# Stacking the middle

It’s yet another baseball cliche: championship teams are strong up the middle.

In his Gold Mine 2008, Bill James explains “Perhaps the first lick of old baseball wisdom that I ever encountered was the championship teams are strong up the middle.”

In the article that follows that statement, James uses Win Shares to demonstrate that championship teams do tend to be stronger at catcher, second base, shortstop or center field than at first base, third base, left field or right field.

For each season of major league baseball from 1900 through 2003, James chose three teams from each league to represent a championship team, an average team and a bad team. He then compared the amount of value each team received at each position using Win Shares. The end result is that championship teams were 98 percent better than bad teams up the middle, and only 73 percent better than bad teams at the remainder of the positions.

The results were intuitive, but there are issues with the study that made me want to look a little deeper.

James answered the question, “Given that a team has won a championship, did it get strong performance up the middle?” This question looks backward in time to explain a championship. We know the team was successful and we’re trying to ascertain why.

I’m more interested in the forward looking question: “Given that team has focused its strength up the middle, how successful will it be?”

You might argue that these questions aren’t all that different, or that the answer to one is the answer to both, but choosing only championship teams may introduce a selection bias that we can eliminate with the later question.

The way we phrase the questions drives how we select the samples. James wanted to answer whether championship teams are strong up the middle, so he understandably identified championship teams. But that removes a lot of teams from the equation—teams good and bad, strong up the middle and weak. I want to know whether teams that get good production from middle of the field perform well in general, so I decided to classify teams by how much value they got from those positions.

Rather than use straight Win Shares, I decided to use Win Shares Above Bench (WSAB) which do a better job of determining the actual value of a given player. I know this is still technically a backwards looking study, but the lessons should apply equally going forward.

I took each team season since 2005 and determined what percentage of the team’s total position player WSAB value could be attributed to the middle positions. Center field proved to be a little tricky because the WSAB calculations don’t separate out the various outfield positions. I decided to let laziness be the better part of valor and simply counted the full WSAB value for the player who played the most games at center field.

The teams were divided into one of three categories based on the percentage of total position player value came from up the middle. Anything above 50 percent was considered high, and anything below 25 percent was low. The rest of the teams were in the middle. This made a nicely symmetrical distribution of 37 teams in both the high and low categories and 46 in the middle.

Let’s take a look at the aggregate winning percentages for each of the levels:

Category | Winning % |
---|---|

High | 0.526 |

Middle | 0.498 |

Low | 0.476 |

You can see quite clearly that teams that are stronger up the middle tend to win more than those who get more value out of the corners.

And this isn’t a result of good teams having more Win Shares in general. We’re not looking at total Win Shares here, but rather the percentage contribution of the position players up the middle.

How well does the relationship hold on the individual level?

The linear correlation (r-value) is 0.28 which makes for a mildly strong relationship. We see though, that the percentage of Win Shares attributed to pitching is correlated more highly with winning percentage at 0.33.

So it appears that Bill James and the baseball cliche are right, at least to an extent. Devoting more of your resources to better players up the middle does seem to give your team a better chance of winning.

The reason is most likely positional scarcity and the defensive spectrum (which are really two ways of saying the same thing). There are fewer athletes who can field the more difficult positions passably, and the most difficult positions tend to be up the middle.

It’s just a lot easier to find quality players who can handle the corner positions, so it’s harder to gain a big advantage over another team that way. Plus, up the middle players may actually cost less per win than corner players because defense and positional value appear to be relatively undervalued compared to big offensive numbers.

In actuality, the relationship appears to be a quadratic rather than linear. The actual data points are fairly scattered, but the quadratic best-fit line improves the correlation up to 0.40.

That may not mean a whole lot, but the key takeaway is that there’s a point of diminishing returns where investing more in your up the middle spots. At the extreme, spending 100 percent of your resources on those four positions means a lot of balls are going to drop in for hits.

But the real point where it’s not really worth it anymore is quite a bit lower. The 13 teams (from the total sample of 120) who got at least two thirds of their position player WSAB up the middle had an aggregate winning percentage of 0.489. Interestingly enough, the tipping point seems be right around the 50 percent mark, which perhaps means a balanced team is more important than anything else.

Despite the notion that a win is a win no matter where it comes from, concentrating your resources on players who play the skill positions seems to lead to more wins. This could be a real effect, or it could be Win Shares undervaluing tough defensive positions. It would be interesting to repeat this study using one of the available WAR measures and see if we get the same outcome. If so, the result may force us to reconsider how we currently value players.

**References & Resources**

Bill James is not the only person to have studied this question in the past.

Derek Zumsteg at Baseball Prospectus looked at the recent championship teams in 2004 and found strength up the middle to be nice but not a must have. He did suggest a similar approach to mine but chose to focus his interest on championship teams.

Matt Meyers wrote an article for ESPN Insider in February that used WARP to explore last year’s league champions and make some predictions about the 2009 season.

There are many other articles that explore the notion with a less statistical approach, although many accept the assumption as proven before starting.

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Very interesting study. I am curious about the distribution of win shares (or WSAR) between defensive and offensive contributions. I would guess that defensive contributions play a big role in the advantages gained from up-the-middle strength. Would it be better to recieve huge offensive production from a Hanley Ramirez/ Dan Uggla combo or super slick fielding from some weaker bats like Viquel/ Castillo (back in the day of course). I would be interesting to see which strategy for a strong up-the-middle crew is best or if it even matters at all.

If distributing your value to different positions changes the quality of the team, then by definition there is a problem with the value metric. This study (and others like it) indeed show that our value metrics undervalue players up the middle.

I would be interested to see a similar study done for each position individually. It would have to use more teams, maybe every team-season in history, to get a large enough sample to see a trend. I am curious if we are only undervaluing catchers, for example, or if it is spread out among all up the middle players.