Chance of Winning a Baseball Game (October 20, 2003)
Just a chart, no analysis. Note the assumptions if commenting on this specific chart.
--posted by TangoTiger at 04:45 PM EDT
Posted 8:08 p.m.,
October 20, 2003
(#1) -
Sky
That's pretty interesting, thanks. The 4.3 RPG is key, but doesn't it also matter the distribution of those runs (which is probably dependant on the component events that result in the runs)?
An extreme example - a league that only hits singles, but hits .300 might average the same number of runs as a league that hits .100, but only hits HRs. I would think the run distrubutions per half inning would be different in those cases...
Posted 8:26 p.m.,
October 20, 2003
(#2) -
Tangotiger
Yes, I should have added what the runs per inning distribution was.
Posted 11:03 p.m.,
October 20, 2003
(#3) -
Clueless
Runs per inning per team?
Posted 12:09 a.m.,
October 21, 2003
(#4) -
Tangotiger
Yes, something like 71% 0 runs, 15% 1 run, 8% 2 runs, etc, etc.
You have to be a little careful here, since the runs per inning distribution is not random between teams, since they play in the same park, and the batting order is a problem as well.
You can also try to extend this to other sports, but again, the points / game distribution would be even less random between 2 teams (probably). Baseball is unique that each team is guaranteed a certain clock (27 outs). Hockey, football, soccer, basketball have their possessions / time determined by both teams.
Still, if someone has a log of scores, including the identity of teams for the other sports, it should be easy enough to construct a similar chart as I have here.
Posted 1:27 p.m.,
October 21, 2003
(#5) -
FJM
You can calculate the run distribution from the Win Probabilities for the bottom of the 9th and a little algebra.
P(0 runs) = 1-2*(.634-.500) = 1-.268 = .732.
P(1 run) = (.268-.194)*2 = .148,
P(2 runs) = (.120-.086)*2 = .068,
and so on.
All of which begs the question: If you go to the bottom of the 9th trailing by one run with the road team's closer coming in, can you really expect to win the game right there 12.0% of the time? And will you really send it to extra innings 14.8% of the time? That suggests a one-inning, one-run expected BS rate of 26.8%. Time for your opponent to get a new closer. Conclusion: Run scoring potential is highly situation-dependent.
Posted 2:28 p.m.,
October 21, 2003
(#6) -
tangotiger(e-mail)
(homepage)
Good job FJM! The actual numbers are
0 - 73.1%
1 - 14.9%
2 - 6.7%
3 - 3.0%
4+ - 2.2%
Rounding errors would give you your results.
If you go to the above link, you will see Phil Birnbaum's chart of actual data. Look for this record:
"H0901-1",4685,887
which is read as "Home team batting, 9th inning, bases empty 0 outs, down by 1 run occurred 4685 times, and won 887 times".
That works out to: 18.9%
My chart, which assumes everyone is always equals, says: 19.4%
With 1 standard deviation being .006, these two differences are not statistically significant.
So, while it would be more accurate to use actual run scoring by inning/score (to simulate the closer coming in, etc), we're actually pretty close to reality, aren't we? That is, all that stuff that we know is true doesn't have anywhere near the impact that we might think.
Anyone feel like reproducing my chart using Phil's data?
Posted 3:40 p.m.,
October 21, 2003
(#7) -
tangotiger
Phil sent me a note saying he will reformat the data to be much easier to import. Look for it in the coming days.
Posted 5:58 p.m.,
October 21, 2003
(#8) -
FJM
That is a very interesting (and surprising) result! Here's one possible explanation. Back in 1979-1990 the role of the closer was not as clearly defined as it is today. Blowing an occasional save didn't carry the stigma it does now. Do you have similar data for the last 3 or 4 years?
Posted 6:12 p.m.,
October 21, 2003
(#9) -
tangotiger
(homepage)
Also note that I don't have a HFA, so that'll cost something there too.
Click on the above link for the ACTUAL results, based on Phil's data.
Posted 8:01 p.m.,
October 21, 2003
(#10) -
FJM
If you define professional closer as one who earned at least 30 saves then there were only 3 of them in 1979. That number jumped to 11 by 1990 and 17 by 1999. (Interestingly, it declined to only 12 in 2003.)It truly is a different game today.
Posted 11:43 p.m.,
October 21, 2003
(#11) -
RossCW
Am I confused about the meanings or is there something strange about these two sets of data. There appears to be 4381 games tied at the beginning of the 8th and 11,507 at the beginning of the 9th:
"V0801 0",4381,2100
"V0901 0",11507,5552
That doesn't make sense to me.
Posted 1:48 a.m.,
October 22, 2003
(#12) -
RossCW
That is a very interesting (and surprising) result!
Is it surprising if one considers that the offensive team is also optimigzing their performance with pinch hitters, pinch runners etc?
Posted 11:56 a.m.,
October 22, 2003
(#13) -
tangotiger
(homepage)
This chart uses probability theory as well, but this time I DO have a HFA. This will make the comparison to the empirical chart much more appropriate.
I kept the run environment at 4.3, but put the home team at 4.5 RPG and the visiting team at 4.1 RPG. The empirical has the home team with winning record .542, while in my probabilistic model I have it at .539. I could have best-fitted it to .542 as well (by setting the RPG to 4.51 v 4.09 or something), but the current HFA is actually lower. Whenever the empirical data gets expanded to cover the recent seasons, the .539 might probably be about right.
Anyway, now the effect that FJM notices in the bottom of the 9th is much stronger, and the likelihood is simply that you have better pitchers in the game.
