NL vs. AL leadoff hitters

 

Often while marveling at Ricky Henderson’s amazing stats, I wondered how much greater a leadoff hitter he would have been if he had spent his whole career in the National League.  He had 11,180 plate appearances in the AL but only 2,166 in the NL. In both leagues, the leadoff hitter leads off the first inning, but is not guaranteed to bat leadoff in any following inning. However, I figured that in the National League, batting after the pitcher, it’d be substantially more common that the person batting first in the order would get to lead off. The pitcher almost always makes an out, so I figured it’d be pretty common for him to make the third out (and because of situations where the eighth batter is walked to get to the pitcher, probably more common than one in three).  The eighth batter isn’t that strong in the AL, but a lot stronger than almost any NL pitcher.

I’ve been working off and on over the past two years (more off before getting tenure, more on after getting tenure) on an extremely flexible python toolkit for examining baseball games and it finally got to the state of development where I could test my findings.  I’m not ready to release the toolkit yet (it needs to be polished enough that I’m proud of it), but here’s the code I used to work:

  gc = games.GameCollection()

  gc.yearStart = 2000

  gc.yearEnd = 2014

  gc.usesDH = True

  allGames = gc.parse()

  totalPAs = 0

  totalLeadOffs = 0

  for g in allGames:

      for halfInning in g.halfInnings:

          for p in halfInning.plateAppearances:

              if p.battingOrder == 1:

                  totalPAs += 1

                  if p.plateAppearanceInInning == 1:

                      totalLeadOffs += 1

  print(totalPAs, totalLeadOffs, totalLeadOffs*100/totalPAs)

 

It gets a collection of games where the DH is used or not used, looks at each game, then at each half inning, then at each plate appearance. If the batter is #1, then it checks whether it’s the first appearance in the inning, then prints out the percentage of all batter #1 plate appearances which are leadoffs.  The results were surprising to me. 

	PAs	Leadoff	%
No DH	183,033	75,364	41.175
With DH	163,1781	63,451	38.885

The average difference in the percentage of leadoff plate appearances between the two leagues (accounting for interleague games) is only about 2.5%. This works out to about 15 PAs a year different for Ricky in his prime. So one hypothesis down, but many more to be investigated soon.

Recent Research

A few recent articles and software of interest and some older articles that might have been missed:

• music21j / 21M.051 -- I've been translating music21 to the web to support my teaching of MIT's "Fundamentals of Music" -- feel free to register for an account an play around.
• The Other Tournai Kyrie -- A lost piece of medieval music was sitting right under our noses.
• music21 -- what exactly is a "Toolkit for Computational Musicology"? Older article. The latest version at GitHub
• Conference / Journal Convergence -- When top journals begin publishing only articles presented at invited conferences, do less connected scholars lose out?
• When Computers Listen to Music, What do they hear? -- on music21 and other Boston area projects (Boston Globe)
• Musical examples in web pages -- an easier way to do this than before, using cuthbertLab's music21j.
• Advanced dotting -- the mathematics behind that simple feature of musical notation: the dot.
• An early fifteenth century canon -- unraveled from a manuscript of Strasbourg destroyed in the fire of 1870.
• Bach's voice ranges -- a how-to on music visualization.
• Changing Musical Time -- how rhythm and tempo have evolved over the last 1000 years.
• Sexism and Age in Politics -- are older folks more sexist when it comes to electing a president? The data is unconvincing.
• Are bullpens underused? -- solve for x, and call the bullpen earlier.

ESPN's MLB Power(??) Rankings

The bottom rungs of the
May 26, 2014 rankings

Each week since week 15 of the 2005 baseball season, ESPN has been compiling "Power Rankings," a list from 1 to 30 of the quality/current trends/strength of each team in Major League Baseball. Each team appears with its ranking, logo, name, current record in wins and losses, and a witty factoid about the direction the team is going in or about a player or two who exemplifies that trend. (Though the meaning of these trends is sometimes obscure as I've discussed before.)

It always rankles me when my favorite teams appear lower than other teams with the worse records than my teams' own. Of course that's part of the point of these rankings: to show subjective impressions of who is actually better than someone else despite having the record not showing their "inner strength" or some mumbo-jumbo like that. Still, when week after week, it appears that your team is getting the shaft, you begin to wonder if perhaps the rankings aren't so much about power on the field as power to draw viewers to the Sunday Night featured game, which doesn't exactly showcase all thirty teams equally.

