THE BOOK--Playing The Percentages In Baseball

Would you consider that normal that the expected plate appearances were higher than the actual plate appearances until you got lower down on the chart?  What would be some of the likely causes of this...? catastrophic injuries? bad estimates? players getting playing time that weren’t listed?

What is the standard variation on plate appearances (actual vs expected) for the complete sample?  Or standard variation by each of your sub group if that’s more telling.

vr, Xei

Regression to the mean, is my guess.  If you project a higher-than-average amount of PAs, you’re more likely to have erred on the side of over-projecting.  If you project a lower-than-average amount of PAs, you’re more likely to have erred on the side of under-projecting.

Related to Xei’s question: why did it flip around the 80 PA mark?  I’d have guessed it would have flipped at about the average projected PA for the entire population we’re looking at, which I would guess is more like 300 PA.

Thanks again, Tango.  This is amazing stuff!

Let me put a pitch in for the fantasy players for you to still do it two weeks out from season start.  Any closer to the season and many of us who would love to use this information in our drafts will have already drafted, and the increase in accuracy isn’t worth the decrease in timeliness/usefulness, IMO.

Thanks again!

The “0” group suggests that people are projecting their estimate of the median or mode, not the mean.  If you think a guy has a 10% chance of being full time (600PA) and 90% chance of not playing, you should project him to 60PA if you’re using the mean.

Nobody who is still in professional ball should be projected at zero.  If you think the guy is only a 10% shot to be a bench player get 100 PA, you should project him at 10 PA.

Perhaps the community gets a bit of extra utility in getting a projection exactly right, which is why they say zero. 

It seams like everyone is projecting too many PA’s.

Just a quick look at the 483 hitters I have in the spreadsheet (which unfortunately at the moment is only guys with lahman ID’s so does not include any players who debuted in 2009).  The list also doesn’t include players who missed the entire season.

These players averaged 345 PA

and system projected an average of:

Marcel/community: 403
Zips: 457
Pecota: 414
Chone: 483

Correlations with actual PA for this pool of players:

Marcel .686
Zips .531
Pecota .525
Chone .545

Based on this quick and dirty analysis, the fans win.

There is a strong bias here, however.  Some of the above system only projected guys that they expected to get significant playing time (for instance Chone didn’t project anyone below 100 AB) and this list of players is the list of guys who had projections from all of the above system, in other words, the guys who were expected to get significant playing time by these systems.

So, the guys who were expected to get significant playing time… got less than expected.

Was the total number of predicted PAs close to the total number of actual PAs?

good question.

I don’t have all the players so I can’t make that comparison.

one more thing, the community’s success in projecting playing time might not translate to fantasy success.

For the 146 players who were expected to get 500 PA or more (average > 500 PA), the kinds of guys who get drafted in most fantasy leagues, marcel didn’t do as well.

R (with actual PA)

Marcel .205
Pecota .174
ZiPS .277
Chone .287

for the guys that the stearmollers projected (projected starters less guys who have yet to appear in the majors)

Marcel .372
Pecota .393
Zips .424
Chone .425
Fantistics .506*

*I added in Fantastics on the advice of an emailer who said that they were good for playing time projections and this seems to support that.

Another thing that occurs to me is injuries.  If some forecasts aren’t discounting the PAs for the possibility of injuries, and others are, that might skew the results.

Nothing wrong with not considering injuries, if that’s what you prefer ... the user can discount them to his preference.  For instance, if you told me Jeter was projected to 650 PA barring injuries, and I thought there was a 10% chance of a DL stint that would last 15 days, I’d discount him by maybe 7 PA.

Good point by Phil.

At the moment, I am projecting playing time by simply Marceling the last three seasons. I will amend that to count how many days out of the season the player was on an active roster, at any level. Will do something like the mean number of PAs for games he was active and if there was a disproportionate number of inactive games. So maybe project games first, then multiply by PAs per game (thinking as I type)

I should point out how I generated the Community playing time forecast.  This is what I asked the Fans:

Number of Games
150+ (Iron Man)
130-149 (Regular)
90-129 (Platoon)
30- 89 (Bench)
1- 29 (Callup)
0

From that, I created the number of games as such:
155
140
115
70
20
0

So, if you forecast 90-129 games, I count that as 115 games, etc.

From that, I create PA per G as follows:
value/100+2.5

So, if you forecast someone with 115 games, I give him 3.65 PA per G.

And from that, PA follows:  115 x 3.65 = 420 PA.

So, anyone who selected the “ 90-129 (Platoon)” selection counted that as 420 PA.

I did all this with a bit of correlation here, and intuition there.  And, most importantly, I made sure that it all added up to around 182,000 PA (actual PA in 2009 was 181,051; I “forced in” an estimate of 182,319).

That was my first problem.  There was 9340 actual PA from which I had a total estimate of zero (basically, guys that I did not put on the ballot).  My bad, because of all the late free agent signings, but also guys not on the 40-man roster that made the team.  Of all the players who actually were on the ballot, they had an actual PA of 171,711 PA.  And THAT should have been the estimate I should have forced to (well, I didn’t know it was going to be that, but I should have taken 95% of the actual of 2008, and presumed that would have been the target for 2009).

Basically, I should have knocked down all estimates by 5%.  The 420 PA from the example above should have been 399.  An estimate of 600 PA should be an actual of 570, and so on.

Had I done that, the Community would have nailed practically every class of playing time estimate.  So, the only reason they don’t look as good as they should is because of me.

Regardless though: because the bias is systematic and not random, insofar as Fantasy Baseball is concerned, it doesn’t matter, since it all cancels out.  That is, if I knock out 5% PA from everyone, this won’t affect the rankings of the nonpitchers.

One of the big issues when making projections is pertinent here.

One knows that the Top 10 AB leaders at the end of the season will have about 6500 AB.

But if you project your Top 10 AB leaders to have 6500 AB, chances are that at the end of the season they are likely to have only 5900. About 10 percent of the expected at bats will go missing, due to random injuries.

Since the injuries are random, to get the right PT total you have to wind everyone down about 10 percent. But when you do that you end up with no players projected to have 600 AB, which looks wrong (and, of course, will be wrong).

The only other logical choice is to guess which players will be hitting the DL, and make them take the hit. This leads to bold and usually wrong projections.

The best choice, it seems to me, is to ignore the overall totals and project as if players are going to play as much as they usually do when they’re healthy, unless they have an injury history that forces an adjustment.

But again, this leads to wrong overall totals.

Does it really matter though (for our purposes)?

If you give Ichiro 600 PA, and Gutierrez 500, and Chavez 400, or you give them 660, 550, 440, respectively, it all cancels out anyway, right?

Really, you might as well give the top guy “1.00 PA”, and everyone is a fraction of that.  It becomes irrelevant for the overall valuation.  The ordinal rankings remain the same.

For our purposes, it doesn’t matter. The proportions are what matter.

I was pointing out why those of us who publish projections might overproject at the top end. It looks wrong to do it right.

Right, I agree with you otherwise.

This is the same idea with the rate stats.  If you presume the league OBP will be .340, and it turns out to be .325, it’s irrelevant.  Your players are forecasted around the league mean anyway.