Hitting .400 / Three True Outcomes
With the Minnesota Twins in town this last weekend, much of the talk about the visitors was about Chairman Joe Mauer hitting a ridiculous .410 average. Mauer's average got me thinking about what it would take to hit .400. Here's what I got:
No batter has a true talent level of a .400 hitter, which requires that a batter get lucky to get there. Because it is easier to get lucky over the short-term, a .400 average is more likely to occur if a player has fewer at bats. A player can get fewer at bats due to manager trickery like batting a great hitter in the 8-hole, but what manager is going to do that? In the player's control, however, is the number of walks he takes and how frequently he takes them.
In 1941, Ted Williams walked 147 times in 606 PA's, having a .243 BB/PA average. Almost a quarter of the time that the Splendid Splinter came up to bat, he got a base on balls. That's ridiculous. The only player I'm aware of who has ever reached a level higher than Teddy in this category is Barry Bonds, who has .376 BB/PA in 2004 and .324 in 2002. Babe Ruth equaled Ted Williams' 1941 output once, and that was in 1923.
Williams also led the league in HR's in 1941, hitting 37, 6.1% of the time he came to the plate. Bonds did better on several occasions, but Williams did beat out Ruth's 1923, where he hit a homer 5.9% of the time he came up. Home runs are quite obviously always hits, so it would make sense for a high-average hitter to have a not-insignificant number of HR's.
By the same token, the high-average batter will also limit strikeouts, since they are never hits. Williams struck out 4.5% of his PA's, better than Bonds in his higher average/OBP seasons ('96, '02, and '04, where he K'd 11.3%, 7.7%, and 6.6%, respectively), and also struck out less than half the time as babe Ruth (13.3% in '23).
But what about some of the other players who have chased .400? How do they compare? In 1995, Edgar Martinez struck out at a comparatively fast rate, 13.6%, but he also walked more than anyone not named Bonds, Ruth, or Williams, checking in at .182 BB/PA. In Tony Gwynn's 1994, where he hit .394 before the strike, he had a BB/PA of .101, HR% of 2.5%, and K'd only 4.0% of the time. When George Brett hit .390 in 1980, He had .113, 4.7% and 4.3%.
So does Mauer have a chance?
I checked out BB-ref this morning and pulled up his stats. He's walking better than Gwynn or Brett, up at .154 BB/PA, and he's striking out like Bonds did in '96 (11.4%), but his HR numbers are ridiculous. Right now, Joe Mauer is hitting homers 8.1% of the time that he steps in. That's better than Bonds' 2002 by 0.6%, and Bonds' '04 by .8%. Nobody on my high-average list not named Bonds (including Williams, Ruth, DiMaggio, Brett, Edgar, Gwynn, Pete Rose, Rod Carew, Ichiro, and Wade Boggs) was even within 20% of what Joe Mauer is doing right now.
On the other hand, Mauer is probably positively influenced by playing in the Metrodome, where turf will help baseballs skid through the infield for hits more than they would outdoors. I don't think it'll make the difference for him, since he's played there his whole career and never batted above .350, but if you're looking for reasons why he might do it, I think that's your big one.
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Comments
This is based on pretty much nothing but intuition
but I’ll go ahead and posit that the chances of a full time catcher hitting .400 over an entire season are close to nil. With modern bullpen use, steroids, advanced scouting and so on, I think it’s very very unlikely that any hitter at all can hit .400 for a season, but for a guy who has so many other responsibilities… he would have to be in a different league entirely. Just my two cents.
"Even the stupidest of men, by some instinct of nature, is convinced on his own that with more observations his risk of failure is diminished."
-Jacques Bernoulli Ars conjectandi 1713
by Bearskin Rugburn on Jun 8, 2009 2:41 PM PDT reply actions 0 recs
I think you've got a point here.
Catchers do have to spend a lot of time with their other responsibilities, but if you think about it another way, a starting catcher is going to have a number of days off: day games after night games, perhaps your backup catcher is a “personal catcher” for one of the starters. A Catcher will have more days off than any other regular position player, and as such will have fewer PA’s. A patient batter with fewer PA’s will have MUCH fewer AB’s, increasing variation and the probability of hitting .400.
