### Why Stolen Bases Matter (At Least More Than Finals)

My baseball nerdiness apparently knows no bounds. I have a final in Contracts tomorrow, but, having outlined the class twice, and taken one practice test, and read another, I've more or less decided that my grasp of the subject of contracts is not going to markedly improve by torturing myself with another night of hardcore studying. Instead, I was thinking about going to the Dodgers game, but it turns out that when I called the ticket office an hour before game time, the cheapest seat was $45. No thanks.

Instead, I ended up devoting the past couple hours to playing around with baseball stats at a depth even I don't normally ponder. I created a new stat. I don't know what to call it yet, though. I have a feeling that the stat itself isn't even new, since there's no way some Bill James type hasn't considered the ramifications of the stolen base, which is basically what I did. The theory is simple - a successful stolen base attempt essentially turns a single into a double (or a double into a triple), while an unsuccessful steal turns a time on base into an out. Therefore, stolen bases can be examined using traditional measures of total bases and times on base, i.e., slugging percentage and on-base percentage.

Since a successful steal has no effect on on-base percentage - the runner is already on base - the only effect here is that every time a runner is caught stealing, one time on base is deducted from the on base percentage formula, that is to say, instead of the old formula of (H+BB+HBP)/(AB+BB+HBP+SF), the formula changes slightly to (H+BB+HBP-CS)/(AB+BB+HBP+SF). Following me so far?

A successful steal does have an effect on slugging percentage, though - it adds one total base to the calculation. Meanwhile, an unsuccessful attempt takes a base away from the calculation. (In theory, an unsuccessful steal of third would take two bases away, since it is effectively a double being turned into an out, but since stolen base stats aren't kept specific to the base being stolen, I treated all attempts as though they were attempts to steal second.) Therefore, the slugging percentage formula changes from TB/AB to (TB+SB-CS)/AB. If you're still with me, believe me, it only gets nerdier from here.

OPS, or on base percentage plus slugging percentage, is frequently used today as a general measure of a hitter's effectiveness, combining his ability to get on base with the frequency of extra-base hits. It's a rough tool - but it doesn't take baserunning into account, and based on the above analysis, that's easy to fix by simply adding the two adjusted figures together, arriving at an adjusted OPS by stolen base success. For the sake of this post, I'll call this new stat OSB (for On base, Slugging, and Base stealing).

To see this in action, let's run a couple of players through the drill. I'm going to pick Carlos Lee, just because he's on my fantasy team. Last season with the White Sox, Lee had an OBP of .366, a SLG of .525, and an OPS of .891. He was 11/16 in steal attempts, a 68.8 percent success rate. To calculate his new OBP, run the adjusted formula: (H+BB+HBP-CS)/(AB+BB+HBP+SF), or (180+54+7-5)/(591+54+7+6), which equals .359. This illustrates what I said earlier - you can't improve your on base percentage by attempting to steal, since you're already on base. On the other hand, the five times Lee was caught stealing dropped his OBP by .007. His adjusted slugging percentage, using the formula, is (TB+SB-CS)/AB, or (310+11-5)/591, which equals .535, an increase of .010. His OSB is now .894 - an increase of .003. That's not particularly impressive, but it does show you that Lee was slightly more productive as a player because of his stolen base attempts as a whole.

In order to have someone to compare Lee to, let's look at another one of my fantasy players, Gary Sheffield. By all accounts, Sheffield had excellent numbers last season - .393 OBP, .534 SLG, .927 OPS. But Sheffield was only 5/11 in steal attempts, a 45.5 percent success rate. Going through the above formula (I'm not going to show you the math here), his adjusted numbers are a .384 OBP, .532 SLG, and a .916 OSB. You can see that his OPS actually dropped .011, which is a noticeable change. From that, you can infer that Sheffield would have been better off not attempting a single steal all season, and that his stolen base attempts as a whole actually hurt the Yankees. Sheffield can also be compared to teammate Hideki Matsui and the Reds' Sean Casey. Both Matsui (.912 OPS last season, 3/3 in SB attempts) and Casey (.915 OPS last season, 2/2 in SB attempts) had an OPS less than Sheffield's. However, even though neither Matsui and Casey tried to steal many bases, they were successful in their few opportunities, and their OSBs (.917 for Matsui, .919 for Casey) are actually equal to or better than Sheffield's.

