The Changing Caught-Stealing Calculus

Leafing through an old Sports Illustrated, I recently happened upon this stellar article by Mr. Albert Chen entitled “Revenge Of The Base Stealers,” in which Chen analyzed the league’s continued shift towards base-pilfering over base-trotting.

With the whimper-death of the Steroid Era, league strategies have swung towards old-school baseball. Most winning teams now employ some combination of great defense, strong base-runningitudes, and notable pitching-miraculosities. As such, wise teams have found employs for otherwise marginalized speedsters.

The net result has been an uptick in the value of a stolen base, according to linear weights:

SB-CS Run Values

This chart shows how the cost of a caught stealing (the red line) is trending towards zero (meaning a caught stealing is costing less — in fact, much than its .400 runs high point in 2000) while the gains from a stolen base (0.161 runs in 2012) have remained strong.

Whither belongs the blame for this change? Simply: Home runs. And where do we wander from here? In short: Deep into the heart of Speedster Kingdom.

In 2000, during the apex of the stolen base depression, teams needed to maintain a 69.7% success rate on the base paths just to simply break even on the run value game (granted: game context — such as the pitchers, stadium, weather, and score — allows for varying levels of acceptable SB-rates). But by 2012, the break even point dipped to 66.6%.

Let us put that in real terms: A 2012 speedster can succeed with, out of 50 SB attempts, about 33 SB and 17 CS. Mr. 2000 speedster needed a balance of 35 SB and 15 CS. These differences seem small on the individual scale, but for a manager setting strategy across an entire roster this difference can have a considerable impact.

Before we expand that concept, we must understand why the run values for CS and SB have changed. In the height of the Steroid Era, home runs came in discount baskets. In the aforementioned 2000 seasons, the HR/PA rate nearly hit 3%. Compared to the 2.68% of 2012. That comes to a difference of almost a whole home run per five or six games.

The higher home run rate meant getting on base ended more often with a tater trot than in present seasons. Now, more teams are sliding across home plate as singles, doubles, and the odd triple must replace the extra weekly dinger.

The relationship between home run rate and the value of a stolen base are indeed quite related. Let’s examine at the break-even value for SB success, defined as the absolute run value of a CS divided by the absolute run value of a CS plus the value of a SB.

Unsurprisingly, the relationship between homers and the run values of steals are considerably and inversely related: The break-even rate for SB success shares a .806 .685 R-squared with HR rates, when looking at MLB seasons from 1950 through 2012.

Moreover, we find this:

CS Calculus

A simple equation of:

Break Even Rate = 0.590 + 3.33 x (HR/PA)

This phat function allows us to predict the optimal break even point not just for a league, not just for a team, but for a lineup.

Take, for example, the San Francisco Giants. They do not hit homers. The led the league in not hitting homers. They are so superb at not hitting homers, they almost did not crack 100 dingers in 2012. They were the only team under 2.00% HR/PA. They posted a 1.72% HR/PA — excluding pitchers. With pitchers, they hit only 1.66% HR/PA — that’s a mere 3 to 3.5 total homers per week.

According to our handy Break Even Rate regression, we can predict the Giants break even SB rate in 2012 was 64.53% — well beneath the league average. Meanwhile, the homertastic Yankees (3.93% HR/PA) had a break even rate near 72.09%. So are teams being too aggressive or passive?

2012 Teams

Team PA HR SB CS HR/PA actual SB success% break even SB success net
Pirates 6014 170 73 52 2.83% 58.40% 68.41% -10.01%
Orioles 6160 214 58 29 3.47% 66.67% 70.57% -3.90%
Diamondbacks 6150 165 93 51 2.68% 64.58% 67.93% -3.35%
Rangers 6216 200 91 44 3.22% 67.41% 69.71% -2.31%
Mets 6091 139 79 38 2.28% 67.52% 66.60% 0.92%
Cubs 5967 137 94 45 2.30% 67.63% 66.65% 0.98%
White Sox 6111 211 109 43 3.45% 71.71% 70.50% 1.21%
Astros 6014 146 105 46 2.43% 69.54% 67.08% 2.45%
Rockies 6183 166 100 40 2.68% 71.43% 67.94% 3.49%
Cardinals 6326 159 91 37 2.51% 71.09% 67.37% 3.72%
Tigers 6119 163 59 23 2.66% 71.95% 67.87% 4.08%
Dodgers 6091 116 104 44 1.90% 70.27% 65.34% 4.93%
Indians 6195 136 110 44 2.20% 71.43% 66.31% 5.12%
Blue Jays 6094 198 123 41 3.25% 75.00% 69.82% 5.18%
Yankees 6231 245 93 27 3.93% 77.50% 72.09% 5.41%
Nationals 6221 194 105 35 3.12% 75.00% 69.38% 5.62%
Rays 6105 175 134 44 2.87% 75.28% 68.55% 6.74%
Mariners 6057 149 104 35 2.46% 74.82% 67.19% 7.63%
Red Sox 6166 165 97 31 2.68% 75.78% 67.91% 7.87%
Reds 6115 172 87 27 2.81% 76.32% 68.37% 7.95%
Braves 6126 149 101 32 2.43% 75.94% 67.10% 8.84%
Athletics 6183 195 122 32 3.15% 79.22% 69.50% 9.72%
Brewers 6224 202 158 39 3.25% 80.20% 69.81% 10.40%
Giants 6200 103 118 39 1.66% 75.16% 64.53% 10.63%
Angels 6121 187 134 33 3.06% 80.24% 69.17% 11.07%
Padres 6112 121 155 46 1.98% 77.11% 65.59% 11.52%
Royals 6149 131 132 38 2.13% 77.65% 66.09% 11.55%
Marlins 6057 137 149 41 2.26% 78.42% 66.53% 11.89%
Twins 6209 131 135 37 2.11% 78.49% 66.03% 12.46%
Phillies 6172 158 116 23 2.56% 83.45% 67.52% 15.93%

