Stolen bases, stolen runs

I'll soon be updating the charts of offensive performance to take into account some minor glitches, but they shouldn't change the results in any significant way.

Meanwhile, I'd like to note what the run values say about the IBL's high steal rate - three times as high as in the majors. A stolen base was worth just 9.1% of a run. But a time caught stealing cost the team 28.1% of a run, plus 15.6% of a run for the out it created, for a total of 43.7% of a run!

The season's 457 steals were therefore worth about 41.4 runs. But the 110 times caught stealing cost teams 48.1 runs. So overall, steal attempts cost IBL teams about 6.7 runs over the season.

Just goes to show that the steal rate was way too high. I'll take a look some time at whether any players had positive net steal values.

Steals, errors and speedy batters

Last time around, I commented on the similarities between the IBL's stolen base leaders and the leaders in reaching base on error. I glibly wrote that "Not surprisingly, baserunning ability is a key factor in the ability to reach base on error."

Is that really so? Let's plot the error rate (reaches on error per at-bat) versus the steal rate (steals per times on base) for the 50 players with at least 80 plate appearances in 2007:



Wow! What a strong correlation! (Note sarcasm.) Not much support for the theory, it seems. Except for a few outliers, most of the players are scattered in a random cloud with no apparent structure.

But if we massage the data just the right way...

Here's the same data, but restricted to the 20 players with the highest reach-on-error rates:



That's better, isn't it? In fact, we get a correlation of .77 and an R-squared of .59, both indicating a high degree of correspondence between the two statistics - for this group of players.

Does this mean anything?

I think it might.

I would suggest that there are two kinds of hits. There's a "power" hit, a solid base hit into the outfield gap, generally either a line drive or a sharp grounder. It's hit far out and between the fielders so that any batter can make it safely to first base.

Then there's the "speed" hit. Maybe it isn't hit as far, or it's not as hard for the fielders to get to. Whether or not it becomes a hit depends on the speed of the batter (and possibly other runners). If he can leg it out to first, he's got the hit. Otherwise, he's out.

A reach-on-error is predominantly a "speed" hit. It is predominantly a ground ball, but one which was (apparently) played poorly by the defense. If despite the error the batter is put out, the play is recorded as a normal out - no defense error is recorded. If the batter beats out the throw, however, he has "reached on error" - as if it was not his own skill and speed that got him on base instead of out.

So faster runners are more likely to reach base on error. There is no need to assume (as I erroneously wrote earlier, and as Tom Tippett seems to imply here) that some batters actually have the propensity to cause the defense to commit more fielding errors by hitting the ball in a hard-to-field way. Rather, the actual error rate may be distributed evenly among batters, but only some of them can consistently exploit defensive errors to get to first base. The others just get out, and no error is recorded.

Furthermore, it stands to reason that some error plays - especially at lower levels of play - are so egregious that even the slowest batter can reach base. This is clearly the case for wild throws, for example. So there should be a "background rate" of reaches on error that affects all batters, however fast or slow they are. This may explain the lack of correlation between steal rate and error rate for the bottom of the pack - all we're seeing there is random noise, not batter skill. Also, the sample size is probably too small to be significant, with just 1-3 reaches on error per hitter on the season.

Finally, if you haven't yet, please see Tom Tango's comments on an earlier post about steals and error rates. The salient point is that speed probably peaks at a younger age than strength (i.e., fielder's throwing ability). I would add to that that fielding skill, unlike running speed, is learned through experience and probably also peaks later. So the younger age in lower-level leagues can be expected to produce more steals and errors.

IBL 2007 stolen base leaders

As long as we've been discussing stolen bases, let's glance at the 2007 leaders.

A total of 457 bases were stolen in the entire season. Of them, 314 were taken by the 20 leaders in this chart:



Now let's look at them again, this time emphasizing pure base stealing ability. The next chart is sorted in order of stolen bases per times on base; that is, SB / (H + BB + HBP - HR). It indicates how often a player stole a base given the number of opportunities he had to do so. (The cutoff point for the chart was 80 plate appearances.)



Mike Lyons of Bet Shemesh not only led the league with 32 steals, leaving Netanya's Josh Doane in the dust with 25, but he was in a class of his own in terms of basestealing frequency, stealing on average over 71% of his times on base. That's 46% more often than #2 John Toussas of Raanana, and over four times as high as the IBL league average of 16.5% (compare that with about 5% in the major leagues!). And Lyons was caught just 4 times, in 11% of his attempts.