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by Two Rs and Two Ls on Jun 8, 2009 2:55 PM PDT up reply actions 0 recs
This is also true
"Even the stupidest of men, by some instinct of nature, is convinced on his own that with more observations his risk of failure is diminished."
-Jacques Bernoulli Ars conjectandi 1713
by Bearskin Rugburn on Jun 8, 2009 3:00 PM PDT up reply actions 0 recs
But doesn't Mauer usually DH when he gets an off day from catching?
He did once in this past series. If he does that throughout the season it won’t affect his number of PAs.
by Snowman1025 on Jun 8, 2009 3:01 PM PDT up reply actions 0 recs
Ah, good catch.
Gardenhire would be crazy to not bat his most productive hitter basically any time he got the chance.
It is a truth universally acknowledged that a zombie in possession of brains must be in want of more brains. -- P&P&Z
by Two Rs and Two Ls on Jun 8, 2009 4:48 PM PDT up reply actions 0 recs
Great post.
I think the turf definitely helps Mauer in his quest. You referenced Brett and Edgar in their runs at .400 and they happened to both play in stadiums with turf at the time.
It would be awesome if Mauer could somehow reach the mark for the entire season.
by Wilder. on Jun 8, 2009 3:04 PM PDT reply actions 0 recs
I don't know if this matters much
but the turf that Edgar and Brett played on is vastly different than modern FieldTurf, which as I understand it plays a lot more like grass – those other two played on 70’s and 80’s Astroturf, which was basically concrete. I don’t know if the effect can be quantified but I’m thinking that FieldTurf is less of a benefit than Astroturf was.
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by pdb on Jun 8, 2009 3:10 PM PDT up reply actions 0 recs
*basically PADDED concrete, I meant
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by pdb on Jun 8, 2009 3:11 PM PDT up reply actions 0 recs
I think you're right on this one.
I’ve played on both kinds of field and yeah, FieldTurf really tries to be a lot more grasslike than Astroturf did, which mitigates the batters’ benefit to a degree, but I still think it’s a faster playing surface than grass.
It is a truth universally acknowledged that a zombie in possession of brains must be in want of more brains. -- P&P&Z
by Two Rs and Two Ls on Jun 8, 2009 4:50 PM PDT up reply actions 0 recs
When did they create the sacrifice? Didn't they tally up into BA when Williams played?
by Kermit. on Jun 8, 2009 3:09 PM PDT reply actions 0 recs
I'm assuming you mean sac flies here
since I’m guessing Ted didn’t sacrifice bunt too often. Or at least I hope not!
by johnbai on Jun 8, 2009 4:22 PM PDT up reply actions 0 recs
I thought he meant burnt offering
"Even the stupidest of men, by some instinct of nature, is convinced on his own that with more observations his risk of failure is diminished."
-Jacques Bernoulli Ars conjectandi 1713
by Bearskin Rugburn on Jun 8, 2009 7:01 PM PDT up reply actions 0 recs
Yeah, I seem to remember them adjusting for that.
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by qrsouther on Jun 8, 2009 4:35 PM PDT up reply actions 0 recs
*Posthumously, that is, adjusting his would-be average factoring in sac flies. I think the figure was .421 or something crazy like that.
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by qrsouther on Jun 8, 2009 4:36 PM PDT up reply actions 0 recs
Cool, wasn't sure how that worked. I knew that the sac fly rule has been on and off again, wasn't sure what the stats have done with that.
by Kermit. on Jun 8, 2009 6:00 PM PDT up reply actions 0 recs
I think it was off at the time.
But like I said, an adjustment looked into what it could’ve been and it was other-worldly.
Addicted To Quack [dot] com; Dear Joevan, Develop motor skills. Love, ATQ.
by qrsouther on Jun 8, 2009 7:39 PM PDT up reply actions 0 recs
Seriously?
.421? That is insane. I had no idea that BA at that time didn’t include sac flies.
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by Edanger6 on Jun 11, 2009 10:35 PM PDT up reply actions 0 recs
The way I see it, the best way to hit .400 would be to get a hit in 40% or more of your at-bats over a full season.
by Vatinius on Jun 8, 2009 4:02 PM PDT reply actions 0 recs
Or alternately one could fail less than 60% of the time
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by pdb on Jun 8, 2009 4:15 PM PDT up reply actions 0 recs
Imagine what the rest of those guys would have hit if they had Jeff Kent hitting behind them.