This data suggests the Pirates — blasphemous on the base paths by league standards — may not have been just as apocalyptically bad as they may have otherwise seemed. Their paucity of home runs allowed for a lower success rate. But their ineptitude still went too far.

Meanwhile, the homer-happy Orioles — perhaps more homer-happy in hindsight than in projection systems — proved likewise overly cavalier on the paths despite a solid 66.67% success rate. They clapped homers with the consistency of club that needs a 70% success rate.

The Phillies and Twins, both teams who appeared judicious on the paths, were in fact cowardly, gutless, un-American — North or South — base runners. They left far more productivity rotting on the table than the Pirates threw into the festering waste bin that was their 2012 season.

Of course, just because teams should be willing to have lower SB totals does not mean the Giants should start sending Pablo Sandoval (Note, however, the relatively efficient and base-stealing fanatical Rays did get 3 SB and just 1 CS out of Jose Molina in 2012). Every manager needs to play with the intention of successful steals, but in general, teams need to accelerate the running game.

SB Attempts per PA

The acceptable SB success rate of the last three years (about 66%) is on par with the late 1980s. But in the early 1980s, teams were attempting steals in about 3% of all PA — compared to the 2.5% of modernity. That’s around 1 steal per week, though probably more, that teams should be attempting, just to match the 1980s’ figures.

The Twins led the American League with 135 steals, but they also appeared to miss out on potentially more runs by not sending the likes of Ben Revere, Alexi Casilla, Darin Mastroianni, and even Denard Span more often.

Here is a look at the stealing tendencies across the league:

The horizontal axis shows the steals per opportunity. The vertical axis shows the team’s steal success rate minus their break-even rate. The bubble sizes indicate the team’s total steals on the season.

The Padres led the league in attempt rates in 2012 (which is roughly SB+CS divided by SB opportunities), but since they still hovered 12% above their break-even success rate, they could have easily afforded an even more aggressive base running style. Instead of running on 9% of opportunities, they could have gone for 10% or 12% — running until opposing teams throw more pickoff moves than strikes.

Obviously, this analysis of the running game is crude. But the ideas welling underneath it point to a concentric theme: Managers need to buckle their courage pants and start beaming the green light again. Home runs may never come back in quite the same fashion, so stealing deserves its renascence.

Chen’s SI article ends where the modern discussion of speed oft ends: Billy Hamilton. The 22-year-old shortstop has golden legs and may be approaching the major leagues at just the right time to challenge Ricky Henderson’s filthy, filthy records. Young players like Hamilton have a chance to begin a new era of baseball, to replace the wood-cracking echos of the 1990s with the sounds of fabric once again sliding on clay, to rebirth the small ball era and make running cool again.

But they will only do such things, of course, if the managers do like my charts’ color schemes, and go green.

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Bradley writes for FanGraphs and The Hardball Times. Follow him on Twitter @BradleyWoodrum.

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Great analysis. Are you strictly talking about swiping 2nd base? How does the calculus change when going from 2nd to 3rd, or 3rd to home?

Aaron (UK)
Aaron (UK)

This! And really, base-out states ought to considered too. I’ve never seen a full table of seasonal RE24 (or WPA) by team on base-steals.

Not to mention the inconsistent treatment of pickoffs, which ought to be part of these sorts of equations but end up being at the scorer’s discretion as to whether or not they are CS. And then there’s hit-and-runs, and missed squeezes, and so on.