I don't have any earthshattering conclusions here. Just the stats, ma'am.

Long-term league quality indicators

First, credit where credit is due

I don't want anyone to get the idea that using error rates to assess league quality is a new idea. In fact, Bill James himself identified fielding percentage as an indicator of league quality. The error rate and the fielding percentage are just two ways of looking at the same information.


Historical charts of major league stats are available at A Graphical History of Baseball (hat tip: Baseball Musings).

Here's the chart of Errors Per Game (per team):


By this standard alone, the IBL would match the early 1900's with 2.2 errors per nine innings. (If it's any consolation, some of the 2007 rookie leagues are in the same zone.)

Stolen base rates, however, do not track the long-term improvements in league quality. Steals fell to their lowest levels around 1950, then rose until the 1980s, and have declined since then:



I don't know what changes in the game gave rise to these trends in the steal rate - perhaps shifts in runner skill versus pitcher skill? Or maybe it was all Rickey Henderson's fault!

(Update: Duh! Of course, a major factor in the number of steals per game is the overall level of offense - the more baserunners, the more steal opportunities. That's why the relevant steal rate is steals per runner on base, not steals per game.)

It certainly remains possible that the steal rate correlates with league quality at any particular point in time, as my earlier graphs seem to demonstrate. But the steal rate would seem to be a far less reliable gauge of league quality than the error rate, so I'm less inclined to downgrade my assessment of the IBL's quality on the sole basis of its high steal rate. (The IBL's steal rate was 2.5 per nine innings, nearly double the MLB's record levels from the early 1900s!)

More on league quality estimation

The previous post on estimating the level of play in the IBL generated some interesting comments, including on the Baseball Fever Sabermetrics Forum and Tom Tango's blog. Also, Rabbi Jason Miller noticed my citation of his game observations, and commented.

I'd like to respond to the comments, and add some more observations of my own.


Why errors and steals?

Tango is surprised that error rates and stolen base rates correlate at all with the level of the league. After all, the reason batting averages, or walk and strikeout rates, don't track the league level is that they are the result of the confrontation between the batter and pitcher/fielders. Better leagues have better hitters, but also better pitchers and fielders. On the whole, they balance each other out, so the majors don't have higher batting averages or walk rates than weaker leagues. Sometimes pitching overpowers hitting or vice versa, but there's no connection between the relative strength of hitters and fielders and the overall level of league play.

You might expect the same to apply to errors and stolen bases. An error is not just the fault of the fielder. Some batters consistently reach base on error far more often than other batters, presumably because they're hitting more hard-to-field balls. Shouldn't that balance out the stronger fielding in the stronger leagues?

A stolen base certainly is not the sole fault of the fielding team; arguably, it's first of all a skill of the baserunner. So why should weaker leagues have higher steal rates? Don't they have less skilled runners?

On the one hand, the graphs speak for themselves. The correlations between league level and error rates per at-bat (0.93) and stolen base rates per runner on base (0.85) are stunningly strong. If you leave out the inconsistent rookie leagues, they're even higher (0.97 and 0.88 respectively). But that doesn't absolve us of an explanation.

The answer, I think, is that the league-level variations we see in both error rate and steal rate are primarily factors of the quality of the fielding. It may be true that some hitters are better able to hit balls that are hard to field, but at lower levels of play that's not the main factor in producing errors. To quote myself:

What I think you're seeing with the top major leaguers is an ability of exceptional batters not just to "hit it where they ain't", but also to "hit it where it's hard to field". What I think we're seeing with high overall league error rates in the minors is at the opposite end of the defensive ability scale - not balls hit where it's hard to play them, but routine plays that the sub-major-leaguers flub: dropped catches, wild throws, bobbled grounders.

That is, I suspect that the further you go down the ability ladder, the more errors reflect unprofessional fielding rather than skillful batting. Hence, overall higher error rates in overall weaker leagues.

A similar argument can be made regarding steals. While running speed is important in baseball, it's not necessarily that much higher in the majors than in weaker leagues. What is substantially higher is fielding ability, as a result of more experience and winnowing out the poor fielders. Plenty of minor league players can run as fast as their major league counterparts, but they aren't as practiced at holding runners on base and picking them off at second.

