*“ AXOIM I: A ballplayer’s purpose in playing baseball is to do those things which create wins for his team, while avoiding those things which create losses for his team.*

**AXIOM II:** Wins result from runs scored. Losses result from runs allowed.”

– *The Bill James Baseball Abstract 1984*

Those simple axioms as James laid them out has led many baseball analysts down a road to converting or translating popular statistics into the currency of runs with which, it is often said, wins are purchased. The most traveled of these roads is the history of run estimators that analysts are continually tweaking in order to measure how well an offensive player does those things that create runs, and therefore wins, for his team.

In my first two articles on baserunning, I’ve concentrated on understanding how often baserunners take extra bases in various situations in order to calculate how many bases and at what rate the best baserunners outdo the worst. I’ve also delved into understanding a bit about the role that ballparks play. In this final installment I’ll convert the calculation of bases into runs to see how well good baserunners create wins for their team by looking at the season leaders and trailers and the leaders and trailers for the five-year period of 2000-2004.

#### The Method

Beginning in the late 1950s and made popular by Pete Palmer and John Thorn in their 1984 book *The Hidden Game of Baseball*, performance analysts have been calculating average outcomes based on the combinations of outs and baserunners in an inning. These eight (representing the eight states in which you can find baserunners) by three (zero, one, and two outs) matrices are often called Run Expectancy tables. For example, below is the Run Expectancy table for the major leagues in 2004.

Runners 0 1 2 xxx 0.538 0.287 0.114 1xx 0.926 0.550 0.246 x2x 1.160 0.710 0.336 12x 1.467 0.958 0.461 xx3 1.454 0.972 0.362 1x3 1.854 1.224 0.522 x23 2.134 1.472 0.618 123 2.255 1.595 0.808

In other words, when the bases are empty with nobody out, the average team scores just over half a run (.538) in the remainder of the inning, while with the bases loaded and one out teams average 1.595 runs. These matrices have been put to a variety of uses including calculating break-even percentages in order to evaluate basic strategic decisions. For example, I wrote both a Pocket PC and desktop version of a software program I call Big League Manager that makes these calculations based on data from 1999-2002 as you change the scenario.

As discussed in the previous articles in this series, the evaluation of baserunning that I’ve done centers around runners taking extra bases, which are transitions from one cell of the matrix above to another. So if a baserunner moves from first to third on a single with one out, he’s helped transition his team from a state where they were expected to score .550 runs to one where the expectation is 1.224 runs. But of course we can’t give full credit to the runner for the additional .674 runs. After all, the hitter does play a role, and in the vast majority of the cases the baserunner could have jogged to second without a play.

So in order to count the runner’s contribution appropriately we should look at what would have normally occurred and compare it with what actually did occur. In this case we’ll assume the runner would have gotten to second anyway, making it first and second and one out (.958), and subtract it from the actual situation (1.224). This allows us to credit the runner with his contribution (.266) to increasing the Run Expectancy. Likewise, if a runner gets thrown out, he’ll receive negative credit since he cost the team a scoring opportunity. For example, getting thrown out at third on a single with nobody out cost the team .917 runs, calculated as the new situation (.550 = a runner on first with one out) minus the situation had he not tried to advance (1.47 = runners on first and second with nobody out). By following this method we can build a derivative table of run values for the various outcomes in the three baserunning scenarios I’ve used to measure baserunning performance. It should be noted that in making these calculations I did not give any credit to a runner for advancing the “standard” number of bases, e.g. one base for a single and two for a double.

That derivative table can then be applied to each actual opportunity in which a baserunner finds himself. So if Juan Pierre moved from first to third on a single with nobody out we’ll credit him with .266 runs for that opportunity, and so on. I call the total across all opportunities Base Runner Runs (BRR).

But just as with measuring the total number of bases gained, BRR needs to be compared against some baseline since the number of runs has a lot to do with the number of opportunities a runner has. So I also used the derivative table to calculate the number of runs the runner would be expected to contribute given the opportunities he had. The difference between that number (Expected Runs or ExR) and BRR I call Incremental Runs (IR). And because IR like Incremental Bases in my previous articles is also weighted by opportunity, I calculate a ratio of IR to BRR called Incremental Run Percentage (IRP), which is a rate statistic akin to OPS that shows at what rate players contribute runs with their baserunning.

Finaly, I then take all of these numbers and park adjust them using a similar technique as discussed last week, although refined a bit by adjusting the BRR, IR, and IRP only for those opportunities that occurred in the player’s home park.

While that sounds confusing—and it is—just remember that BRR is the total number of runs a player contributes with his baserunning, IR as that portion of the runs he contributes that are over and above what would have been expected given his opportunities, ExR as the number of runs that he would have been expected to contribute, and IRP as a means of comparing two runners regardless of the number and type of opportunities.

#### The Results

First, let’s take a look at the yearly leaders and trailers in IR. I’ve included the Incremental Base Percentage (IBP) from my previous articles for reference.

