You can check out all parts of the Twinkie Town Analytics Fundamentals series by clicking the tag at the top of the post. If you have other topics you’d like to be explored in this series, please leave a comment and let me know!
Game three of the 1991 World Series was a tense affair. The Twins had the series advantage after winning the first two games in Minnesota and game three reached the bottom of the twelfth inning tied at four. Atlanta cleanup hitter David Justice reached with a one-out single. Justice would remain at first base when the next hitter flew out and set the stage for some two-out heroics. On the 3rd pitch of the next at-bat, with the hitter down in the count 0-2, Justice was put in motion on the base paths and successfully stole second base. The hitter at the plate eventually worked a walk and brought Mark Lemke to the plate to deliver the winning single to left field that scored Justice on the play at the plate shown in the feature photo above.
Game six was tied at three into the eleventh inning. Atlanta’s Sid Bream led off in the top half with a single. Keith Mitchell came off the bench to run for Bream, giving the Braves, who led the series three games to two, better speed on the bases to increase their chances of ending the series and winning the championship. Mitchell took off for second base on Rick Aguilera’s first pitch to Brian Hunter. This time, Twins catcher Brian Harper was able to cut down Mitchell for a caught stealing and the inning’s first out. Hunter and the next batter both popped out on the infield, ending the frame and setting the stage for Kirby Puckett’s iconic walk-off homer to lead off the bottom half and force a deciding seventh game.
Game seven was yet another nail-biter. Jack Morris and John Smoltz were locked in their famous scoreless duel into the eighth inning. Atlanta’s lead-off man, DH Lonnie Smith, kicked off a rally with a lead-off single. Two-hole hitter Terry Pendleton next lined one into the left-center field gap, a sure double off the bat that had a very strong chance to score Smith, who was running on the pitch, from first base. Smith, who didn’t read the ball well off the bat and may have been deked out by the Twins middle infielders miming a double play groundball, pulled up at second base before realizing his mistake and carrying on to third.
Instead of the go-ahead run scoring, the Braves had two in scoring position with nobody out. Smith held at third on an infield chopper that resulted in the first out. Minnesota intentionally walked the next hitter to load the bases and set up a potential double play, which they got when Sid Bream grounded one to Kent Hrbek, who partnered with Brian Harper on an inning-ending 3-2-3 double play.
All of these instances make the 1991 World Series a useful backdrop against which we’ll have the next installment in our Analytics Fundamentals series, focused on baserunning and the metrics we use to evaluate it.
Speed Is Not Everything
In some ways, evaluating how well players and teams run the bases has issues similar to those we deal with in measuring defense. It’s far easier to measure something that did happen – like a stolen base or moving up a base on a fly ball out – than it is to measure something that did not, like a runner holding at the same base on a pitch that gets away from the catcher or not going first to third on a single through the right side. Some runners make those plays and others don’t even attempt them.
The earliest attempts at measuring how well players ran the bases focused on data that could easily be counted, like stolen bases and triples, and relied on broad rules of thumb and heuristics, like the idea that a player needed to run fast to be a good base runner.
The earliest “advanced” statistic about base running is Bill James’ Speed Score, which was calculated using six factors: stolen base percentage, stolen base attempts as a percentage of opportunities, triples, double plays grounded into as a percentage of opportunities, runs scored as a percentage of times on base, defensive position, and range.
It might seem intuitive that speed is necessary to run the bases well – and we now know there is a fairly strong relationship between running speed and effective baserunning – but it is not necessarily a requirement. Making good decisions about when to go and when to stay have little to do with speed and a lot to do with understanding game situations, being alert for opportunities, and making snap judgments of risk and reward.
Like the World Series examples in the introduction illustrate, sometimes it’s the play not made that can differentiate a good base running play from a mediocre one or winning a game from not. The context in which the play occurs informs whether it was good or bad. To measure that, we rely on the concepts covered in parts three and four of this series, run expectancy, and linear weights.
Stolen bases will likely always be the first thing that comes to mind when people think about baserunning. A stolen base attempt is on the shortlist for most exciting plays in baseball, and its decline over the last few decades, especially in the analytics-driven 2010s, is decried as one of the biggest reasons the gameplay has become less interesting for casual fans.
As you can see in the plot below, on a per-plate appearance basis, attempted stolen bases have been on a declining curve since the early-1990s. From 1976 through 1992, there were about three stolen base attempts for every one hundred plate appearances, thanks to the proclivity of such thieves as Vince Coleman, Tim Raines, and all-time stolen base king Rickey Henderson.
