Bill James' Pythagorean theorem of baseball
Joe Stallings
Runs scored [squared] / (Runs scored [squared] + runs allowed [squared]).
This formula was designed to relate a team's runs scored and runs allowed to
its won-lost record.
I watched this figure pretty closely last season and it did a very good job
of representing Anaheim's W-L record as a derivative of their RS/RA.
Anyway, my point is if this is still a fairly reliable indicator, the Angels
have some winning baseball ahead of them.
Currently, we are 150-146 in the RS/RA stat; a winning record. Based on the
theorem, we should be at .514 winning pct or 16-15. We are 14-17 so I think
the future still looks good.
Question for the stat guys. Why square the values? Why not just take the
RS and divide into the total runs in the games? That would give you the pct
of runs we've scored in our games. Just curious.
Thanks.
By the way, it's irrelevant I know, but I wonder what our ex. W/L was at
this point last season. I am pretty sure it was better. I think we above
.500 after 31 games last year.
Joe Stallings
Meridian, ID
Ron Johnson
<joesta...@yahoo.com> wrote:
>Not sure how many of you follow Bill James' Pythagorean theorem of baseball:
>Runs scored [squared] / (Runs scored [squared] + runs allowed [squared]).
>This formula was designed to relate a team's runs scored and runs allowed to
>its won-lost record.
>
>I watched this figure pretty closely last season and it did a very good job
>of representing Anaheim's W-L record as a derivative of their RS/RA.
>
>Anyway, my point is if this is still a fairly reliable indicator,
It is. Standard error is in the 3-4 win range.
>the Angels have some winning baseball ahead of them.
Not quite. It suggests that the team has been somewhat unlucky. But
luck doesn't even out. Besides there are issues of sample size.
>
>Currently, we are 150-146 in the RS/RA stat; a winning record. Based on the
>theorem, we should be at .514 winning pct or 16-15. We are 14-17 so I think
>the future still looks good.
>
>Question for the stat guys. Why square the values? Why not just take the
>RS and divide into the total runs in the games? That would give you the pct
>of runs we've scored in our games. Just curious.
Simple answer, that's what works. More complicated answer, he
remembered something from one of his economics classes and wondered
whether it was applicable to baseball teams. Turns out he didn't
recall the theory correctly.
Actully exponents in the 1.85 range work slightly better (precise
exponent to use if a function of offensive context.)
James knew this more than two decades ago. His explanation as to why
he didn't use the "right" exponent was simple. There's a squared
button on his calculator and no power of 1.85.
Remember he started his work before the PC revolution.
Joe Stallings
If the standard error is in the 3-4 win range, than again, the theorem is
working.
7 of 17 our losses so far have been by 2 or less runs. So 10 of the 17 have
been by 3 or more.
( 30 RS vs. 41 RA ). Allowing nearly 6 runs per game is just not usually
going to get a W.
"Ron Johnson" <r...@canada.com> wrote in message
news:7jS5PpNUewJbUL...@4ax.com...
Wayne Alan Simon
Randall Bart
alt.sports.baseball.calif-angels stood in awe as "Joe Stallings"
<joesta...@yahoo.com> uttered:
>Question for the stat guys. Why square the values? Why not just take the
>RS and divide into the total runs in the games? That would give you the pct
>of runs we've scored in our games. Just curious.
The idea is to predict wins and losses. It turns out that an exponent of
1.8 ends up very close to the won-loss record of the team.
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Joe Stallings
1.85 works? Is that just the number that seems to work best, working
backwards? Did he start with the RS/TR and then start "tweaking" the
formual from there until he got to 1.8 and then realized it was close enough
to the square to just use the square? Is the square the function that is
+/- 3to4 wins or is 1.8/18.5 the correct function for +/-3to4. Curious
about this is all. Amazing how math works in ways it does.
Randall Bart wrote in message ...
Randall Bart
>So not to get laborious with the question but does anyone know why 1.8 or
>1.85 works? Is that just the number that seems to work best, working
>backwards? Did he start with the RS/TR and then start "tweaking" the
>formual from there until he got to 1.8 and then realized it was close enough
>to the square to just use the square? Is the square the function that is
>+/- 3to4 wins or is 1.8/18.5 the correct function for +/-3to4. Curious
>about this is all. Amazing how math works in ways it does.
This is the magic nature of statistics. It is self-evident (see Ambrose
Bierce) that won/loss record will be more extreme than runs
scored/allowed. How much more is not obvious, but Bill James found that
using the x^2 key n his calculator was a close approximation.
Baseball-Reference uses an exponent of 1.83:
http://www.baseball-reference.com/about/faq.shtml#pyth
When a team has a better won/loss record than James' Pythagorean formula
projects, it means:
1) They are lucky,
2) They are good at pulling out close games,
3) When a game gets away from them they give up lots of runs.