LeadersOpp IBP BRR ExR IR IRP 2000 Luis Castillo 57 1.23 14.42 9.16 5.25 1.57 2001 Juan Pierre 41 1.20 9.06 5.14 3.92 1.76 2002 Jacque Jones 47 1.14 11.46 7.38 4.08 1.55 2003 Raul Ibanez 55 1.12 13.52 8.91 4.61 1.52 2004 Reed Johnson 53 1.15 13.68 8.68 5.00 1.58Trailers2000 Joe Randa 50 0.80 2.81 6.86 -4.05 0.41 2001 Adrian Beltre 25 0.70 -0.57 4.05 -4.61 -0.14 2002 Frank Thomas 40 0.77 0.42 5.88 -5.45 0.07 2003 Edgar Martinez 39 0.87 4.11 9.22 -5.11 0.45 2004 Bill Mueller 47 0.76 2.17 7.40 -5.23 0.29

From these tables you can see that the leaders generally create an additional four to five runs while the trailers cost their teams an equivalent amount. The magnitude of the impact of baserunning accords very well with the research that James Click published in the 2005 *Baseball Prospectus*, although our individual leaders and trailers vary somewhat.

A couple surprises here are that Raul Ibanez and Reed Johnson float to the top in 2003 and 2004 although neither is known for exhibiting speed through stolen bases. On the flip side Adrian Beltre and Joe Randa are a bit surprising since both are considered to have average speed.

Over the five-year period from 2000 to 2004 the leaders and trailers in IR are:

Top 10Opp IBP BRR ExR IR IRP Luis Castillo 272 1.10 51.92 38.19 13.73 1.36 Juan Pierre 259 1.11 45.50 33.02 12.47 1.38 Mike Cameron 168 1.14 39.73 29.11 10.61 1.36 David Eckstein 216 1.11 40.07 29.46 10.61 1.36 Ray Durham 203 1.11 36.65 26.72 9.93 1.37 Cristian Guzman 209 1.11 36.41 26.56 9.85 1.37 Jay Payton 168 1.10 37.48 27.80 9.68 1.35 Rafael Furcal 220 1.09 39.36 29.83 9.53 1.32 Jimmy Rollins 180 1.11 37.16 28.16 9.01 1.32 Johnny Damon 256 1.07 43.40 34.47 8.92 1.26Bottom 10Rich Aurilia 151 0.92 13.96 22.86 -8.90 0.61 Frank Thomas 143 0.88 11.83 21.04 -9.21 0.56 Mike Lieberthal 139 0.87 11.55 20.92 -9.37 0.55 Ben Molina 138 0.86 13.27 22.81 -9.54 0.58 Rafael Palmeiro 207 0.88 17.04 27.17 -10.12 0.63 Bill Mueller 191 0.87 17.50 27.67 -10.17 0.63 Carlos Delgado 237 0.90 28.64 39.50 -10.86 0.73 Richie Sexson 157 0.88 13.78 24.80 -11.02 0.56 Dmitri Young 156 0.87 11.38 22.83 -11.45 0.50 Edgar Martinez 178 0.89 17.53 30.11 -12.58 0.58

So over the course of the five years the spread is +/-13 runs. These lists are a bit more in line with what you’d expect, with the possible exception of Eckstein ranking so highly. In looking at his season-by-season totals, he’s garnered more than 3.25 runs twice and almost two and half another time in just four years to make a pretty impressive showing.

But as mentioned earlier, ranking by IR only gives the advantage to those with more opportunities, so we’ll also show the yearly leaders and trailers by IRP for those who had more than 20 opportunities.

LeadersOpp IBP BRR ExR IR IRP 2000 Tom Goodwin 40 1.21 9.18 5.58 3.59 1.64 2001 Cristian Guzm 26 1.28 7.77 4.16 3.60 1.87 2002 Ray Durham 40 1.23 6.80 3.71 3.09 1.83 2003 Omar Vizquel 22 1.10 3.44 1.55 1.90 2.23 2004 Chase Utley 21 1.20 4.16 1.71 2.45 2.43Trailers2000 Jose Canseco 28 0.80 0.39 3.05 -2.66 0.13 2001 Javy Lopez 23 0.74 -0.69 2.31 -3.00 -0.30 2002 Ben Molina 32 0.73 -0.14 4.09 -4.23 -0.03 2003 Craig Counsel 28 0.78 -0.85 2.70 -3.55 -0.32 2004 Mike Piazza 27 0.71 -0.32 4.22 -4.54 -0.08

Here two players with good baserunning reputations, Tom Goodwin and Omar Vizquel, finally make appearances while the surprise leader in 2004 is Chase Utley. Although he had just 21 opportunities, he parlayed them into 2.45 incremental runs for an IRP of 2.43 (143% more runs than would have been expected given his opportunities).

And now the leaders and trailers in IRP over the five-year period that includes 2000 to 2004 for those that had 75 opportunities or more:

LeadersOpp IBP BRR ExR IR IRP Miguel Cairo 105 1.14 18.87 12.41 6.45 1.52 Tom Goodwin 97 1.16 23.48 16.07 7.40 1.46 Jack Wilson 117 1.14 21.62 14.85 6.77 1.46 Larry Bigbie 86 1.10 15.00 10.44 4.56 1.44 Pokey Reese 86 1.12 19.24 13.87 5.37 1.39TrailersRichie Sexson 157 0.88 13.78 24.80 -11.02 0.56 Mike Lieberthal 139 0.87 11.55 20.92 -9.37 0.55 Dmitri Young 156 0.87 11.38 22.83 -11.45 0.50 Daryle Ward 77 0.88 4.25 9.00 -4.75 0.47 Fred McGriff 111 0.86 5.94 12.89 -6.95 0.46

Once again a few surprises here, including Miguel Cairo who comes out on top, as well as the new Rockie Larry Bigbie.

#### Conclusions

Since I’m sure you’re tired of looking at tables by now I’ll mercifully end this article and series with a few random thoughts.