Since 2015, the league-level rate of stolen base attempts has fallen below two per one hundred plate appearances. There were 19 seasons, by eight different players, of at least 75 stolen bases in the 1980s. Since the 1990 season, there have been only five such occurrences, by four different players, and the last was in 2007.
A lot of that decrease has been (rightly) pinned on the proliferation of analytics and their influence on decision-making in front offices and dugouts. Analytics have led to a much better grasp of the relative values of different events on the field, especially the cost of making an out on the bases, say, for example, via a caught stealing, relative to the prospective benefit of a successful stolen base attempt.
The cold, hard truth of the numbers is that the cost of making an out on the bases often far outpaces the benefit of gaining 90 feet. We know this because we understand the run expectancy (RE) of different base-out situations using the RE24 formula.
Using the helpful historic run expectancy values at Baseball Prospectus, we can look up the 1991 run expectancy table and use the two stolen base examples from the introduction to illustrate.
With Mitchell on first with no outs in Game 6, the average run expectancy was .8588 runs scoring before the end of the inning. He was thrown out, which dropped Atlanta’s run expectancy to .2557 runs, a loss of .6031. If he had been successful in stealing second base, the run expectancy of a runner on second with no outs would have been 1.0929. This example effectively illustrates the risk and reward calculus. Stealing second base safely would have been worth +.2341 runs (1.0929 minus .8588). But getting caught cost them .6031 runs (.2557 minus .8588), slightly more than twice as much as being safe would have gained.
That’s a multiple that tends to hold as a useful rule of thumb. Pending the run-scoring environment and game situation, the average cost of a caught stealing tends to be somewhere between twice and three times the potential gain of a successful steal.
That means that players generally need an expected rate of success in stealing bases of about 67% to 75% to break even on the risk. In high-scoring periods, like the early 2000s, the break-even rate is closer to the high end of that range, and in lower-scoring periods, like the late 1960s, it is closer to the lower end.
That said, the game situation can change the risk-reward calculus significantly.
When You Go Makes All The Difference
With Justice on first base and two outs late in Game 3, the average run expectancy for Atlanta was .2175 runs. By stealing second safely, Justice raised Atlanta’s run expectancy to .3257, a gain of .1082 runs. Hypothetically, though, if he had been thrown out, the inning would have ended with no runs, a loss of .2175 runs from where it started with him on first base. (Again, the cost of an out would have been just more than twice the potential gain of being safe.)
But, it was the bottom of the 12th inning of a tie game and the Braves were down two games to none in the series. In that situation, they were not necessarily interested in maximizing the number of runs they scored. They were interested in increasing their chances of scoring just one run because, as the home team, that’s all they needed to win the game.
We know intuitively that a runner on second is more likely to score than a runner on first (hence the colloquial term “scoring position”). On average, teams with a runner on first and two outs will score a run about 13% of the time. A runner on second base with two outs will score about 22% of the time. In a situation where one run scoring is disproportionately valuable (i.e., ending the game), teams should be more willing to take the risk on the bases. The break-even math supports this, with the required success rate being closer to 60% in such situations.
With more teams and managers understanding these factors and adopting them in their decision making the past two decades, teams have gotten much more judicious and efficient about deciding when to run. Getting a man on base remains the hardest thing to do for a baseball offense, so recklessly putting him at risk on the bases often just is not a great strategy.
But, a steal is still a useful tool in specific situations when the risk-reward balance tilts in favor of the offense. There is evidence that teams have gotten better about identifying those spots and taking advantage. Take a look at how the rate of successful stolen base attempts has risen over time:
While the overall number of attempted steals has declined, teams have gotten significantly more efficient at stealing. It’s not so much that analytics have killed the steal. It’s more that teams have gotten smarter about when attempting one is a good play and they’ve stopped attempting steals that will hurt them.
This is a major part of the argument for the rule change to increase the size of the bases to 18 inches square being implemented in 2023. The data indicates baserunners will still run when it makes sense and the league is banking that slightly larger bases will alter the calculus to create more situations when the potential reward justifies the risk.
Valuing Steals: wSB
Ultimately, simple counts of successful stolen bases and caught stealings is an incomplete way to measure the value of those actions. To do that more effectively, we return to linear weights and use the statistic weighted stolen base runs (wSB), which estimates the number of runs a player contributes via his base stealing, compared to the average player. If you are familiar with weighted runs above average (wRAA) – read part four of this series, if not – you can think of wSB as its baserunning counterpart. Baserunning is a smaller aspect of the game, so the amount of value that comes from it is less than what comes from batting. That means, unlike wRAA, which can reach upwards of +40 runs in a season, the range of the most and least productive base stealers is more narrow, usually from about -5 runs to +15 runs in a given season.