The suggestions above would indicate that Lee's base stealing has very little impact on his productivity, while Sheffield's adversely affects his output. But neither of those players are known as base stealers. How is the productivity of a player known for stealing bases increased as measured by OSB? To examine this, let's take a look at Dave Roberts, a role player last season (319 at-bats, .337 OBP, .379 SLG, .716 OPS) whose notable contribution last season, appropriately, was on the basepaths, where he was 38/41 in steal attempts, a 93.7 percent success rate. Roberts's OSB is an astonishing .818 - an improvement of .102! His success on the basepaths increased his adjusted slugging percentage to .489. Clearly, Roberts's ability to move himself into scoring position with his feet, rather than his bat, is a significant contribution to his team.

The question that needs to be asked, given the implication that stolen base attempts have an affect, either positive or negative, on a player's contribution as measured by OPS and OSB, is this: What is the threshold success rate of stolen base attempts at which a player must fall below before it is counterproductive? Armed with the answer to such a question, a manager should only send a runner when that runner has a chance of being successful above that threshold rate.

(Yes, I am aware that this stat measures individual production, and that really, the question that needs to be asked is this: Whether, given a runner's chance of successfully stealing a base, it is worth the risk, in terms of probability of scoring a run that inning, of sending the runner. Go read Moneyball.)

Intuition would indicate that the threshold rate would be 2/3, or 66.7 percent, since times caught stealing are counted against you twice (both in OBP and SLG calculations), but successful steals are only counted once (only in SLG calculations). Therefore, in order to break even, you would theoretically need two stolen bases for every time caught. The flaw with this thinking is that it only works if a player's only times on base are via regular at-bats, since the denominator in OBP is actually AB+BB+HBP+SF. In reality, a player will have more plate appearances than at-bats, which means that the failed steal attempts that go into the OBP equation are given slightly less weight than those that go into the SLG equation. The result is that the threshold rate is going to be different for every player (because of the varying number of non-at-bat plate appearances). The rate generally will be a little bit below 66.7 percent.

In a demonstration of nerdiness of Barry Bonds's head-sized proportions, I actually tried to estimate the threshold rate. Using 11 players with at least six stolen base attempts (including Lee, Sheffield, and Roberts), I plotted the difference between each player's OSB and OPS against that player's stolen base success rate, and then found the trendline. You can see the product of my nerdiness here:

The point at which the trend line crosses zero is the threshold rate. Based on this sample, the estimated rate is 63.6 percent - just under 2/3, as I predicted. (If you're wondering, Sheffield is the dot on the left, Roberts is the dot on the right, and Lee is the third dot from the left. Other than Sheffield, the only player in my sample whose stolen base attempts were counterproductive was Jason Kendall.) Players who succeed less often than the threshold rate generally shouldn't try to steal, since it decreases their productivity. The exception is when the probable success rate of a steal attempt is actually above the threshold - for example, when Sheffield is on base against a pitcher with a slow windup and a catcher with an inaccurate arm, the rate of success might still be above the threshold, even though Sheffield normally can't steal bases with that kind of success. The flip side of that coin is that a player like Lee shouldn't attempt to steal when his chances decrease, such as when a hard-throwing lefty is on the mound and Pudge Rodriguez is behind the plate.

Another conclusion to draw from this graph is that catchers who nail runners more than 36.4 percent of the time are decreasing the opponent's productivity, while catchers who are less successful allow the opponent to be more productive. Last season, Brian Schneider, Henry Blanco, and Damian Miller were the only three regular catchers in baseball who caught runners more frequently than that.

I think, looking at all of the above analysis, managers have generally intuited all of this. That's why they don't try to steal often against strong catchers (and why only three catchers nail baserunners more often than the threshold rate) - because stealing when it is mathematically ill-advised is usually the same thing as when it would be ill-advised by common sense. A manager doesn't need a chart to know that Jim Thome can't steal a base; it's pretty apparent that if he tried enough steals, he would fall below the threshold. As a result, he doesn't attempt to steal. This is also why nine of the 11 players in my sample are above the threshold, I think. Their managers know enough to send them in situations where they will succeed at a rate above the threshold rate.

Whew. So that's my breakdown of my new stat - OSB. The stat has probably already been created and analyzed elsewhere. It's actually not applicable to team strategy. Guess what? I don't care. I got to spend a few hours examining it, and that's a few hours I didn't spend studying. See, I really will do anything to avoid studying.