Barry Bonds had it sooooo easy
by Kermit. on Jun 8, 2009 5:59 PM PDT up reply actions 0 recs
I don't really think the guys who have hit 0.400
rely on that much luck. Looking at the list most players had several seasons in the high 300s in addition to their 400+ season(s).
Also how the hell did Joe DiMaggio win the MVP over Ted Williams in 1941. That has to be one of the biggest oversights ever.
by Edgar for Pres on Jun 8, 2009 11:27 PM PDT reply actions 0 recs
The setting of previously unheard of records does tend to bias the voters a bit
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by pdb on Jun 9, 2009 6:58 AM PDT up reply actions 0 recs
Which do you think will happen first,
another 56 game streak or a .400 avg? I’m leaning the hit streak. ’41 was a long time ago, and pitchers prepare differently for batters now than they did then, especially ~.400 hitters.
"Even the stupidest of men, by some instinct of nature, is convinced on his own that with more observations his risk of failure is diminished."
-Jacques Bernoulli Ars conjectandi 1713
by Bearskin Rugburn on Jun 9, 2009 8:19 AM PDT up reply actions 0 recs
Yeah, I'd say the hit streak would be broken first
but the fact that the most recent challenger to that record (Utley in ‘06) “only” got to 35 games before the streak ended tells me it’ll probably be a while before even that one gets broken.
Nice Guys Finish Third - My semantics are a waste of time.
by pdb on Jun 9, 2009 8:28 AM PDT up reply actions 0 recs
Definitely hit streak simply because the record gets challenged more frequently.
Albeit, like you said, 35 games is the longest streak over the last several years, so it is likely to be a longtime before we see it happen. But hey, Zimmerman and Ichiro already had a couple of good runs this season.
by Wilder. on Jun 9, 2009 8:40 AM PDT up reply actions 0 recs
Ichiro could have literally doubled his run and not broken the record
I don’t think we’ll see either of those accomplishments for a long time yet
by seattlebruin on Jun 9, 2009 9:03 AM PDT up reply actions 0 recs
i don't know if it is challenged more frequently.
It’s just that a streak can start or end any time during the season so any time a guy gets a hit for over 20 games the number 56 crops up. 35 gets you, basically, 2/3 of the way there. In 2004, Ichiro batted .423 for Jul, Aug, Sept/Oct. in other words, he was half way to the record. He also batted near .400 in May, but was hurt by a .255 April and .273 June. So… I dunno. Seems like Ichiro in 04 came about as close to a full season .400 as Utley did to a 56 game streak.
"Even the stupidest of men, by some instinct of nature, is convinced on his own that with more observations his risk of failure is diminished."
-Jacques Bernoulli Ars conjectandi 1713
by Bearskin Rugburn on Jun 9, 2009 9:30 AM PDT up reply actions 0 recs
Are you kidding me?
I mean, they’re both very difficult, but the odds of that streak were infinitesimal. I know this is simplifying the argument a bit, but think about this:
How many .400 avg player-seasons have there been in baseball history?
How many 56 game hit streaks have there been in baseball history?
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by Eyebrows on Jun 9, 2009 11:00 AM PDT up reply actions 0 recs
A lot of math and simulations
found here (skip to page 12/13 for the summary).
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by Eyebrows on Jun 9, 2009 11:12 AM PDT up reply actions 0 recs
Exactly zero each in modern baseball.
by Poochie on Jun 9, 2009 11:21 AM PDT up reply actions 0 recs
How do you define "modern"?
DiMaggio’s streak was in 1941, right>
(I don’t ask snarkily, I’m just unsure when the “modern era” started)
Nice Guys Finish Third - My semantics are a waste of time.
by pdb on Jun 9, 2009 11:24 AM PDT up reply actions 0 recs
Technically "modern" baseball started in 1901
(which is a stupid arbitrary line because they had been playing the same style of baseball in the 90s)
But, for me, I don’t see how modern baseball could start before integration.
by Poochie on Jun 9, 2009 11:55 AM PDT up reply actions 0 recs
Isn't 1954 the earliest RotoSheet goes back to?