The upshot of this analysis is that both of these measures are, at least at league level, essentially indicators of fielding ability. We still have no independent measures of league level based on batting ability or pitching ability. The assessment is very one-dimensional. Unfortunately, stats such as wild pitches or hit batters do not seem to be available for the minor leagues; they could be good indexes of pitcher skill.


More about the stats and graphs

Tango is probably right in suggesting that I had the denominators wrong - errors should be measured per at-bat, and steals per runner on base. In practice, though, those changes don't affect the results in any significant way.

On reflection, I would drop the "unearned runs" and "defense efficiency" measures. The former is just a roundabout and unreliable way of measuring the error rate - it might be useful if you don't have error stats, but it's generally better to measure errors directly. The latter measures the defense's success in putting out batters on balls in play. However, the correlation between batting average on balls in play (BABIP = (H - HR) / (AB - HR - SO)) and league level is very weak (see below). In practice, then, the DER graph is also just another way of measuring the error rate. That leaves us with two relevant stats: errors per at bat and stolen bases per runner on base.

We can plot them against each other for another picture of the league quality level (click to enlarge):



In this graph, I've indicated the league level by the plot symbol: blue spheres for the majors, green spheres for AAA, gray spheres for AA, red spheres for A+, gold spheres for A, gray diamonds for A-, orange spheres for rookie leagues. Three independent leagues have been marked with stars: the Atlantic League (red), Canada's Intercounty Baseball League (orange), and the Israel Baseball League (blue). The regression line is based only on the majors and ranked minor leagues, including the rookie leagues but excluding the independents.

With the exception of the steal-frenzied IBL, the relationship between the steal rate and error rate is clear and strong (0.92 for the ranked leagues). Also, the grouping of leagues by level is mostly distinct. AAA and AA seem quite close in level here - maybe fielding levels aren't different enough to distinguish between them. Note that the Atlantic League falls in the AA-AAA area, as both the league and observers generally claim. A and A- leagues are quite close, but A+ is clearly at a rank of its own. And the rookie leagues show a wide range of levels, but they cluster quite close to the SB/E regression line (with the Canadian IBL somewhere in the middle).

Arguably, the distance along this line could be used as an estimate of league quality, at least as indicated by fielding ability. I'll try to calculate those estimates, time permitting.

Without further ado, here's the graph of BABIP I promised. There's a correlation between BABIP and league level, but it's weak (0.33), and not much value in assessing league quality.



A final comment on the stats. Sabermetricians have often derided the error stats and fielding percentage, not without good reason: "Errors and therefore fielding percentage are an inadequate way of measuring fielders because of the subjective nature of the decisions and because they only record failures and thus fail to take into account the fact that good fielders cover more ground and therefore record more outs" - Dan Agonistes.

But in the aggregate, I think I've shown that errors are a relevant measure of league quality level, and one of the few such measures that are widely gathered and published for baseball leagues of all levels of play. Keep that in mind next time someone touts his new top-secret formula for assessing fielding ability or league quality.

And now back to the rabbi.

Rabbi Miller defers to the judgment of Jay Sokol, who attended the IBL game with him:

Jay is the General Manager for the Delaware Cows of the Great Lakes League, which is a summer league dedicated to helping college players get used to the wooden bats they'll use in the minor leagues. Jay thought the level of play in the IBL was very similar to the wood bat summer league. He even recognized an IBL player whom he previously scouted for the Cows.

I certainly defer to Sokol's baseball judgment - I'm just a fan and a novice sabermetrician. I would point out, though, that the game they watched was between Netanya and Raanana, two of the IBL's weaker teams (at least until Netanya's closing weeks). The game's box score and play-by-play log indicate that Raanana committed five errors - high even by their own averages (2.1 errors per game, the highest in the IBL). So I wouldn't rely on a single game to assess the IBL's level of play. But thanks for the input!

How good was the IBL really?

I'm not done yet with run estimation; I'm doing some work on the Linear Weights method. But I'd like to take a break to examine a different question, one which was on the minds of many fans last summer: What level of baseball did the IBL play?

It was clearly far from major-league standards, but did it reach minor league levels? If so, which level of the minors - AAA (the highest)? AA? Single-A? Rookie ball?

There are a few ways to go about answering the question. We can:

1. Look at people's subjective impressions.

2. Look at where the IBL players were recruited from.

3. Compare the performance of IBL players with other leagues they played in before or after the IBL.

4. Identify statistics which vary based on the level of play in a baseball league, and see how the IBL measured up.

I'd like to try all of these.


