THE BOOK--Playing The Percentages In Baseball

You might be interested in this THT article MGL.  From Dan the Turk:

http://www.hardballtimes.com/main/article/stacking-the-middle/

And I’m almost 100% sure that another THT author did a two part series on the same topic earlier this year, but for the life of me I can’t recall who.  studes?

Fairly interesting article on the same topic. Thanks.  I could not help but think “correlation does not equal causation.”

Lets say that the teams that had a higher percentage of their WS concentrated among the middle position also were the best teams, talent-wise. Of course they will be better teams.  What does that tell us?  It simply tells us that the way GM’s construct their teams is such that the better teams tend to acquire better players up the middle, for whatever reasons.  That is not a particularly interesting result. 

That certainly has no bearing whatsoever on how a team should construct its team.  As the author mentions, working your way backward can yield completely different and independent results than working your way forward.  That is another way of saying that correlation does not equal causation.

A classic example of that is when a team gets behind in a series, like 3-0 in a 7-game series.  The commentators love to say something like, “No team in 30 years has ever come back from from a 3-0 deficit to win the series,” as if, while true, that has ANYTHING to do with the current situation (it doesn’t).  That is true for two reasons, of course.  One, a team has to win games in a row, obviously.  A team with a .500 chance per game will only do that 1 out of 16 times of course.  Two, the team down 3-0 is on average the much poorer team, so that 1 in 16 is usually more like 1 in 25.  Two, they only brought that up because likely not many teams have done it on a fluke basis.  So rather than the expected 1 in 30, it was 0 in 30 - just a random fluc.  It could have just as easily been 2 in 30.  My point is that whether it WAS 0 in 30, 1 in 30, or 4 in 30 (all of them could have easily happened), those numbers have NO direct bearing on the current situation.  Occasionally the better team is down 3-0 of course. If it is, then they might have as high as a 1 in 8 or 1 in 10 chance of winning the series, even being down 3-0.  Telling us what other teams have done in the last 30 years (also clearly a selective sample of years, on top of everything else, as the commentators will give us the precise number of years in which hardly any team came back) tells us NOTHING we need to know to estimate the current team’s chances unless perhaps we don’t know that an equal team has around a 1 in 16 chance of winning 4 games in a row.

Now, if someone finds that somehow teams with a higher concentration of talent up the middle outperform their expected win totals or get to the post-season more often than expected given their overall talent, THAT would be a completely different story and quite the revelation.

IOW, the fact that Texeira is the Yankees best player (I’m not sure that he is - there is still someone named A-Rod on the team, I think) tells us nothing about their chances of winning, over and above their expected team talent, as Rob seems to imply, just like telling us that teams down 3-0 never win any series tells us nothing about any team’s current chances of winning 4 games in a row after losing the first 3 games of a 7-game series.

That it is preferable that your best player is “a bit” younger seems obvious simply because you can then keep them around longer.

By the same logic it might make sense that if your best player or players are “up the middle” you can more easily fit them in a few years down the road when/if their defense deteriorates. (Because there are more positions to chose from.)

But I don’t see this as a big issue for the Yankees, baseballs ultimate “right now” franchise.

"By the same logic it might make sense that if your best player or players are “up the middle” you can more easily fit them in a few years down the road when/if their defense deteriorates. (Because there are more positions to chose from.)”

Wow, I don’t know if that is true or not.  I’d have to think about that.  Obviously a player’s longevity in general does not depend on the position they play (other than the fact the speedy players tend to age better than slow ones).  For example, when a 1B deteriorates on defense, his overall value goes down around the same amount that a SS’s overall value goes down as HIS defense deteriorates and he moves to another position.

Now whether it is easier to replace a 1B or a SS with an X WAR player, I don’t know.

My point is more about roster flexibility than about value really. Since players (i belive so anyway) tend to move towards the easier defensive positions as the age if a lot of your value already comes from positions such as LF/RF or 1B you might get an “overcowding” effect where you have players that in theory have positive value but who you can’t fit in your lineup.

If what was your 5 win 1B a number of years ago is now a 2 win DH there is only on spot to put him, and if you already have an other player worth 2 wins or more at DH he can’t provide any extra value. A SS or CF with the same reduction in total production has more different possible ways to fit on your team.

But then again, I don’t think the Yanks worry to much about whats gona happen to Teixera five (or even three) years from now. If their roster doesn’t fit, they’ll just buy the piece(s) they need.

"My point is more about roster flexibility than about value really.”

I understand that.  And more flexible = better, everything else being equal.