To test whether there's something more happening, I looked at all of the power rankings from Week 15 of 2005, when ESPN started them or at least put them online in their current format, to the latest incarnation, Week 10 of 2014. (No, I didn't look at them all directly, I have computers for that.). For each team each week, I assigned a "bias point" for every rank that a team was above them with a worse win-loss record than them. For instance, if a the Jays at 25-20 were ranked 2 and the teams in ranks 3 and 5 had better records then them then the Jays would get 4 bias points, one for the team with rank 3 and three for the team in rank 5. Similarly teams would get negative bias points for teams ranked above them with worse records. In the illustration above, the Padres (my favorite, generally losing team) would get -1 points for being a position below the Red Sox (my next favorite, generally winning team). The Cubs and Diamondbacks would exchange no bias points even though percentage wise the Snakes are slightly ahead.

Over about ten years of Power Rankings, the teams most often ranked above their records were

1. Yankees (2052 points)
2. Red Sox (1101)
3. Tigers (968)
4. Angels (945)
5. Blue Jays (918)

The bottom five were

30. Pirates (-1141)
29. Astros (-1113)
28. Orioles (-977)
27. Rockies (-848)
26. Marlins (-805)

Since I started this to look at the Padres (-774), I'll just note that they ranked 24th.  For the most part, these numbers make sense -- even though these bias rankings already take into the power ranks assigned on the basis of current records, the people at ESPN wouldn't be earning their keep if they didn't take into account historical trends. In fact, looking at weeks 8 and beyond, the amount of bias is  less, and there's some shuffling throughout the ranks, though not at the very top:

1. Yankees (285)
2. Indians (241)
3. Phillies (210)
4. A's (178)
5. Angels (122)

30. Brewers (-380)
29. D'backs (-326)
28. Astros (-220)
27. Cardinals (-175)
26. Mariners (-153)

(Padres jump to 18th at -30 points, actually beating the Red Sox who drop all the way to 22nd at -70! Clearly those second half spurts and slumps, respectively, make a difference.)

A stronger showing of bias would be whether there's a long-term difference between the record of a team and its bias measure. The five most winning teams over the ten-year period were 1. Yankees, 2. Angels, 3. Red Sox, 4. Cardinals, and 5. Phillies and the most losing were 30. Royals, 29. Pirates, 28. Astros, 27. Mariners, and 26. Orioles (Cubs fans, be glad I didn't extend this list one more spot! oops.; Padres hit #21).  Subtracting the win-loss rank from the Power Rankings bias rank gives a ranking of systematic difference that cannot be explained by records alone.

Most biased for:
1. Cubs (WL rank: 24.5; PR rank: 12; = difference: 12.5)
2. Blue Jays (17 - 5 = 12)
3. Royals (!! Rob Neyer?) (30 - 22 = 8)
4. Indians (19 - 13 = 6)
5. Tigers (7 - 3 = 4)

At the bottom:
30. Cardinals (4 - 16 = -12)
29. Brewers (11 - 20 = -9)
28. Rockies (22 - 27 = -5)
27. Reds (15 - 19 = 4)
26t. D'backs, Padres, Marlins (20 - 23 or 21 - 24 or 23 - 26 = -3)

In both of these lists there are good, average, and pretty bad teams. There are some adjustments that could be made. For instance, since the records only reflect the regular season we could adjust for World Series wins and pennant wins, subtracting a system bias point for each (i.e., 2 pts for winning the Series and one for losing). To keep the numbers exactly constant we'll add one point per team (I love it when the math works out: 3 pts per season and 10 years in the dataset = 30 points, or exactly one per team). At the top nothing changes, since none of the top four teams have done anything in late October, except that the Tigers disappear from the most overrated (two pennants will do that for you) to be replaced by the Nationals. At the very bottom, nothing changes -- in fact four World Series appearances for the Cardinals just makes the bias even worse. San Francisco and Philadelphia make their way into 27 and 26.

Technically by this method, the Red Sox tie Philadelphia, but as #2 on the PR positive bias, they're hardly being discriminated against by any measure, but they do have a legitimate beef against the way they've been treated in the last two-thirds of the season.

There are a lot of ways to slice the data; some of which make the Padres look exploited, and others the give them more credit than they deserve. However, any way you look at the numbers -- adjusting or not for postseason success, including or excluding the start of the season -- there are some teams that the ESPN staff are definitely fans of: the Cubs, Royals, Indians, Nationals, Rays, and Jays. And there are some that get no love: Rockies, White Sox, Reds, Rangers, Giants, Diamondbacks, and Brewers. But most of all its the St. Louis Cardinals who time and time again get the shaft on the Power Rankings.  Maybe it's time for the crew to stop batting their eyelashes at the Friendly Confines and look for inner strength down I-55.