Instead, I ended up devoting the past couple hours to playing around with baseball stats at a depth even I don't normally ponder. I created a new stat. I don't know what to call it yet, though. I have a feeling that the stat itself isn't even new, since there's no way some Bill James type hasn't considered the ramifications of the stolen base, which is basically what I did. The theory is simple - a successful stolen base attempt essentially turns a single into a double (or a double into a triple), while an unsuccessful steal turns a time on base into an out. Therefore, stolen bases can be examined using traditional measures of total bases and times on base, i.e., slugging percentage and on-base percentage.

Since a successful steal has no effect on on-base percentage - the runner is already on base - the only effect here is that every time a runner is caught stealing, one time on base is deducted from the on base percentage formula, that is to say, instead of the old formula of (H+BB+HBP)/(AB+BB+HBP+SF), the formula changes slightly to (H+BB+HBP-CS)/(AB+BB+HBP+SF). Following me so far?

A successful steal does have an effect on slugging percentage, though - it adds one total base to the calculation. Meanwhile, an unsuccessful attempt takes a base away from the calculation. (In theory, an unsuccessful steal of third would take two bases away, since it is effectively a double being turned into an out, but since stolen base stats aren't kept specific to the base being stolen, I treated all attempts as though they were attempts to steal second.) Therefore, the slugging percentage formula changes from TB/AB to (TB+SB-CS)/AB. If you're still with me, believe me, it only gets nerdier from here.

OPS, or on base percentage plus slugging percentage, is frequently used today as a general measure of a hitter's effectiveness, combining his ability to get on base with the frequency of extra-base hits. It's a rough tool - but it doesn't take baserunning into account, and based on the above analysis, that's easy to fix by simply adding the two adjusted figures together, arriving at an adjusted OPS by stolen base success. For the sake of this post, I'll call this new stat OSB (for On base, Slugging, and Base stealing).

To see this in action, let's run a couple of players through the drill. I'm going to pick Carlos Lee, just because he's on my fantasy team. Last season with the White Sox, Lee had an OBP of .366, a SLG of .525, and an OPS of .891. He was 11/16 in steal attempts, a 68.8 percent success rate. To calculate his new OBP, run the adjusted formula: (H+BB+HBP-CS)/(AB+BB+HBP+SF), or (180+54+7-5)/(591+54+7+6), which equals .359. This illustrates what I said earlier - you can't improve your on base percentage by attempting to steal, since you're already on base. On the other hand, the five times Lee was caught stealing dropped his OBP by .007. His adjusted slugging percentage, using the formula, is (TB+SB-CS)/AB, or (310+11-5)/591, which equals .535, an increase of .010. His OSB is now .894 - an increase of .003. That's not particularly impressive, but it does show you that Lee was slightly more productive as a player because of his stolen base attempts as a whole.

In order to have someone to compare Lee to, let's look at another one of my fantasy players, Gary Sheffield. By all accounts, Sheffield had excellent numbers last season - .393 OBP, .534 SLG, .927 OPS. But Sheffield was only 5/11 in steal attempts, a 45.5 percent success rate. Going through the above formula (I'm not going to show you the math here), his adjusted numbers are a .384 OBP, .532 SLG, and a .916 OSB. You can see that his OPS actually dropped .011, which is a noticeable change. From that, you can infer that Sheffield would have been better off not attempting a single steal all season, and that his stolen base attempts as a whole actually hurt the Yankees. Sheffield can also be compared to teammate Hideki Matsui and the Reds' Sean Casey. Both Matsui (.912 OPS last season, 3/3 in SB attempts) and Casey (.915 OPS last season, 2/2 in SB attempts) had an OPS less than Sheffield's. However, even though neither Matsui and Casey tried to steal many bases, they were successful in their few opportunities, and their OSBs (.917 for Matsui, .919 for Casey) are actually equal to or better than Sheffield's.

The suggestions above would indicate that Lee's base stealing has very little impact on his productivity, while Sheffield's adversely affects his output. But neither of those players are known as base stealers. How is the productivity of a player known for stealing bases increased as measured by OSB? To examine this, let's take a look at Dave Roberts, a role player last season (319 at-bats, .337 OBP, .379 SLG, .716 OPS) whose notable contribution last season, appropriately, was on the basepaths, where he was 38/41 in steal attempts, a 93.7 percent success rate. Roberts's OSB is an astonishing .818 - an improvement of .102! His success on the basepaths increased his adjusted slugging percentage to .489. Clearly, Roberts's ability to move himself into scoring position with his feet, rather than his bat, is a significant contribution to his team.

