Simulating the NL Central Race

[rluzinski]

Normally, I'd include a bunch of uneeded charts and graphs to a post like this but time is short, so I'll get to the point. I used the teams' pythagorean record to simulate the rest of the season 100,000 times to see how the NL Central might end up. I was specifically interested in the chances of a two or three way tie occuring. I have no time to check my work, so take these numbers with a grain of salt:

 

Cubs win outright: 48.2%

Brewers win outright: 27.9%

Cards win outright: 9.6%

 

And for the tie scenarios:

 

Two-way Tie:			13.3%
Crew/Cubs			8.4%
Crew/Cards			2.0%
Cards/Cubs			2.8%
Three-Way Tie:			1.0%

 

So, the Brewers have about a 39% chance of at least tieing the NL Central. Assuming a 50% chance of winning a two way tie and a 33% chance of winning a three way tie, that gives the Crew about a 33% chance of making the playoffs.The Cubs have about a 54% chance; the Cardinals a 13% chance.

 

Here are the odds for the final win total for the Brewers (83 wins is the average):

 

Wins	Prob
87+	6%
86	7%
85	11%
84	15%
83	16%
82	16%
81	12%
80	8%
79-	8%

[trwi7]

Does this take into account how the teams have played at home and on the road and how many of each the teams have left?

[rluzinski]

Does this take into account how the teams have played at home and on the road and how many of each the teams have left?

 

Yes. Each of the games remaining for the Brewers, Cubs and Cards were simulated. I used league average home/road splits, which I'm sure some would take objection to.

[Fatter than Joey]

Not to be nitpicky --

 

But is it fair to assume that if there is a 3-way tie one team has a 33% chance of winning?

 

I am assuming that the way they handle a 3 way tie is that Teams A-B play a game and then that winner plays Team C. If so, one team has a 50% and the other 2 have a 25% chance.

 

I cannot imagine a round-robin format working, you would have to play 6 games and then you wouldn't be guaranteed of a winner.

 

I know this is a quick and dirty (and informative) post, and again, I do not want to pick, but I am more intrigued by the 3 team tie format.

[rluzinski]

I am assuming that the way they handle a 3 way tie is that Teams A-B play a game and then that winner plays Team C. If so, one team has a 50% and the other 2 have a 25% chance.

 

I didn't really give it much thought, considering that there's only a 1% chance of it happening. 33% of 1% vs. either 25% or 50% is less than the error of only simulating 100,00 times, I would assume. I assume you'd have to be correct about the format though. If anyone has specific information, please let me know.

 

I wanted to actually calculate the tie breaker odds in more detail but I'm going to wait to see who gets home field advantage first.

[Fatter than Joey]

33% of 1% vs. either 25% or 50% is less than the error of only simulating 100,00 times, I would assume.

 

This is fair, and again, I realize minuscule compared to what you are trying to do with this simulation.

 

I just thought it was an interesting aspect.

 

I know BFnet will be superpissed if we have play 2 games in a 3-way tiebreaker and the Cubs/Cards only have to play one.

[Baldkin]

From here:

 

Scenario #4: If three Clubs are tied for first place in a Division (or Wild Card) with an identical winning percentage at the conclusion of the championship season and the tied Clubs do not have identical records against one another in the championship season, the tie for the Division Championship (or Wild Card) shall be broken as follows:

If the three tied Clubs have identical records against one another in the championship season, the Office of the Commissioner shall supervise a draw that results in the Clubs' being designated Club "A," "B," and "C."

If the tied Clubs do not have identical records against one another in the champoinship season, they will be designated Club "A,""B," and "C" based on their records in head-to- head competition during the championship season as follows:

If Club 1 has a better record against each of Clubs 2 and 3, and Club 2 has a better record against Club 3, then Club 1 shall choose a designation as Club "A," "B," or "C," and Club 2 shall choose a designation from the remaining two designations. Club 3 shall be assigned the remaining designation.

If Club 1 has a better record against each of Clubs 2 and 3, and Club 2 and Club 3 have the same record against each other, then Club 1 shall choose a designation as Club "A," "B," or "C," and the Office of the Commissioner shall supervise a draw between Clubs 2 and 3, the winner of which shall choose one of the remaining two designations. The remaining Club shall be assigned the remaining designation.

If Club 1 and Club 2 have the same record against each other but each has a better record against Club 3, then the Office of the Commissioner shall supervise a draw between Clubs 1 and 2, the winner of which shall choose a designation as Club "A," "B," or "C." The Club losing the draw shall choose a designation from the remaining two designations. Club 3 shall be assigned the remaining designation.

If Club 1 has a better record against Club 2, Club 2 has a better record against Club 3, and Club 3 has a better record against Club 1, then the three Clubs shall be ranked on the basis of overall winning percentage within that three-Club group, and the Club with the highest winning percentage from among that three-Club group shall have first choice among designations as Club"A," "B," or "C," the Club with the next highest winning percentage from among that three-Club group shall have the next choice between the two remaining designations, and the Club with the lowest winning percentage from among that three-Club group shall be assigned the remaining designation. If two or more of the Clubs within such three-Club group have the same winning percentage among the group, the Office of the Commissioner shall supervise a draw between the Clubs so tied to determine priority of selection among the designations.