Posted 2:03 p.m.,
October 22, 2003
(#14) -
FJM
The one run, one inning BS probability still seems high to me at 26.6%. The 1979-90 Actual data implies it was 26.2% back then, before most teams had true closers. I still think it's significantly lower today.
I don't know what the HFA was back then. Your selection (4.5 vs. 4.3 overall) imples 4.7%. Last year it was only 1.2% in the AL (4.93 vs. 4.87 overall) and 1.8% in the NL (4.69 vs. 4.60).
Posted 2:24 p.m.,
October 22, 2003
(#15) -
tangotiger
HFA was around .540 for the longest time, but over the last 10 years, that has shrunk considerably, for unknown reasons.
As for "significantly lower" and "true closers", you seem to be implying that by having a "true closer" that you must have much better pitching in the 9th these days than in the old days (relative to their league). I would say that the "true closer" is not even necessarily the best reliever on the team, and I would highly question your presumtion of the "true closer" impact, and even if you are right, I would be shocked if it's "significantly lower".
Posted 3:09 p.m.,
October 22, 2003
(#16) -
tangotiger
1999-2002
row1: all PAs, in the 9th or later innings, with a score differential within +/- 1 run
row2: all PAs
close/late: .254/.350/.389
all: .267/.338/.429
1974-1978
close/late: .255/.338/.353
all: .258/.325/.377
Taking the ratio of OBAxSLG and we have
1999-2002: Close/Late: 94% of league average
1974-1978: Close/Late: 97% of league average
I probably should have removed IBB, but oh well.
So, setting the league average runs scored to 4.3, that gives us:
1999-2002: Close/late: 4.04 runs per game
1974-1978: Close/late: 4.17 runs per game
So, yes, the good inning late relievers of today are better than their peers of 30 years ago, relative to league average (for reasons of skill and dilution). But the impact is pretty small.
Using the Tango Distribution, this is what it works out to:
Runs/inn 4.04 4.17
0 0.7440 0.7379
1 0.1460 0.1483
2 0.0627 0.0644
3 0.0270 0.0280
4+ 0.0203 0.0214
Posted 8:02 p.m.,
October 22, 2003
(#17) -
FJM
Doesn't it seem strange that, if the best pitchers are on the mound Close & Late, the OBP-BAA in these situations would be far higher than it is overall? As you suggest, IBB would explain some of the difference, but certainly not all.
One problem I see with your data is it includes situations where the game is tied and where the team being studied is trailing by one run. Most teams don't use their closers in those situations.
I took a different approach. I selected all pitchers who had at least 10 Save Opportunities in 2002. (I used Sv. Opps. instead of Saves to avoid any chance of biasing the results toward the more successful closers.) There were 40 of them. Here are their combined stats: .228/.293/.344.
Comparing your C&L results with mine, your group BAA is 26 points (11%) higher. Your SLG is 45 points (13%) above mine. That's about what I would expect, since mine is a more restricted sample. But here's the kicker. The OBP for your group is 57 points (19.5%) worse than mine. And if you look at OBP-BAA, the difference is huge: 96-65=31, a 48% disparity. Something is definitely out of whack there.
Posted 9:42 p.m.,
October 22, 2003
(#18) -
FJM
I should add that, of my Fab 40, only one (Matt Herges) had an OBP of .350 or higher. (According to your data, .350 was the average OBP over all C&L situations!) And Herges just barely made my cut, with 10 Sv. Opps. and 4 BS's. There was only one other closer over .340 (Kelvim Escobar.) At the other end of the spectrum, 15 of them were under .280 and 24 were under .300. Now that's the kind of pitching I would expect to see, down by one run going to the bottom of 9th.
Posted 9:48 a.m.,
October 23, 2003
(#19) -
tangotiger
Situation: home 9th inning, home team down by exactly 1
1999-2002: .250/.325/.386, 86.5% of league, 3.72 equivalent RPG
1974-1978: .254/.316/.360, 92.8% of league, 3.99 equivalent RPG
Tango Distribution
3.72:
0 runs - 75.9%
1 run - 14.0%
2+ runs - 10.1%
3.99:
0 runs - 74.6%
1 run - 14.5%
2+ runs - 10.9%
So, with the current relievers, they lose the game in the 9th 10.1% of the time, and go into extra innings to lose another 7% for a total of 17.1% loss.
With the 70s style/talent, they lose in the 9th 10.9%, and another 7.2% for a total of 18.1% loss.
Phil's data from 1978-1990 says 18.9%.
The "theoretical everyone is equal, with HFA" says 20.4%
Posted 12:02 p.m.,
October 23, 2003
(#20) -
FJM
Thanks for your latest post, Tom. We're now only 10-12% apart on all the stats. I can live with that. It does raise an interesting question, though. Do closers perform better with a 2- or 3-run lead than they do with only 1 run to work with? Or perhaps they do better at home, where they get to do their thing in the top of the 9th?
Posted 1:22 p.m.,
October 23, 2003
(#21) -
FJM
I don't have the data to test the 2- or 3-run lead hypothesis. But I did test my closers for HFA. They came in at .221/.283/.331. Looks like they are about 3% better at home than overall, which implies they are 6% worse in the bottom of the 9th than they are in the top half. Note that their HFA is about twice as large as the HFA overall. This explains about 1/3 of the remaining discrepancy between your data and mine.
One correction on Matt Herges. He did have 6 saves in 2002. But that was out of 14 Sv. Opps., not 10. That's 43% success. 84% was average. Nobody else finished below 60%. No wonder he wasn't a closer very long!