves using hitters in such a way to ensure that your team scores one run; more runs are not expected.  For example, Batter A walks, steals 2nd, reaches 3rd on a ground ball to the right side, and scores on a sacrifice fly.  1 run on 0 hits.  Walks are really used extensively in both small ball and big ball, but the stolen base is used extensively in small ball.

So, I ran a correlation analysis between stolen bases and runs per game.  I found a correlation of -10.397%.  This means that stolen bases not only don't contribute to a team's success on offense, it actually deters a team from scoring, albeit a little bit.  I attached a scattergram below to show this relationship.  While the relationship looks fairly weak, there is a slight negative relationship.  A team that steals 200+ bases is slightly less likely to score runs than a team that steals 50 or fewer bases in a season.  Please note that there is an R^2 value on these graphs.  R is the coefficient used for correlation, so if you take the square root of the number, you should get the approximate correlation.


So what about home runs?  Big ball.  If a runner gets on first, you give up the more likely opportunity to get one run to try to get a curvy number on the scoreboard.  In these cases, a runner walks and then the next three hitters swing away while the runner stays at first base.  What kind of correlation is seen between home runs and runs per game?

The answer is that there is a fairly strong positive relationship.  There is a correlation of 75.850% between home runs and average runs per game.  In other words, home runs explain about 75.850% of a team's success on the scoreboard.  Again, I attached a scattergram, and unlike the stolen bases chart, there is a definite relationship and it's positive.

So, when determining whether big ball or small ball scores runs, it seems clear that big ball works best.  Could there be another way to determine how good an offense is?  Well, one of the most used statistics in baseball is batting average.  How well does batting average correlate to average runs?

The answer is that batting average correlates well, although perhaps not as well as some would expect.  The correlation is 80.635%, which is a solid positive relationship, but only about 5% more than the home run counting statistic.  Batting average includes not just home runs, but all hits.  This just shows how much more important home runs are than singles, doubles, and triples.  A home run is an automatic run.  A single (or even three consecutive singles) is not.  Again, a scattergram is below to show the relationship.

So far, we determined that stolen bases are a terrible way to contribute to offense, hitting the ball out of the ball park is better, and having a high batting average is slightly better.  What if we take the small ball out of batting average?  Batting average treats a walk and a sacrifice fly in the same way, yet a walk gets a runner on base and a sacrifice fly gets an out.  Batting average treats a home run and a single in the same way, yet a home runs is an automatic run and a single doesn't.  There are two statistics that take the small ball out of batting average: On-Base Percentage and Slugging Percentage.

On-base percentage is basically the same thing as batting average but there are two major differences.  Walks are treated as if they count with on-base percentage, with batting average, they don't count (as a matter of fact, if you go back in time a long ways, walks were once treated as outs in batting average).  The other difference is that sacrifices count as outs, instead of not counting at all.  How does this correlate with runs scored?

Surprisingly well.  While batting average and runs per game correlates at an 80.635% clip, on-base percentage and correlates with runs per game at an astonishing 89.188% clip.  In other words, the difference between using batting average and on-base percentage to determine a team's offensive prowess is larger than the difference between using batting average and home runs.  Walks matter in a positive way; sacrifices matter in a negative way.  The scattergram is seen below.

The other statistic that can be considered batting average without the smallball is slugging percentage.  In smallball, a leadoff single scores by strategic outs.  A stolen base there, a sacrifice there, and a wild pitch there, and the goal is to score one run.  A double would be treated the same way.  Maybe you don't need the stolen base, but a smallball team will try to score a single run with strategic outs.  In big ball, a home run is worth more than a single.  A leadoff single scores with a series of hits.  A leadoff double scores with maybe one hit.  Slugging percentage determines the average number of bases per at-bat.  A 1.000 slugging percentage means that a player averages one base every at bat.  They can do that by hitting a home run every 4 at bats or hitting a single every at bat.  Hitting a home run every 4 at bats would give the same player a mediocre .250 batting average and hitting a single every at bat is a 1.000 batting average.  Which is better at determining the average runs per game?

The answer is slugging percentage.  The slugging percentage is 90.917%, even better than on-base percentage.  Again, the difference between using slugging percentage to determine how well someone contributes to runs and using batting average is almost double the difference between using batting average and home runs.  Scattergram is below.

One statistic that is gaining steam in the baseball world is OPS, also known as On-Base Plus Slugging.  As the name implies, it is simply the sum of on-base percentage and slugging percentage.  Logically, this statistic doesn't really make all that much sense.  On-base percentage is the percentage of time someone gets on base; slugging percentage is the average number of bases a player gets every at-bat.  We're adding a counting stat (slugging percentage, which isn't really a percentage) and a percentage (on-base percentage).  However, does this give us a good offensive stat.

The answer is no.  Actually, it gives us a great baseball stat.  The correlation is an astonishing 95.198%.  Over 95% of a team's runs can be explained using OPS.  It makes sense; the statistic not only gives a team credit for walks and negative credit for sacrifices, but it also gives a team more credit for a double than a single and more credit for a home run than for a double.  The scattergram is below.

Is there any way to get a better statistic than OPS?  Should on-base percentage or slugging percentage be weighted differently?  I played around with the numbers for a little while, but I came to the conclusion that OBP needs to be weighted about twice as much as slugging percentage and that there may be a little work that can be done with exponents.  However, for the most part, the correlation only went up marginally: from 95.198% to 95.821%.  The scattergram is below.

So, by and large, using big ball to score runs is a better way to score than using small ball.  That's not to say there aren't situations where small ball works.  A tied game with a runner on 1st in the bottom of the 9th and the 7-8-9 players coming up may be one of the situations.  A runner on first with a light-hitting pitcher may be one of those situations.

However, this is why I really scoff at the notion that small ball wins games.  It doesn't.  Any manager that uses small ball in the 4th inning of a game where they're down 3-0 should not be managing baseball games (or at least shouldn't be calling the shots).  Any GM that values stolen bases over home runs is going to be fired soon since their teams won't win.