Club"A" shall play Club "B" at the ballpark of Club "A" on Monday, September 29. The following day (Tuesday, September 30), the winner of the first game shall be the home Club in a second game, against Club "C." The winner of the game between Club"C" and the Club that won the game between Club"A" and Club"B" shall be declared the Division Champion.

Example of Scenario #4: The Chicago White Sox, Kansas City Royals and Minnesota Twins tie for the AL Central Division Championship. The Seattle Mariners have a better record than all three tied Clubs and would be the Wild Card. Based on their head-to-head records through games of September 7 (CWS 7-5 over each Minnesota and KC; KC 11-8 over Minnesota), the White Sox would choose their designation as Club "A," "B," or "C," and Kansas City would choose a designation from the remaining two designations. Minnesota would be assigned the remaining designation.

[gregmag]

Very cool, Russ. Worrisome, but informative. Thanks for putting in the work.

 

Greg.

[patrickgpe]

according to baseball prospectus the odds are as follows

 

cubs win outright 45%

brewers win outright 38%

cards win outright 18%

 

http://www.baseballprospectus.com/statistics/ps_odds.php

[Fatter than Joey]

cubs win outright 45%

brewers win outright 38%

cards win outright 18%

 

This equals 101%?

 

I realize that the 1% is due to rounding -- where are the tie factors? --Are those built in?

[rluzinski]

I realize that the 1% is due to rounding -- where are the tie factors? --Are those built in?

 

Those aren't outright probabilities:

"Champions is how often, in percentage terms, this team won the

championship of their division. Ties are not broken, but credited as 0.5

championships apiece (for a two-way tie), .333 apiece for a three-way tie, .25

for four-way, etc. This is why the final decimal place is not an error!"

 

They cheat, just like me. Now that I know home field advantages, though, I can take it to that next, incredibly important level, however!

 

Next week.

[mls4]

Scenario #4: If three Clubs are tied for first place in a Division (or Wild Card) with an identical winning percentage at the conclusion of the championship season and the tied Clubs do not have identical records against one another in the championship season, the tie for the Division Championship (or Wild Card) shall be broken as follows:

The way I read this, it basically means that, in a three-way tie situation, the Brewers would really need to win 2 more games to become the division winner. The Cubs have already won the season series over the Brewers 9-6 and would be able to choose their situation before the Brewers would choose. Even if the Brewers win their remaining three games against the Cardinals, they will have an overall losing record against the other two teams and cannot finish above both the Cubs and the Cardinals in that qualification.

 

[Oldcity]

Russ I'm interested in whether the Brewers would jump ahead of the Cubs if they pulled ahead by one game tonight? Or would the Cubs pythagorean still give them a slight edge?

[rluzinski]

Russ I'm interested in whether the Brewers would jump ahead of the Cubs if they pulled ahead by one game tonight? Or would the Cubs pythagorean still give them a slight edge?

The Cubs' pythagorean edge over the Brewers equates to less than 1 extra win over their remaining 20 games, so the Brewers will be the (ever so slight) favorites when I update the odds. Statistically, the Brewers and Cubs are very close to evenly matched this year.With only 20 games left, if either team can pull out to a 3+ game lead, it would be very tough for the other team to catch up.

 

[dlk9s]

The stupid thing about that whole three-way tie breaking procedure is that the teams get to choose "A," "B," or "C." I can't think of any scenario why a team would not choose the first letter alphabetically if given the opportunity. Thus, I don't understand why MLB doesn't just assign the letters to the teams based on the tie breakers.

[rluzinski]

Updated some numbers. Here are my probabilities of winning the Central:

 

Brewers: 49.3%

Cubs: 45.8%

Cards: 5.5%

 

About a 11% chance of the Brewers and Cubs tieing in the regular season, with a 56% chance of the Cubs taking the tiebreaker game. The chance of a three way tie has been reduced to .8%.

 

Here are the probabilities of the Brewers finishing with so many wins:

 

W Prob

75 0.0%

76 0.1%

77 0.3%

78 0.9%

79 2.6%

80 5.8%

81 10.3%

82 14.8%

83 17.5%

84 17.1%

85 13.8%

86 9.1%

87 4.7%

88 2.1%

90 0.7%

91 0.0%

 

About an 80% chance of a winning season and a 30% chance of 85 or more wins.

 

Finally, the probability of the Brewers beating each of their final opponents:

 

@ Pirates: 51%

Reds: 59%

@Astros: 54%

@Braves: 43% (4 game series, ouch)

Cardinals: 59%

Padres: 50%

 

If you want to see the spreadsheet I used, you can download it here:

 

http://spreadsheets.google.com/ccc?key=pjOhZzPpnP_N9gWKD2W0jSg&hl=en_US

 

Hitting F9 will resimulate the season but the actual probabilties won't update (need an add on program for that). It's crazy to see how vastly different the season can end up based on chance. One simulation will have the Brewers destroying everyone and running away with the division, the next will show a complete collapse.