1. Subjective impressions

• With the quality of players we expect to attract, we are going to be able to provide a high-caliber level of play, probably most akin to Rookie League/Class A ball in the U.S.

-- The IBL, in advance of the season opening, expected to match the lowest levels of the minor leagues.


• It's a little higher level than I'm used to in college.

-- IBL pitcher Aryeh Rosenbaum describing his first two weeks of the season.


• The quality of play sometimes approached major league standards, while occasionally sinking to a high school level.

-- IBL pitcher Travis Zier writing after the season.


• The level of play was somewhere between college ball and AA minor league.

-- Rabbi Jason Miller, after attending a game.

There's something of a consensus: better than college ball, somewhere around the lowest ranks of the minor leagues.


2. Where the players came from

I don't have a complete breakdown, but it's clear that many of the players had only played college ball before coming to the IBL. Others had played in the lower ranks of the minor leagues, and some had played in independent leagues in the U.S., Europe or elsewhere. This is consistent with the assessment by method 1.


3. Comparing IBL player performance with their play in other leagues

I'm working on this, but it will take some time to gather and organize the data.


4. Compare the IBL with other leagues in terms of statistics which distinguish level of play

See, for example, the suggestion of "SABR Matt" at the beginning of this Baseball Fever posting:

Think about what kinds of events happen in the weakest of leagues and look for them in any league to measure its' quality relative to the strongest of leagues.

Bill James wrote down in one of his abstracts something like a dozen different kinds of things that happen a lot in bad baseball leagues and rarely in good ones. That list included Errors, "rare events" (like triple plays, baserunning outs, mistakes of aggression, base hits on pop-ups (why do you think we call those Texas Leaguers?) etc), passed balls, wild pitches, hit batsmen etc.

The problem here is that it's hard to find statistics for most of these "rare events". Baseball Reference, for example, a tremendous repository of baseball statistics, doesn't report HBPs, passed balls or wild pitches for the minor leagues. And neither do the websites of the leagues themselves.

About the only statistics I could find which fit this description are related to errors and stolen bases. It seems obvious that there should be more errors in weaker leagues, since the fielding isn't as good. For the same reason, presumably, there are more steals - the defense isn't as good at catching them.

(Note that you can't use batting-related data to distinguish level of play. A harder league has both better batters and better pitchers, so there's no relationship between, say, batting average and level of play.)

I collected data for the 2007 season of both leagues of the MLB and all the minor leagues listed on Baseball Reference and computed the following stats: Stolen bases per nine innings, Errors per nine innings, Unearned Run Average (which is like the ERA, but for unearned runs), and Defense Efficiency Ratio, a measure of defensive play which also takes errors into account.

Then I assigned each league a "level of play" rating: 1 for Rookie, 2 for A/A-, 3 for A+, 4 for AA, 5 for AAA and 6 for MLB. (I combined A and A- based on the preliminary results, which indicated they were too similar in level to distinguish between them.)

And now, the graphs. The horizontal axis represents the league level rating, and the vertical axis is the statistic in question. The IBL is marked by a large blue star.









The IBL seems to fall somewhere in the Rookie Ball spectrum, though obviously that's a rather broad spectrum. The level of play seems much more closely correlated with the league ranking for the post-rookie leagues than for rookie ball. I was actually surprised by how nicely linear the graph is for the most part.

Out of curiosity, I added to the graph two other independent leagues with no official ranking level, because IBL players have played there either before or after the IBL. Ryan Crotin, one of the IBL's leading hitters, played several seasons in Canada's IBL - the Intercounty Baseball League - where he was also a batting leader. And two pitchers from Israel's IBL, Rafael Bergstrom and Jason Benson, were signed by the indepedent Atlantic League after the season ended in Israel.

Judging by the graphs above, the Canadian IBL also ranks as a rookie league in level of play, not far from the Israeli IBL in level of difficulty. The Atlantic League, by contrast - labeled "ATL" on the graphs - ranks at about 3.5, somewhere between A+ and AA ball. This contrasts with descriptions categorizing the Atlantic League as "between AA and AAA", but I wouldn't place too much faith in the handful of statistics presented here. There's much more that goes into quality of play than errors and stolen bases, and anyway you could move the ATL point to 4.5 without getting too far off the regression line.

(My, those IBL players just kept stealing bases! Could that be a sign that I've got the level pegged too high? I guess I need data on college ball....)