(attachments: Excel Spreadsheet and, in case anyone wants to look at NFL, NBA, or NHL Power Rankings, the Python program that generated the data)

Managing with no idea about random fluctuations

Ah, Jerry Manuel, "manager" of the Mets, is up to it again. Now he's suggesting that he will bench or move Jason Bay or David Wright for batting .241 and .240 after 54 and 50 at bats, respectively. Of course batting .240 after an amazingly huge sample size of 50 at bats definitely proves that you're doing terribly, right? I mean it's utterly inconceivable that a .280 or .300 batter would go through a 50 at-bat period where they batted that low.

Okay, enough sarcasm, let's run the statistics for Jason Bay. Here's a little program in python than can do it for us.

------

import random
l = 0
for k in range(1000):
    i = 0.0
    for j in range(54):
        if random.random() < .300:
            i += 1.0
    if (i/54) < .241:
        l += 1
print "%2.0f%%" % (l/10.0)

------
What do we learn? It turns out that if Jason Bay were a pure .300 hitter -- that is he had a 30% chance of getting a hit on every at bat, there's a 22% chance that he'd have an average as low as .241 after 54 at bats. If he were a decent .275 hitter, he'd have 35% chance of having an average that low.

The numbers are about the same (or even a bit more disappointing) for Wright, which surprised me. I would've thought 4 extra at bats would far more than cancel out one point of BA, but it doesn't because the last digit isn't significant yet! With 50 at bats, it's impossible for Wright to be slightly better than Bay by batting, say .242, because each hit still represents a BA difference of .020! If Wright had one more hit, he'd be batting a respectable .260. If one or two fewer, he'd be at .220 or .200 and probably already traded by the kinds of short-sighted people who get paid millions to run things that they don't understand. (see: Management, Mets [or most non-winning teams]).

The point isn't that Bay and Wright are great hitters going through bad times. They could have morphed into terrible terrible hitters who are lucky to even be batting the .240 that they have. The point is that we just don't know yet. And given the number of millions you're paying them based on prior performance, maybe, just maybe, it makes sense to let them play long enough so we can find out what's actually happening?

Addendum, 3 hours later: I originally decided to leave out a criticism of the utter stupidity of messing with an approach that is causing Wright to be leading the league in walks (with a .457 OBP), but nah, they deserve all the criticism they can get. So there you are.

Adjusted ERA+ and leaders

The most important stat for determining the quality a pitcher (at least over the course of a career) is ERA. There's really no argument that can be made against it. Wins are far too dependent on how the rest of the team (i.e., batters) do; strikeouts certainly show domination, and career strikeout numbers show longevity as well. But in terms of doing his job, preventing runs, career ERA is the single number that shows how well this was accomplished. (Okay, perhaps ERA over a 5-10 year peak period might be better, to not diminish the careers of those who choose to keep playing into their "worse than average but far better than replacement" years). The main problems with ERA are that it does not adjust for ballparks, leagues, mound heights, steroid usage of batters, or other factors that changed over the years.

Fortunately, the concept of adjusted ERA takes care of all this. And adjusted ERA+ makes reading adjusted ERA even easier. An aERA+ of 125 roughly means an ERA 25% lower than the league, adjusting for park effects etc. (okay, actually it's 20% lower; since an aERA+ of 200 means an ERA 50% of that of the league). An aERA+ of 125 also means you're likely to need to prepare a speech for Cooperstown. The vast majority of pitchers above 125 and almost all eligible starters above 130 are in the Hall.

For a long time, there was a big gap between aERA+ #1 and #2, with Pedro Martinez's 160 towering over Lefty Grove's 148. This disappointing season has lowered Pedro to a mere 157, but it would take more than a few years of (relative) mediocrity to drop him below Grove or Walter Johnson. (Next on the list, for those curious, is Dan Quisenberry which is probably the best Hall of Fame case for Quisenberry that could ever be made).