[Fear The Chorizo]

good to see the predictions continually improving for the Brewers as they continue to play well - This is a HUGE week for the Brewers. If they play well while the Cubs and Cardinals beat up on each other, a 3-4 game cushion is very possible by week's end.

With that 4 game series with the Pads looming to end the season, a little breathing room right now would be great!

[rluzinski]

Update:

 

100,000 simulations
	W	L	win outright
Cubs	82	80	39.7%
Cardinals	81	81	1.7%
Brewers	77	85	44.2%
Tiebreaker Matchups
Crew @ Cubs			12.3%
Cards @ Crew			0.8%
Cards @ Cubs			0.7%
Three-Way Tie:			0.4%
Final
Brewers			50.2%
Cubs			47.2%
Cards			2.4%

[Samurai Bucky]

 <font><font face="courier">The latest prospectus has Milwaukee at 56%:
[url=http://]http://www.baseballprospectus.com/statistics/ps_odds.php[/url]

Average wins by position in NL Central: 84.4 82.1 78.6 74.2 72.0 69.8
[url=http://www.baseballprospectus.com/statistics/nlcent.png]NL Central[/url] W L Pct3 Avg W Avg L Champions Wild Card Playoffs
[url=http://www.baseballprospectus.com/statistics/Brewerspsodds.php]Brewers[/url] 74 70 .503 83.4 78.6 56.80585 .10874 56.91459
[url=http://www.baseballprospectus.com/statistics/Cubspsodds.php]Cubs[/url] 73 71 .505 82.7 79.3 38.73313 .13909 38.87223
[url=http://www.baseballprospectus.com/statistics/Cardinalspsodds.php]Cardinals[/url] 69 73 .462 78.8 83.2 4.44078 .00143 4.44221
[url=http://www.baseballprospectus.com/statistics/Redspsodds.php]Reds[/url] 65 79 .465 73.6 88.4 .01983 .00000 .01983
[url=http://www.baseballprospectus.com/statistics/Piratespsodds.php]Pirates[/url] 64 81 .429 71.5 90.5 .00010 .00000 .00010
[url=http://www.baseballprospectus.com/statistics/Astrospsodds.php]Astros[/url] 63 81 .419 71.0 91.0 .00031 .00000 .00031</font></font> 

[Fatter than Joey]

We were at 43% yesterday -- a 13 point swing again.

 

Obviously we are in "must win" territory http://forum.brewerfan.net/images/smilies/smile.gif

[JoeH33]

Update:

 

100,000 simulations
	W	L	win outright
Cubs	82	80	39.7%
Cardinals	81	81	1.7%
Brewers	77	85	44.2%
Tiebreaker Matchups
Crew @ Cubs			12.3%
Cards @ Crew			0.8%
Cards @ Cubs			0.7%
Three-Way Tie:			0.4%
Final
Brewers			50.2%
Cubs			47.2%
Cards			2.4%

I don't get it, those figures have us winning the division 45% of the time, but also have us finishing 8 games under .500? Is that just a labeling error, or am I missing something?

[Ennder]

Update:

 

100,000 simulations
	W	L	win outright
Cubs	82	80	39.7%
Cardinals	81	81	1.7%
Brewers	77	85	44.2%
Tiebreaker Matchups
Crew @ Cubs			12.3%
Cards @ Crew			0.8%
Cards @ Cubs			0.7%
Three-Way Tie:			0.4%
Final
Brewers			50.2%
Cubs			47.2%
Cards			2.4%

I don't get it, those figures have us winning the division 45% of the time, but also have us finishing 8 games under .500? Is that just a labeling error, or am I missing something?

 

My guess is that is just how the last simulation of the 100,000 turned out.

[endaround]

Russ reversed the numbers

[rluzinski]

My guess is that is just how the last simulation of the 100,000 turned out.

 

Opps! Sorry. That is correct. The Brewers finish with an average of a little over 83 wins in my simulation. Here are the breakdowns:

 

W	Prob	Prob Atlst
75	0.0%
76	0.0%	100.0%
77	0.2%	99.9%
78	0.8%	99.7%
79	2.5%	98.9%
80	5.7%	96.4%
81	10.7%	90.7%
82	15.7%	80.0%
83	18.5%	64.3%
84	17.7%	45.8%
85	13.6%	28.1%
86	8.4%	14.6%
87	4.1%	6.1%
88	1.6%	2.1%
89	0.4%	0.5%
90	0.1%	0.1%

80.0% of finishing with at least 82 wins and a winning season. Here's an example of the end of the season simulated 30 times, just to illustrate how much the Brewers are still going to have to rely on lady luck:

 

http://i14.photobucket.com/albums/a345/rluzinski/seasonfinishsim.jpg

It's just scary how many different ways the season could still go. I'll pick that last one, please.

[brewcrewkid14]

I looked at the sims in which we lost todays game, and it's scarying me that 85 is the highest win total with a loss on 9/12, and that it seems there are a lot of 80s-82s.

 

Let's hope your statistical findings prove to be wrong, Russ.