So the question STILL is whether, if you are/own/run a team, and you have a total team value of X, would you rather have a 5 WAR player at 1B and a 2 WAR player at SS, or a 5 WAR player at SS and a 2 WAR player at 1B.  Obviously for this season and any future seasons, as both of those players age on offense and defense (and we are assuming for this question, that both players age the same in terms of diminishing total value), your total WAR remains the same.  IOW, does that indeed give you and advantage in “flexibility” down the road?  We’ll also assume that these two players cannot be traded of course. 

Again, I don’t think the answer is obvious, although you may very well be right…

The cost to obtain a 5 WAR SS is the same as it is to buy a 5 WAR 1B or a 5 WAR CF.  They’d have to be.

So, if you start with a 2 WAR SS and a 5 WAR 1B and after 4 years, your SS is out of the league and your 1B is now a 3 WAR 1B, you go out and buy youself a 5 WAR SS.

Alternatively, you can start with a 5 WAR SS, a 2 WAR 1B, and after 4 years, you have a 3 WAR SS and you buy yourself a 5 WAR 1B.  End result is the same.

The entire idea of WAR is to make sure that everyone is on the same scale.

Now, by definition, the average player at all positions is more or less exactly equal in overall talent (can you say “more or less” or “almost” and “exactly” in the same sentence when referring to the same thing?).

I might be misunderstanding your point but I don’t think you can say that this is true “by definition” when it’s easy enough to think of leagues where this isn’t true.  For instance, in High School the average SS is *much* better than the average RF.  Almost all HS SS’s hit better and, if asked, could go play RF better than their team’s RF.  Obviously, this isn’t the case in MLB but I think it makes the point that these positions don’t have to be of the same average ability. 

Let’s say you have a pool of 60 players who are good enough to play middle infield in MLB (I now that players can’t just move back and forth seamlessly between 2b and ss all with the same defensive adjustment but play along).  Of those 60, the ones with the most defensive value will be the shortstops and the half with the most defensive value will, overall, have more overall value.  This is simplistic but I think it’s likely that the average talent at SS is more than the average talent at 2b.

Or, let me put it another way:

I think it could be shown that MLB players were more likely to play CF/SS in HS/college than 2b/lf.  They’re probably also more likely to have played CF/SS when they were in the low minors.

Now imagine a league with a level of play higher than MLB, a superstar league.  Doesn’t it follow that the players who graduate to this superstar league would have been more likely to play SS/CF in MLB than 2b/lf?

There is another way to interpret what Neyer said, and it seems to make more sense to me. It is as follows: Since it is easier to find high WAR players at the least difficult positions like 1B, most teams will have pretty good players at those positions. The really good teams will also have high WAR players up the middle.

I’ve heard some version of that expressed ever since I was a little kid who was first getting interested in baseball, which was a long time ago. Now, whether or not that is true is another question. However, just for grins, I went over to Fangraphs and looked at the top twenty WAR players for 2009. Here are the number of players broken down by position: c-1, 1b-7, 2b-2, ss-3, 3b-4, of-3. Now, that doesn’t mean anything in itself, but it does suggest that it might be worthwhile to look at the WAR distribution at each position, if enough data exists to make for a study that would have statistical significance.

#10,

Theoretically, as previous commenters said, an X WAR 1B and an X WAR SS should cost the same to acquire.  But what if there are a lot of, say, 5 WAR 1B out there and only one or two 5 WAR SS?  The scarcity may make it practically more difficult even for a team with a virtually unlimited budget like the Yankees to upgrade that position.

I understand that in a perfectly efficient market, they should be able to acquire one of those 5 WAR SS for the going rate.  But it may be that in real life, if they start with a young 5 WAR SS (or whatever position is scarce at that level), it will be easier to upgrade their team later by adding one of the plentiful 5 WAR 1B.

I think it’s almost certainly true that the best players in baseball will disproportionately play 1B and corner OF, not up the middle.  We know that the spread of hitting talent is greater, and that it is hitting talent much more than fielding ability that distinguishes starters from replacement players.  So it almost has to be true that the best players in baseball will tend to be great hitters with weak defensive skills (because the odds of a great hitter also being strong defensively are low).  Now, the very, very best players will be those who have both skills, and among inner-circle level players you find a good proportion who played up the middle.  But if you’re talking about something like the best 5-10% of players, I think the middle positions will be underrepresented.

For an average fielding team with all 2 WAR players except a 5 WAR SS and an average fielding team with all 2 WAR players except a 5 WAR 1B, one difference is distribution of offensive talent in the lineup. 