But why bring all this up now? Because despite Martinez's struggles, there's now (as of last week) a much bigger gap between #1 and #2:

  1.  Mariano Rivera   197
  2.  Pedro Martinez   157

What happened? Rivera pitched his 1000th inning last week, making him eligible for career ERA awards. Perhaps the IP requirement should be raised so that the list isn't dominated by closers. But maybe that's not necessary. With the development of the minor-league (or even high school) relief specialist, fewer and fewer will reach this plateau with each passing year. Bochy and Bud Black's cautious use of Trevor Hoffman since he returned from surgery six years ago has kept him from breaking the 1000 IP mark. As of this evening, he's 22 IP short. Since he's been averaging .35 IP per game over the past four seasons, he's likely to end the season (and possibly his career? the fan in me hopes not) about five innings short. His aERA+ of 145 would place him 9th or 10th all time. Prior to this disastrous season, he would have been third.

(For the complete list, see Baseball-Reference.com)

The only other reliever on the ERA title horizon is Billy Wagner, whose aERA+ of 180 would place him comfortably in second, though still at a great distance below Rivera. However with only 819 IP, he will likely need three more seasons to qualify. And anything could happen by then. Troy Percival, with an aERA+ of 151 but only 687 IP, averaging fewer than 50IP/year at age 38, seems highly unlikely to qualify.

Of the other active high saves players, Roberto Hernandez already qualifies at 131; a Hall of Fame number for a starter, but unlikely to get a notice for a reliever with "only" 326 saves. Jose Mesa is what we always thought him to be, exactly an average pitcher (aERA+ of 100), and thus probably a below average reliever. Todd Jones is a little better, but nothing to write to Cooperstown about. Ditto Jason Isringhausen, 100IP short; though kudos to him for having such dreadful recent performances that his manager is bringing back the (great) idea of a closer by committee.

And as far as the brilliant young closers of today. Yes, very exciting. Yes, I know Papelbon has an aERA+ of 269(!); K-Rod at 186; Nathan at 152; Lidge at 147. But for an article on a stat that requires 1000 IP, please ring again when there's just a few hundred innings left to go. Why so pessimistic? Robb Nen, John Wettland, Randy Meyers, Tom Henke, Jeff Montgomery, Rod Beck, Ugueth Urbina, and (ah heck, throw in the newest member of the fraternity) Eric Gagne. If these names mean something to you, you'll understand.

Hate the stat, love the statter

I spent part of the last week of July reading the various, mostly extremely short, obits of Jerome Holtzman, sportswriter extraordinaire (and the Chicago cubs follower who did not incite the city of Sandy Eggo to riot by calling the selling of Sushi and the installation of baby-changing stations in Men's rooms at S.D.'s ballpark "the beginning of the decline of America." q.v., one M. Royko). Throughout all the obits, the discussion centered on Holtzman's invention of the "save" as baseball statistic.
(N.Y. Times obit.)

What puzzled me the most is, with the notable exception of The Hardball Times, how often commentators were blasting Holtzman for what a bad statistic the save is. To be sure, it is a bad statistic: it rewards (in the end, financially) players for participating in one facet of the game that has never been shown to be more significant than several others. It gives the same benefit to pitchers who bail their team out of the toughest of all situations as to closers who record a few outs with a pretty sizable lead. But consider again what the save replaced: a world where relief pitching had no worth on paper (and in a world where the "Win", another terrible stat, was even more important). Also consider what it meant in the early 60s to introduce a new stat into the world. Computing saves retroactively for every baseball player was not as simple as a few lines of Perl and a download from retrosheet. And, the tinkering that Holtzman and others applied to the save suggests that he did not believe he had discovered the perfect, never to be supplanted statistic. Admire what he did for the time in which he lived.

No, marshal your scorn for those who with the hindsight of time and better access to information still defend the save. Those who cling to a bad idea are far worse than those who throw the idea out to the marketplace in the first place.

P.S. I wish there were a stat with more sophistication than Ari Kaplan's "Fan Save Value", but with fewer lookup charts than his more accurate "Save Value." The former is not much of an improvement over the Save (and couldn't easily translate to a generalized "relief value") while the latter has too many "hidden" constants relating to expected runs (that aren't really constant, but actually change from year to year that I can't see it actually being adopted.

Here's a simple(r) formula for calculating expected runs, that you can carry around with you:

ER = (5 + total_runners + 3 * (total bases occupied)) 
            * outs_left / 30

total bases occupied simply means to sum up the base numbers with runners. So runners on second and third is 2+3 = 5. Outs left is 3 - outs. So no outs = 3.

