Silver is obviously not a commie homo-loving son of a gun...

Silver predicts a perfect linear decline, meaning each total is lower than the preceding year.

That's not what linear means, and the projection is not linear. In fact, it's not even declining at a constant non-linear rate. Any projection ought to predict his home run totals declining by year, with the understanding that random events will cause the actual outcomes to fluctuate around the decline, sometimes resulting in totals increasing.

Aaron's career HR totals were helped tremendously by his move to Fulton County Launching Pad at age 32. Rodriguez will get no similar boost unless The New Yankee Stadium (that's what we're supposed to call it, right?) plays far differently than expected. Or he gets traded to Texas.

The New Yankee Stadium (that's what we're supposed to call it, right?)

The Bronx Bombshelter?
The House That Ruthless Avarice Built?
John Sterling's Liquor Emporium?

That's not what linear means, and the projection is not linear.

The author here. JCB - Could you go a little bit further into why that's not linear, just for learning purposes?

Fair point about the projection consistently declining and not accounting for random fluctuations. But if you are always assuming a decline, doesn't that skew the projection downward? If it starts at 33, that is his highest total going forward? Seems unlikely.

Linear means constant decrease each year, e.g. 21-17-13-9-5-1. The word you're probably looking for is monotonicity, which means constantly non-increasing or non-decreasing, but nothing about the rate of change.

3. The problem with being on pace to be the greatest home run hitter of all time is that you aren’t going to have too many people similar to you.

This is the most valid point to me. It's kind of like with Jamie Moyer - I don't pay any attention to his projection. How do you even project his numbers? All the pitchers his age I can think of are knuckleballers.

Note: After checking Moyer's b-ref page I see his nearest comp by age is Tommy John, who fell off the shelf for his age 46 season. Still, it is not much of a sample size.

Fair point about the projection consistently declining and not accounting for random fluctuations. But if you are always assuming a decline, doesn't that skew the projection downward? If it starts at 33, that is his highest total going forward? Seems unlikely.

What's the alternative? Try to predict the up and down bumps along the trend line?

Projections aren't meant to get into that level of granularity. Doesn't stop the critics from using that as a means of outright dismissing them in favor of their infinite personal wisdom.

Really, the only alternative you have to pick small enough sample size that an unusual single performance, say Hank Aaron's 40 HR at age 39, is enough of a perturbation to break the overall trend. I don't think this is desirable.

What's the alternative? Try to predict the up and down bumps along the trend line?

Obviously that would be foolish, and I'm not saying it should start at 55 either. But he published the results of the simulation on ESPN.com and opened up the discussion. It just one man's opinion, but I'm betting against it.

I remember watching an episode of Baseball Tonight (this was back when I was drinking DayQuil and Red Bull slings for breakfast, to numb the symptoms of my post-concussion syndrome suffered in the Octagon) and Eduardo Perez was saying that as A-Rod enters his peak, we will surely see him start to hit 80-90 HR per season. He was so sure of it, he actually said it twice. And no one else on the show batted an eye.

It just one man's opinion, but I'm betting against it.

How brave. You get EVERY OTHER POSSIBLE COMBINATION OF HR TOTALS and he gets 1. Again, this shows you don't understand how projections work.

How brave.

Okay... I'll take the over?

Over what? The total homeruns hot here forward? That doesn't address your complaints about the shape of the projects decline.

Here's what you need to do: Use whatever method you want and project EXACTLY what Silver does: how many more seasons A-Rod will play and the # of homers he will hit in each season.

Apples to apples, right? Then we can compare. Good luck.

This is the most valid point to me. It's kind of like with Jamie Moyer - I don't pay any attention to his projection. How do you even project his numbers? All the pitchers his age I can think of are knuckleballers.

That's not how projections are done. Projections are primarily based on a large multivariate model run on all players. ZiPS and PECOTA (and maybe others now) then do a small tweak based on comparable players which allows them to essentially run a small, localized regression.

The projection for someone like Moyer isn't based on a handful of knuckleballers, it's based on thousands of pitchers. It is a fair point to say that there are only a handful of "points of support" out at Moyer's end of the age curve and it's possible that the model shifts dramatically for post-45 pitchers ... but there's no reason to think it does and so Moyer's projection is basically an extrapolation of the standard model. Or to put it another way, while there have been only a handful of 46-year-old pitchers in baseball, there have been a lot of pitchers (and a lot of "old" pitchers) who've had 3 seasons fairly comparable to Moyer's last 3 seasons.

