Is It Bad to Have an Optimistic Forecast?

by
January 26, 2010

Just because you are optimistic overall doesn’t mean you are doing anything good or bad.

It may reduce the absolute error by guessing the median higher than the mean. For example, what’s the better guess:

Guess1	Guess2	Actual
490	575	700
490	575	675
490	575	650
490	575	625
490	575	600
490	575	550
490	575	500
490	575	400
490	575	200
490	575	0

Guess1 represents the actual average, while Guess2 represents the median.

Here is the absolute error for each pick:

Guess1	Guess2	Actual	Error1	Error2
490	575	700	210	125
490	575	675	185	100
490	575	650	160	75
490	575	625	135	50
490	575	600	110	25
490	575	550	60	25
490	575	500	10	75
490	575	400	90	175
490	575	200	290	375
490	575	0	490	575

The average of Error1 is 174 and the average of Error2 is 160. So, guessing higher reduces the overall average error.

Guess1 totaled 4900 PA while Guess2 totaled 5750 PA. The actual PA was 4900. So, in this particular illustration, if it represents anything resembling reality, fans are justified in guessing PA 10% above what the group total would suggest.

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Basically, fans are not only justified but are probably correct: they are not guessing on random events; they are not guessing randomness by distributing things evenly to everyone.

Indeed, in this particular illustration, the Fans could have set the forecast at anything between 550 and 600, and the average error would remain at the (minimum) of 160.

So, it is NOT a requirement that things actually add up at the league or team level. Indeed, being optimistic may very well be the right thing to do.

At the same time, you now have to be careful in trying to take things out of context. You can’t add up all the team’s forecasted WAR or forecasted HR and think that’s what is the best forecast at the team level. If we add up all the individual forecasted WAR, we’re going to get a total like 1500, when in reality, it’s going to come in at 1000. Just be careful in taking things out of context.





 

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Bluebird
15 years ago

I’d work on making those charts a little more readable, but regardless nice premise. This is pretty much what was being discussed at THT not long ago

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