Starting at the farthest back that complete gamelogs go might be one to periodize baseball and come up with “modern” – at least in terms of statistical analysis.
by Decatur on Jun 9, 2009 12:10 PM PDT up reply actions 0 recs
My uncle studied this for SABR
I don’t remember what his calculations ended up being, but 56 games was definitely the least likely scenario. So I would also believe that beating 56 games is far less likely than .400.
...and now I'm here
by Librocrat on Jun 9, 2009 12:36 PM PDT up reply actions 0 recs
I should add that what he was really studying was the "hot streak"
and Dimaggio’s played some role in that, showing something like it was the only time in baseball (or all sports?) that a hot streak existed. I don’t remember the details of the study and could be butchering it dramatically since I was like… 18 and not paying attention, but if I find it I’ll try to post it.
...and now I'm here
by Librocrat on Jun 9, 2009 12:45 PM PDT up reply actions 0 recs
Some guy had 18 or so consecutive hits. Nothing is ever made of it, but I think the odds on that are quite a bit higher than 56 games.
by Kermit. on Jun 9, 2009 2:03 PM PDT up reply actions 0 recs
12, actually
Had to look this one up, but Walt Dropo had 12 consecutive hits in 1952. That’s kinda mind-boggling.
Nice Guys Finish Third - My semantics are a waste of time.
by pdb on Jun 9, 2009 2:20 PM PDT up reply actions 0 recs
Thanks, I was looking high and low for that
by Kermit. on Jun 9, 2009 6:53 PM PDT up reply actions 0 recs
I find B-A to be a good source for records of this nature
they’re not cutting-edge statistically, but they’re a good repository for stuff like this.
Nice Guys Finish Third - My semantics are a waste of time.
by pdb on Jun 9, 2009 9:32 PM PDT up reply actions 0 recs
Haven't there been a couple of players who have had 9-10 consecutive hits?
Or maybe I am thinking about a consecutive reaching base record?
by Wilder. on Jun 10, 2009 7:42 AM PDT up reply actions 0 recs
it's all there in the link you know
Nice Guys Finish Third - My semantics are a waste of time.
by pdb on Jun 10, 2009 7:57 AM PDT up reply actions 0 recs
I should click on links more often.
Good find.
by Wilder. on Jun 10, 2009 5:49 PM PDT up reply actions 0 recs
You have to get lucky to hit .400
the argument being made is that a great hitter can get himself to the high-.300s but needs additional luck and an amazing season to get to .400. It’s just one of those magical numbers that’s oh-so-hard to get to. Kind of like 56 games
by seattlebruin on Jun 9, 2009 9:04 AM PDT up reply actions 0 recs
I gotta say, I just noticed that the player links in this post
go to Tony Gwynn, Jr. and to the LAD pitcher Edgar Martinez and not the Mariner. I find this fact a little upsetting.
It is a truth universally acknowledged that a zombie in possession of brains must be in want of more brains. -- P&P&Z
by Two Rs and Two Ls on Jun 9, 2009 10:12 AM PDT reply actions 0 recs
Luck
I did poorly in college statistics but I’d be interested to see how much luck it would take to hit .400.
What I mean is that a hitter will have a ‘natural’ average. Lets say it’s .300. That’s the hitters skill level leveled out over league average pitching balanced against the average stadium he will play in. In theory if this hitter had infinite at bats his average would be .300.
But he won’t have infinite at bats. He’ll have hundreds. And that means the chance of statistical clumping. I think it’s an interesting question to ask what the odds are that a .300 ‘natural’ hitter will get lucky and hit .400 for an entire season. These numbers shouldn’t be too hard to do in the base form and we could see what kind of ‘natural’ average a player would need to have plausible odds of hitting .400.
Even Rob Johnson can go 2 for 5 in a game. That’s .400. He would just have to get really really luck for that to last for an entire season. But technically it’s possible (and yes, I play powerball).
