Pirates pitchers have the highest ground ball rate in the Major Leagues, 52.1 percent. In fact, they are currently on pace for the highest ground ball rate since 2002, the first year for which Fangraphs.com carries batted ball data. Moreover, Pirates' infield defenders have done an above-league-average job of turning ground balls into outs -- they rank eighth in the Major Leagues, with a .225 BABIP. The combination of high ground ball rate and strong defending against grounders has been an important part of the Pirates' run prevention success this year. But how important?

**The Question**

Approximately how many wins the Pirates have gained from the combination of a high ground ball rate plus solid infield defense?

**Total Defense Tool (TDT)**

In order to find the answer, I used a measure of team defense that I developed last year called Total Defense Tool (TDT). I have explained TDT in the past, so some of what follows is lifted from a previous post on this site.

TDT is a runs allowed estimator. By using a modified **wOBA** formula, the TDT equation turns out an estimate of total runs allowed, which can be turned into an estimate of runs allowed above average and then estimated wins/loses above/below average. The formula is as follows:

TDT-wOBA: = [(LW * # HR allowed) + (LW * #HBP) + (LW * #ROE) + (LW* #NIBB) + (Park adjusted wOBA for ground balls * number of GBs) + (Park adjusted wOBA for fly balls * number of FBs) + (Park adjusted wOBA for line drives * number of LDs)] / Adjusted plate appearances.

"LW" in the equation refers to linear weight of each event. They are updated by Fangraphs.com yearly. (Notice that a separate wOBA coefficient is derived for each type of batted ball type, and they are park adjusted.) (For more on linear weights and wOBA, follow link.)

When the actual team totals for the 2013 season are plugged into the TDT formula, it churns out very accurate results. For the 2013 season, the TDT estimates a total of 7215 runs allowed by National League teams. The actual number of runs allowed is 7066 (a difference of 149 runs for 15 teams). The team-by-team correlation between predicted and actual runs scored is .97 and the R-squared is .93.

While TDT is not necessarily the most sophisticated run estimator (though it matches up very well with others), its greatest strength is its flexibility. By simply changing the combination of variables that are set to league-average, the impact of different skill sets can be isolated and compared.

For example, in this study we are interested in the impact of the Pirates' high ground ball rate and above-league-average ground ball defense. In order to isolate the impact of the high ground ball rate we first plug in all of the Pirates actual numbers and derive a run estimate, in this case 413. Then, we go into the equation and change the number of ground balls, fly balls and line drives allowed to league-average rates and come up with a new estimate of runs allowed. By comparing the two numbers, we derive an estimate of the number of runs that the Pirates have saved due to their ground ball rate, which then can be translated into wins.

(Important: The wOBA coefficients for batted ball types represent "range" and do not include errors. The reason is because the linear weight of a ground ball error is likely different from an error on a line drive. The weights for errors of different batted ball types was not available. Errors are included in a teams overall TDT-wOBA coefficient at the standard .92 rate.)

**Results: Total Defense**

Here are the results with the actual offensive statistics against plugged into the formula for each National League team. The Pirates have gained 7.9 wins above average purely from their run prevention. They have gained the most wins from their run prevention in the National League. (**wRAAA** = weighted runs allowed above average. The Pirates have allowed 73.66 fewer weighted runs than average. **Wins** are based off of the current runs per win estimate of 9.323. So, -73.66 divided by 9.323.)

(Click all tables to enlarge)

Now adjustments are made to the TDT formula to account for the following three hypotheticals.

**Results With League-Average Ground Ball Rate with Actual Ground Ball Defensive Efficiency**

What if the Pirates had allowed a league-average ground ball rate, but maintained the same level of defensive efficiency (i.e. they were as rangy) against ground balls? (So, the ground ball rate is made league-average, but the ground ball wOBA coefficient remains actual.)

In this scenario, we would expect the Pirates to have allowed 21 more runs, at the cost of two games. They still would have gained 5.56 additional wins above average from ground ball defensive efficiency (League Avg. Bucs, "Wins") plus other forms of run prevention (fly ball and line drive defense, strikeouts, etc.)

**Results With Actual Ground Ball Rate And League-Average Defensive Efficiency**

What if the Pirates' pitchers had thrown at their current ground ball rate but had a league-average ground ball defense behind them? (Ground ball rate is kept at actual, but the ground ball wOBA coefficient is changed to league-average.)

If their ground ball defense was merely league-average, we would expect the Pirates to have allowed almost 15 more runs at the cost of almost two games. However, they still would have gained 6.34 wins via ground ball rate and other forms of run prevention (i.e. fly ball and line drive defense, strikeouts, etc.).

**Results With League-Average Ground Ball Rate And League-Average Infield Defense**

What if the Pirates' pitchers had thrown an average rate of ground balls with an average infield defense behind them? (Ground ball rate and ground ball wOBA coefficient set to league-average.)

We would expect them to have allowed 33.82 more runs at the cost of 3.63 games. They still would be gaining 4.27 wins via their fly ball, line drive and strikeout run prevention.

**Conclusion**

According to the TDT calculator, the Pirates have gained almost four expected wins (3.63) by throwing ground balls and fielding them well. In other words, it is a combination that has served them well and, if it is sustainable, should continue to add wins in the future. If they were merely league-average in both these regards, they still would have gained four wins from other forms of run prevention.

**Notes**

TDT is a decontextualized statistic. Therefore it does not account for the "timing" of events. As such, these numbers represent the "expected" number of wins, not actual. In real life, the sequencing of events and luck plays an important role. However, it is largely taken for granted that the sequencing of events is somewhat random -- that, in other words, it's a phenomenon like "clutch" pitching or fielding are not really repeatable skills and are expected, given enough time, to flatten out. So, in sum, these numbers represent what we would expect given the rate of events that have occurred with the Pirates' in the field, and ignores the sequencing.

One issue with this method is that when you change the rates of batted ball types, plate appearances should be adjusted as well. More line drives will equal more hits, which will equal more plate appearances. However, I am not sure how to estimate that change, so this represents as close of an approximation as I can get right now. I'm open to suggestions, however.

Special thanks to statcorner.com, fangraphs.com and baseballreference.com for much of the data used in this study.