FanGraphs calculates wSB by comparing each player’s stolen base runs created per opportunity with league average stolen base runs created per opportunity. You can explore the formula in the link above, but for these purposes all you need to know is that a steal is credited as +0.2 runs and the value of a caught stealing fluctuates based on the overall run environment and cost of an out. As with other “above average” type metrics, the league average is set to zero, which makes wSB useful for comparing players in different eras.
Going Beyond Steals: UBR
We know that baserunning involves more than just steals. The players that are adept at moving up a base on a batted ball out, or going first to third on a single can add significant value (or vice versa). That’s especially true given the game context, like the 1991 World Series Game 7 example of Lonnie Smith discussed in the introduction.
Ultimate Base Running (UBR) is the statistic FanGraphs uses to account for the value a player adds to their team via base running on non-stolen base plays. This run value is determined using linear weights, with each individual base running event receiving a specific run value. As before, to calculate UBR you need to know the average run expectancy for a given batting event given the base-out state, and then the actual run expectancy change that occurred during the play.
Let’s illustrate. Smith was on first base when Pendleton hit a double. With run expectancy, we know the frequency and run value of the league average outcome in similar situations. Smith can advance to third, score, or be thrown out. If we weigh all of those results by their frequency and run value based on run expectancy, we get an average value for that situation. ‘
To calculate Smith’s UBR for that particular play, you take the actual run expectancy change relative to the average run expectancy change for that event and credit or debit Smith for the difference. It’s widely believed that the average outcome on that play in 1991 was the runner from first base scoring, which means Smith only reaching third was almost certainly a below-average outcome and he would have earned a negative amount for the play.
To determine a player’s total UBR for a season we simply add up the value of all of their relevant base running plays. League average is always zero and the range from worst to best within a season runs from about six runs below average to six runs above average in a given year.
Avoiding Twin Killings: wGDP
The last element factored into how we measure baserunning with advanced analytics is weighted grounded into double plays (wGDP) which is the number of runs above or below average a player has accumulated based on their ability to stay out of double plays. This gives players credit for not hitting into double plays no matter how they avoid them – whether it's from their speed to avoid being doubled up on the relay, because they avoid hitting the ball on the ground with men on base, or something else.
This is a smaller contribution to the baserunning measurements than wSB and UBR because it is scaled by the opportunity to hit into a double play. To find a player’s wGDP, FanGraphs takes the average rate of ground ball double plays and applies it to the number of opportunities the player had. If they have fewer than average ground ball double plays, they get a positive value and if they have more ground ball double plays than average, they are decremented. Again, zero is average and the run values range from about -2.5 runs to +2.5 runs in a given season.
Putting It All Together: BsR
Finally, we’ve reached the summation. To measure the total baserunning contributions of a player, we have FanGraphs’ Base Running (BsR), which is simply wSB plus UBR plus wGDP.
Since those inputs are all designed as above-average or below-average metrics, summing them together tells us how many base running runs a player contributed relative to average in a season. That summation is the baserunning input into Wins Above Replacement.
BsR is not the only way to measure baserunning contributions. Like a lot of baseball stats, different sites have different metrics. Baseball Reference has Rbr, Baserunning Runs, for example. In the case of measuring baserunning, though, all the main metrics are based on the linear weights approach outlined in this post.
- Baserunning is a comparatively small part of player value. Most players will contribute less than half a win (~5 runs) from their baserunning in a season
- Baserunning takes place somewhat on the margins in aggregate but can become critically important in certain game contexts and situations
- Running speed is not a prerequisite to being a good base runner (although it can help), and not all fast runners are good base runners
- The cost of making an out on the basepaths tends to outweigh the gain of successfully stealing a base. A good rule of thumb is that attempting a steal is only worth the risk if the base runner has at least a 70% chance of making it safely. Game context can raise or lower that break-even threshold
- Stolen bases and caught stealings are incomplete measures of base running contributions. Run expectancy and linear weights give us more comprehensive ways to value base running events with stats like wSB, UBR, and wGDP.
- Baserunning metrics (like BsR) take into account three main skills: the ability to steal bases (wSB), the ability to advance on the bases (UBR), and the ability to avoid grounding into double plays (wGDP). Adding together a player’s contribution in those three areas makes up the total base running inputs into Wins Above Replacement calculations
The data sources are cited or linked throughout this post. Like others who have tried to write and explain these subjects before, I relied significantly on the following resources:
- Book: Smart Baseball by Keith Law
- Book: The Book – Playing the Percentages in Baseball by Tom Tango, Mitchel Lichtman, and Andrew Dolphin
- Fangraphs’ indispensable library: library.fangaphs.com
- Numerous links to previous research and explainers included throughout