Is anyone aware of any work done in this area?  For the same team total wRAA, is there a difference in runs scored between an elite hitter surrounded by average to poor hitters, and a top to bottom lineup of average hitters?

I think it’s almost certainly true that the best players in baseball will disproportionately play 1B and corner OF, not up the middle...

Guy, this definitely made me think but I come to the opposite conclusion.

Let’s say that someone says that player X is 30 runs above average and asks you to estimate player X’s hitting, fielding and baserunning abilities relative to the average player.  Your best guess for each category would be something above average.  It might be something like +20 hitting, +7 fielding and +3 baserunning since the spread of offensive talent is greatest but you would guess that this player is above average in all 3, right?  And, if this player is an above average defender they’re somewhat more likely to play a tough defensive position.

note: that +7 isn’t a UZR, it’s not relative to an average at any position.  It’s supposed to be a position-less “fielding talent” number.

Out of curiosity, I made a table with each team’s W total, W%, total rWAR from non-pitchers, and a flag that indicated whether or not the team’s best non-pitcher, by rWAR, was an up-the-middle player (C, 2B, SS, CF), and then I ran a regression of wins on total rWAR and the up-the-middle flag. Since 1954 (when I’ve got OF split into LF-RF-CF), the equation was:

Wins = 1.03 rWAR + .29 flag + 61.80

The p-value for the rWAR coefficient was 0, and the p-value for the up-the-middle-flag was .54.  The rWAR confidence interval contained 1.00, if anyone cares about that.  I got similar results when I ran the correlation for post-1961 seasons (since the 162 game schedule) and for post-1996 seasons (since the last work stoppage), except that the coefficient for the up-the-middle flag ranged from -.31 since 1996 to .38 since 1961.  I also ran a correlation of W% on rWAR and the up-the-middle flag for all teams since 1901 (using wins created a problem because teams after 1954 were more likely to have the up-the-middle-flag since I couldn’t count CF before that, and teams since 1954 have won more games on average because of the expanded schedule, so it created a false correlation between the flag and total wins), and got similar results (0 p-value for rWAR, .61 p-value for the flag).

This doesn’t really say anything about whether there are benefits of having additional flexibility with the up-the-middle player as he ages, or whether having an elite up-the-middle player gives you an advantage in making it easier to have a high team WAR total, but as far as whether it makes a difference if a team’s best player is an up-the-middle player or not, aside from the team’s total WAR, this doesn’t really find any evidence of it.  If you’ve got x number of total WAR, it seems that you’d expect y number of wins whether your best player is a corner or an up-the-middle player.  So, in the case of the Yankees, where you already know they have a ton of projected WAR, I don’t think it really makes any difference whether their best player is up-the-middle or not.  I know that’s not nearly as interesting as addressing the other issues of whether up-the-middle players make it easier to build a higher total team WAR, but maybe it’s helpful to some to know how rWAR and the up-the-middle flag have related to team wins historically and that having your best player up the middle hasn’t really changed the effect of the total rWAR.

Doesn’t anyone else see a problem in using WAR as a measure “best player” playing up the middle when WAR contains a positional adjustment which awards a player in the middle position extra value and subtracts value from players not playing up the middle?

What do you mean by “awards a player in the middle position extra value and subtracts value from players not playing up the middle”?  As long as you are measuring defense against average for the position, you have to account for the baselines being different somehow.  The position adjustments don’t just say, here are some bonus points for playing up-the-middle.  They take all of the defensive measurements that are measured against different baselines and put them on the same baseline.  So, I’m not seeing why attempting to put the measurements of value for each player on the same baseline creates a problem in comparing them.  Not putting the values against the same baseline would create problems when you try to compare players across positions.

Doesn’t anyone else see a problem in using WAR as a measure “best player” playing up the middle when WAR contains a positional adjustment which awards a player in the middle position extra value and subtracts value from players not playing up the middle?

If it were wins above average I would have a problem with it but I do think that replacement level is replacement level so as long as 0 WAR lines up with cheap available talent at each position we’re okay.  Of course, I don’t know that to be the case.

"Doesn’t anyone else see a problem in using WAR as a measure “best player” playing up the middle when WAR contains a positional adjustment which awards a player in the middle position extra value and subtracts value from players not playing up the middle?”

No. Best player is best player.  If you didn’t do that, then the corners, DH, and 1B would be massively better than the middle infielders.  What do you propose - using hitting only, plus defensive runs above average?  Of course using WAR with positional adjustments is the only way to compare players.