I guess this is screwed up a bit because pitchers are going to pay special attention to a hitter who is flirting with .400. They just won’t get the same pitches to hit as they did when they were batting .300.
by Snuffleupagus on Jun 10, 2009 9:11 AM PDT reply actions 0 recs
I think what you are looking for is a binomial distribution
In, say, 400 at bats, a true .300 hitter has a less than a .0005% chance of hitting .400 in that span due solely to luck.
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by vivaelpujols on Jun 15, 2009 10:43 PM PDT up reply actions 0 recs
I like the reasoning that hitting .400 is impossible
because Barry Bonds didn’t do it. If it were possible, Bonds would have, so therefore by modus tollens it must be impossible.
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by Llewdor on Jun 10, 2009 1:08 PM PDT reply actions 0 recs
Bonds was the only guy I could think of who had that many walks in a season, or HR/PA.
I looked at Rickey Henderson, too, since he held the record for career walks before Bonds did, and he was never close.
For what it’s worth, Bonds, Rickey, Ruth, and Williams are 1-4 on number of walks taken in a career.
On the other hand, Bonds did only lead the league in BA twice, in ‘02 and ’04, and only batted above .330 two other times in his career (’93 and ’03).
It is a truth universally acknowledged that a zombie in possession of brains must be in want of more brains. -- P&P&Z
by Two Rs and Two Ls on Jun 10, 2009 5:58 PM PDT up reply actions 0 recs
Watching Albert Pujols this weekend had me thinking about this magic mark. Here is a guy who could theoretically do this, because he is a lifetime .330 hitter and is feared by every pitcher in the league (even Cliff Lee had to calm himself down after every AB tonight).
BUT, the guy is currently surrounded by no one of merit. So, pitchers will throw to him because the worst possible outcome is a solo home run. I often saw Albert expand his strike zone because no one else was hitting around him.
So, not only do you need to have incredible will power to take walks (as odd as that sounds), you also have to have players around you that will make the opposition pay for walking you. Otherwise, it’s human nature for the star player to “do too much” to help his team win.
by Toxicadam on Jun 14, 2009 8:51 PM PDT reply actions 0 recs
"So, pitchers will throw to him because the worst possible outcome is a solo home run"
If he has no one hitting around him, then they don’t need to throw to him because the worst possible outcome would be a walk. In addition, the more walks he gets, the worse a chance he has to beat the hit streak because he will have less chances to get a “hit.”
...and now I'm here
by Librocrat on Jun 14, 2009 9:39 PM PDT up reply actions 0 recs
That may be true of lesser pitchers or rookies ..
But I never see elite or very good pitchers avoid hitters with no men on. They may give up on him if the count hits 3-1 .. but they are going to attack him the same way the attack all hitters.
by Toxicadam on Jun 14, 2009 9:51 PM PDT up reply actions 0 recs
I think I am arguing as follows:
1) The assumption that having bad players around him gives him more strikes – If you have a theoretical team that hits .000 with the exception of one player that hits 1.000 with a lot of home runs, then you would just walk that one player because he can’t hurt you one first base. “The worst outcome is a solo homer.” Yes, that’s the worst outcome. Because walking him is not that bad an outcome, especially when you are surrounded people that can’t hit.
2) That they change how they pitch to him, ever, with the exception of a few situations – Pitchers are always going to pitch around great hitters a little bit, unless they are forced to pitch to them, such as when the bases are loaded. I don’t think it matters whether the lineup is that great around them more than a tiny bit.
Also, as a side, having better people hit around him could theoretically give him more at bats, which would make it harder for him to break .400.
But otherwise yeah, I do think Pujols has one of the best chances, because he is feared enough to be walked often while still maintaining incredibly consistent contact skills. Not entirely sure that getting better people around him will improve those odds, though.
...and now I'm here
by Librocrat on Jun 14, 2009 10:17 PM PDT up reply actions 0 recs
Exactly
It would probably decrease the odds; at least it would make it harder to get lucky. However, I doubt that hitting .400 is Pujols’ goal. If that was the case, he would take his walks a lot more often. Instead, he is trying to hit homeruns to help his pathetic offense score some runs.
St. Louis relievers... defying win expectancy since 2008
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by vivaelpujols on Jun 15, 2009 10:46 PM PDT up reply actions 0 recs