The question that needs to be asked, given the implication that stolen base attempts have an affect, either positive or negative, on a player's contribution as measured by OPS and OSB, is this: What is the threshold success rate of stolen base attempts at which a player must fall below before it is counterproductive? Armed with the answer to such a question, a manager should only send a runner when that runner has a chance of being successful above that threshold rate.

(Yes, I am aware that this stat measures individual production, and that really, the question that needs to be asked is this: Whether, given a runner's chance of successfully stealing a base, it is worth the risk, in terms of probability of scoring a run that inning, of sending the runner. Go read Moneyball.)

Intuition would indicate that the threshold rate would be 2/3, or 66.7 percent, since times caught stealing are counted against you twice (both in OBP and SLG calculations), but successful steals are only counted once (only in SLG calculations). Therefore, in order to break even, you would theoretically need two stolen bases for every time caught. The flaw with this thinking is that it only works if a player's only times on base are via regular at-bats, since the denominator in OBP is actually AB+BB+HBP+SF. In reality, a player will have more plate appearances than at-bats, which means that the failed steal attempts that go into the OBP equation are given slightly less weight than those that go into the SLG equation. The result is that the threshold rate is going to be different for every player (because of the varying number of non-at-bat plate appearances). The rate generally will be a little bit below 66.7 percent.

In a demonstration of nerdiness of Barry Bonds's head-sized proportions, I actually tried to estimate the threshold rate. Using 11 players with at least six stolen base attempts (including Lee, Sheffield, and Roberts), I plotted the difference between each player's OSB and OPS against that player's stolen base success rate, and then found the trendline. You can see the product of my nerdiness here:

The point at which the trend line crosses zero is the threshold rate. Based on this sample, the estimated rate is 63.6 percent - just under 2/3, as I predicted. (If you're wondering, Sheffield is the dot on the left, Roberts is the dot on the right, and Lee is the third dot from the left. Other than Sheffield, the only player in my sample whose stolen base attempts were counterproductive was Jason Kendall.) Players who succeed less often than the threshold rate generally shouldn't try to steal, since it decreases their productivity. The exception is when the probable success rate of a steal attempt is actually above the threshold - for example, when Sheffield is on base against a pitcher with a slow windup and a catcher with an inaccurate arm, the rate of success might still be above the threshold, even though Sheffield normally can't steal bases with that kind of success. The flip side of that coin is that a player like Lee shouldn't attempt to steal when his chances decrease, such as when a hard-throwing lefty is on the mound and Pudge Rodriguez is behind the plate.

Another conclusion to draw from this graph is that catchers who nail runners more than 36.4 percent of the time are decreasing the opponent's productivity, while catchers who are less successful allow the opponent to be more productive. Last season, Brian Schneider, Henry Blanco, and Damian Miller were the only three regular catchers in baseball who caught runners more frequently than that.

I think, looking at all of the above analysis, managers have generally intuited all of this. That's why they don't try to steal often against strong catchers (and why only three catchers nail baserunners more often than the threshold rate) - because stealing when it is mathematically ill-advised is usually the same thing as when it would be ill-advised by common sense. A manager doesn't need a chart to know that Jim Thome can't steal a base; it's pretty apparent that if he tried enough steals, he would fall below the threshold. As a result, he doesn't attempt to steal. This is also why nine of the 11 players in my sample are above the threshold, I think. Their managers know enough to send them in situations where they will succeed at a rate above the threshold rate.

Whew. So that's my breakdown of my new stat - OSB. The stat has probably already been created and analyzed elsewhere. It's actually not applicable to team strategy. Guess what? I don't care. I got to spend a few hours examining it, and that's a few hours I didn't spend studying. See, I really will do anything to avoid studying.

## :

At Tuesday, May 03, 2005 11:24:00 PM, Anonymous said…

Dear lord. That

almostmakes me want to go back to studying for my CivPro final tomorrow. Almost. Good luck with the Contracts final - ours was Monday. Stupid closed-book exams. Grrrrr.Randomness finding this - I found an old listing of all my old IM names, popped it in, and found your link. We should catch up once this hell on earth is over. So, as Frau Quinn would say, Vielen Gluck! (well, she'd say it with an umlaut, but whatever.) ;)

-A.N.

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