Here's how this version of expected runs compares to the standard expected runs chart:

Outs 1B 2B 3B  My ERs   Table  Difference
0    0  0  0    0.50    0.54   -0.04
0    0  0  1    1.50    1.46    0.04
0    0  1  0    1.20    1.17    0.03
0    0  1  1    2.20    2.14    0.06
0    1  0  0    0.90    0.93   -0.03
0    1  0  1    1.90    1.86    0.04
0    1  1  0    1.60    1.49    0.11
0    1  1  1    2.60    2.27    0.33
1    0  0  0    0.33    0.29    0.04
1    0  0  1    1.00    0.98    0.02
1    0  1  0    0.80    0.71    0.09
1    0  1  1    1.47    1.47    0.00
1    1  0  0    0.60    0.55    0.05
1    1  0  1    1.27    1.24    0.03
1    1  1  0    1.07    0.97    0.10
1    1  1  1    1.73    1.60    0.13
2    0  0  0    0.17    0.11    0.06
2    0  0  1    0.50    0.38    0.12
2    0  1  0    0.40    0.34    0.06
2    0  1  1    0.73    0.63    0.10
2    1  0  0    0.30    0.25    0.05
2    1  0  1    0.63    0.54    0.09
2    1  1  0    0.53    0.46    0.07
2    1  1  1    0.87    0.82    0.05  

As you can see, the formula slightly over-predicts expected runs (though with the important exception of the most-common occurrence, no outs, no one on, which almost balances out the rest of the error). The only case where it's over 13 hundreths of a run off is the rare case of no outs, bases loaded, which it over-estimates by 1/3 of a run. If a formula is to overestimate any situation, I'm happy with it being this rare situation: an "oh shit!" moment for any incoming reliever. In any case, it's an easier formula to remember than 24 "random" numbers.

Are bullpens underused?

This post was mostly written during Spring Training, so 2007 figures are used throughout. Life prevented posting until now.

Back in the "good old days" of baseball, bullpens were nearly non-existent. Two-man rotations were common, 600 inning-pitched seasons were possible, and one man pitched every inning of an entire major league season (Wondering who? See below). Since then, we've created four-man rotations, dedicated bullpens, closers, five-man rotations, long relievers, setup men, and, coming soon to a ballpark near you, the seventh-inning specialist. And throughout all thus, grumpy old men--along with grumpy young men, grumpy old women, grumpy young women, and grumpy transexuals of all ages--have decried the changes as a weakening of the quality of starting pitching.

But is it possible that everyone is wrong? Could the problems with pitching be traced to an underuse of those 6 to 8 "guns" not considered durable enough to start a game? Let's consider some baseball axioms before we look further. I like math, so I'll use some weird symbols, but try to explain them.

Axiom 1: ∂(ERA)/∂(IP) > 0

That is just to say that we expect ERA to rise for every additional inning pitched. I'll admit that this axiom might not hold for a former AA-pitcher getting his first few innings in at the major league level, or for someone coming back just off the disabled list. But for the most part, it's hard to disagree with, whether we're dealing with innings pitched within a game or innings pitched over a season.

Axiom 2: ERA(closer) < ERA(ace) ; ERA(setup man) < ERA(#2 starter) ; etc...

The ERA of your relief squad tends to be lower than the starting pitchers. Or to put it in another way, if you only had to put your best pitcher in for one inning of work, he would almost certainly come from the bullpen. Compare the best reliever to the best starter on almost every club and you'll see that the best reliever comes out ahead. Usually even the best two or three relievers have better ERAs than aces--this holds true for great teams and miserable ones. In 2007, the Detroit tigers had three relievers log more than 40 innings with a lower ERA than their ace, Justin Verlander, and two more with a lower ERA than their second best pitcher to log at least 15 starts. The Padres (the team I know best): Even a triple-crown winning Cy Young pitcher (Peavy) had an ERA bested by a setup man, Heath Bell (with 93 2/3 IP, not a small sample); and four more relief pitchers (Hoffman, Brocail, K. Cameron, and Justin Hampson) bested Chris Young, their second best pitcher. We see the same patterns even for lousy teams: four Royals relievers outpitched Gil Meche's 3.67 ERA.

Compare the ERAs of bullpens as of mid-2007 to this analysis of starters at the end of the season. The average bullpen is about as good as the average no. 2 starter! In other words, it does not really matter if by the sixth inning your starter is still "feeling good." Unless he's your ace, or throwing a shutout or no hitter, or your bullpen is absolutely drained from a recent 18-inning game, it's time to call in some new arms. Do so and your expected chance of winning just went up.

All else being equal, every inning that you have someone on the mound with a higher ERA than someone else you could put out there is an inning of poor managing. All else being equal, bullpens should be used more until their ERAs rise to meet that of the starters.