Hmmm ... maybe that could have been clearer. Let's just put it this way. This is oversimplified but essentially Moyer's projection looks like this (this should roughly be Marcel):

xFIP09 = .5 xFIP08 + .3 xFIP07 + .2 xFIP 06 + .25 Over32

So a weighted average of his last 3 years' performance and .25 penalty for being a year older and being "old". In the real systems, those coefficients would be based on a regression featuring thousands of pitchers. All that PECOTA or ZiPS does is maybe tweak that number a bit based on comps so if Moyer's comps didn't decline quite as much as .25, he'll get a bit of a boost but his projection will be somewhere between the above and the comps. (PECOTA and ZiPS underlying models are more complex than the basic Marcel above).

Or as Dan says in the new ZiPS intro, the comps are mainly just for fun.

Anyway, I can't access Silver's original article -- did he present the confidence bands? I'm guessing things start looking pretty silly pretty quickly.

Walt - are you sure that's how the projections are done? Though I don't know, I like to imagine PECOTA is more like:

xFIP09 = (a) xFIP08 + (b) xFIP07 + (c) xFIP 06 + (d) age adjustment

where (a)-(d) are found from regressions over all players, but weighted by a similarity score to the player being projected, where the regression is unique to the individual and the coefficients could vary significantly from player to player (obviously, it depends on the scaling of the similarity score).

It just one man's opinion, but I'm betting against it.

No, it's not. It's one man's "mean case" scenario. He's not saying that it's at all likely to actually come out exactly that way.

I will add though that I agree with the general sentiment that these projections aren't that useful for projecting individual performance. They're basically actuarial tables -- it's how the average player of a given age with roughly those last few seasons is expected to do. You see this in the distributions which ZiPS and PECOTA present. Dan's stopped doing the player spotlights but, for example, he did one for Lowrie in his Red Sox projection. He projects an 88 OPS+ for Lowrie but the 95% confidence interval around that projection is, roughly, 50 to 140. I coulda told you that with the added info that there's no way they'll play him if he puts up a 50 OPS+. Ellsbury's projection is basically the same. That's not really useful (which is not a knock against Dan). Even someone with a reasonable track record like Beckett has a 95% CI on his ERA+ of about 90 to 160. You don't need models to tell you that stuff though it should be comforting to Red Sox fans that the chances of Beckett really sucking are minimal (if only his injury risk was).

The standard error on the mean of a group will be quite small. So we can say with great confidence that players who've averaged a 120 OPS+ over the last 3 years will, on average, hit a lot better next year than the group who've averaged a 100 OPS+ over the last 3 years. But for any individual player, the projection is pretty much a crap shoot -- and that's one year out. Multi-year projections for an individual are kinda silly.

If memory serves, in the analysis of the Swisher-Betemit trade, although Swisher's mean projected OPS+ was about 15 points higher than Betemit's, Betemit still had something like a 40% chance of outhitting Swisher in raw terms (much less position-adjusted). Dan's confidence intervals aren't symmetric (good) but, roughly speaking, the SD on an OPS+ projection is about 15-20 points depending on how much data it's based on. The SD on the difference between any two players (assuming they're independent) is going to be about 20-30 points of OPS+.

We really shouldn't express as much confidence on player comparisons and projections as we do.

I'm reminded of some folks who were trying to sell some software for analyzing mortgages. They were very proud of their interest rate projection model. They boasted about how it captured the big downturn in interest rates in the early 00s. It was hilarious. All their model did was take the interest rate from 5 years before and project it forward to be the same with increasing variance. It was a random walk. 5 years out, they were projecting that interest rates would be somewhere between 2% and 16%. Well, duh, anybody in the room could have told them that. (And you wonder how the subprime mess came to pass.)

I will bet anyone reading $100 that this doesn’t happen to A-Rod. First one to take the bet in the comments is on,

Hmm, if I actually wanted to go to his site, I'd accept his wager of $100 and put forth mine of 46¢.

Here's what you need to do: Use whatever method you want and project EXACTLY what Silver does: how many more seasons A-Rod will play and the # of homers he will hit in each season.

Apples to apples, right? Then we can compare. Good luck.

Heeeeeey Fridas. Guess what?

http://fackyouk.blogspot.com/2009/02/dueling-projections.html

You got your wish!

Thank you for the information, Walt. You must have explained it well if even I understood it.

It was certainly not my "wish". You were the one ripping a projection, it's good to see you're actually willing to put your money where your mouth is. Good luck.