Now here's the argument I'm ready to hear: all else is not equal. Not every inning is as important as every other. That's definitely true! The best relievers pitch in the most important situations: with the game close, and a win on the line if only he can not allow any runs. So it makes sense that you want some of your lowest ERA-men pitching then. But when do starters begin pitching? They begin with the game tied, where any run allowed or not makes a huge difference in the probability of winning or losing the game -- nearly as important a situation as what setup men and closers pitch in. But there are several members of the bullpen who tend to pitch in less important innings; that is, blowouts in either direction. So if anything, the ERAs of bullpens should be substantially higher than starters. That they are not, shows that the bullpens are being over-rested and under used.

Trivia answer: Jim Devlin of the 1877 Louisville Grays pitched every inning in a 61 game season, compiling 559 innings pitched and allowing a total of 4 HRs. Though his ERA was a very good 2.25 (146 ERA+), it says something about the way official scorers have changed over the years: though he allowed only 140 earned runs, he allowed a total of 288 runs, or 8 more unearned runs than earned.

(Before I'm accused of copying this trivia information from Wikipedia, be sure to check who added it there in the first place).

Context and baseball statistics

From this week's MLB Power Rankings on ESPN.com:

In May, Hideki Matsui has more multi-hit games (nine) than he has games in which he hasn't gotten a hit (five)

We're supposed to take this as to mean that Hideki Matsui is doing great this month. But what does it actually mean? How many hitters would we expect to have more multi-hit games than no-hit games? 1%? 10%? Stats like this out of context drive me crazy. It's pretty easy to figure it out at least for simple cases.

The probability of not getting a hit in any at bat is (1 - Batting Average), so the probability of going 4 at bats without a hit is (1-BA) to the 4th power. Here's a little program (in Python) for figuring this out:

def noHit(BA):
    return (1-BA)**4

>>> noHit(.250): 0.32
>>> noHit(.300): 0.24
>>> noHit(.400): 0.13

So we can see that for even an average player, a no hit game happens only 1 in 3 games, and for a good batter, or a good batter on a real roll, these things happen rather seldom. What about Multi-Hit Games? If you have four at bats per game, there are 11 different ways of getting two or more hits (one way of getting four hits, 4 of 3, and 6 of 2). In the chart below, x = hit, and o = not hit:

xxxx = four hits

oxxx = three hits
xoxx
xxox
xxxo

xxoo = two hits
xoxo
xoox
oxxo
oxox
ooxx

xooo = one hit
oxoo
ooxo
ooox

oooo = no hits

(For those interested, the number of ways of getting 4, 3, 2, 1, 0 hits, that is, 1, 4, 6, 4, 1 is the fourth row of Pascal's triangle). So one way of calculating the probability of multi-hit game is to find the probability of a single hit game (4*BA*(1-BA)^3) add to it the probability of a no-hit game, and subtract it from 1:

def multiHit(BA):
    return 1-(noHit(BA) + 4*(BA*(1-BA)**3))

>>>multiHit(.250): 0.26
>>>multiHit(.300): 0.35
>>>multiHit(.400): 0.52

So as long as you're getting 4 ABs per game, you don't really need to be a great hitter to expect to get more multi-hit games than no-hit games. In fact, a BA of just .267 will do it for you. Returning to the original post, we see that Matsui is doing better than 1:1 in May, getting a 9:5 Multi:No ratio. How good do you have to be to get that? A .320 BA will suffice. Matsui's BA has actually been slightly better than that in May, .337, but he's also been getting just under 4 ABs a game (3.83).

4 ABs a game (or even 3.8) is really only manageable if you're not having many plate appearances that don't count for at bats -- in other words, if you're not walking much. In April, Matsui was averaging only 3.1 ABs per game. This makes it much harder to have so many multi-hit games: if you have 3ABs per game, you need to be batting above .348 to get more more multi-hit games than no-hits, and have a whopping .411 to have Matsui's ratio.

Looking closely at the numbers, there's much less to cheer about for fans of Godzilla: the rise in multi-hit games came almost entirely from a drop in walks (from 12 to 7), resulting in a OBP 40 points lower in May than in April. He did not make up the difference in SLG either, dropping 50 points there. So upon closer inspection, the numbers tell an entirely different story: in everything but BA Matsui had a May that was worse than April and below his career levels.

The sort of mixed metaphors I love

"You talk about just inside! That was about a hemidemisemiquaver inside."
-- Jerry Coleman (Hall of Fame Broadcaster, 83 years old)