Yankees Lose! Yankees Win! Yankees ? ? ? ? ? Yes It Could Go 7...

Fret not, Yankees fans: Log 5 Probability is on your side! After a home split leaving the Series at 1-1, the Yankees advantage has only slightly moved down from the first day. A home loss basically dropped their win probability for the Series from 56% to 54%.

Additionally, if you look at the Yankees' winning percentage on the road vs. the Phillies' percentage at home--all of a sudden, home not so sweet home for the Phanatics: .571 vs. .553. I will admit, though, that the number as calculated does NOT take into account the fact that the Yanks winning percentage during the season was accomplished with the DH, not the pitcher, as will be the case in Philadelphia. But it still goes to show that the Yankees are by no means down away from home.

Of the remaining scenarios, 5-game, 6-game or full 7 game Series, the Yankees have the advantage in all of them by roughly 3%-5%, with the most likely outcome being a 7-game Series in which the Yankees have about a 3% chance better than the Phillies to win.

World Series	H PWP	A PWP	Win	Next Game only
Phillies	0.553	0.592	46%	48%
Yankees	0.621	0.571	54%	52%

H PWP = Home Pythagorean Winning Percentage

A PWP = Away Pythagorean Winning Percentage

These numbers were used to calculate the log5 win probabilities for each team and each game in the series. No I did not look at pitcher vs. team since the sample size is too small. See my post from last year about what it is and how it works.

Winning the First Game on the Road Gives Huge Boost to Win Probability for Phillies

WS	H PWP	A PWP	Win	Sweep
Rays	0.628	0.515	30%	0%
Phillies	0.598	0.561	70%	16%

Taking away the home-field advantage from the Rays puts the Phillies in position to do what they could not in 1993: win the World Series. Although they do have 70% chance of winning now, the Rays still have a 60% chance of winning Game 2, which could swing things back to at least toss-up status.

Phillies Are No Slouches--Rays Have a Tough Series Even With Home Advantage

Back when the Cubs were the team to beat, I always thought the Phillies would present the toughest challenge. I should have known better that, once October rolls around, even a team made up of Florida Seniors could beat them. One thing I also knew, is that both Boston or Tampa Bay were better than any NL team. So if we look at the numbers alone, sans context, the World Series will be a toss-up, with the slight advantage going to the Phillies, based on their Road record particularly. 

The big caveat in this, though, is that the Phils play in the National League which is not as strong a league as the AL, and particularly not as strong as the survivor of the AL East, which is a beast (and I will stop the rhyme there).

Whoever wins the first game will certainly get the edge, because then, in either case, that winner will hold a 70% chance of taking the Series.

WS	H PWP	A PWP	Win	Sweep
Rays	0.628	0.515	49%	5%
Phillies	0.598	0.561	51%	7%

Home for Three

Rays are back in it, as are the Dodgers. The Dodgers have the second best winning percentage at home, Red Sox have the best. I bet LA will win at least one more home game. The Red Sox could very well sweep at home (hence the great chance of winning still, even though the series is 1-1).

ALCS	H PWP	A PWP	Win	Sweep
Rays	0.628	0.515	41%	0%
Red Sox	0.652	0.534	59%	0%
NLDS
Phillies	0.598	0.561	72%	0%
Dodgers	0.637	0.407	28%	0%

Who Will Be Here Today, Gone Tomorrow?

Rays/Red Sox is a toss-up--couldn't be a closer matchup. I thought at the beginning of the year that the Red Sox were the best team in the majors and there's no reason to change my mind now. My initial (though un-posted) prediction of the World Series was BoSox over the Cubs. Insert lamentation here. Or just insert Phillies.

This is looking kind of like last year, where I had the Cubs beating Arizona, and Phillies beating the Rockies. Then I had Arizona beating the Rockies--I wasn't right until I finally had the Red Sox over the Rockies. But the numbers don't lie: the Phils are better than the commuter-train-dodgers (sorry, that's bad). If the Dodgers can demoralize the Phillies by taking two in the City of Brothelly Love, they can pull off an upset again.

ALCS	H PWP	A PWP	Win	Sweep
Rays	0.628	0.515	49%	19%
Red Sox	0.652	0.534	51%	13%
NLCS
Phillies	0.598	0.561	66%	22%
Dodgers	0.637	0.407	34%	10%

Die Another Day

The Angels and White Sox live to fight another day and keep slim hopes alive: both of them have the exact same odds to overcome, a 1 in 5 chance of winning their ALDS series. And in case you so enjoyed my anatomy of a stat, here's another one. What are the chances of the White Sox facing the Angels in the ALCS?

1/5 x 1/5 (each is the chance that they will make it to the next round) = 1/25 or 1 in 25 chances would this happen. I've seen worse odds...

Congratulations to the LA Party Poopers, I mean Dodgers, and the Phillies.

ALDS	H PWP	A PWP	Win	Sweep
Angels	0.539	0.556	20%	0%
Red Sox	0.652	0.534	80%	0%
Rays	0.628	0.515	80%	0%
White Sox	0.644	0.441	20%	0%
NLDS
Cubs	0.649	0.593	0%	0%
Dodgers	0.637	0.454	100%	100%
Phillies	0.598	0.561	100%	0%
Brewers	0.635	0.522	0%	0%

Anatomy of a Baseball Stat: Explaining Win Probability

Since many of you might not read Bill James' Baseball Manifestos, I thought I would show you how arrive at the numbers that I've been showing as the probability of victory for any given playoff team. We will draw upon two formulas from Bill James, one from his 1981 Baseball Abstract and the other from his 1984 Baseball Abstract.

First, let's look at his Pythagorean Win Expectancy "theorem". I use quotes because even though he called it that, he never thought that it quite stood the test of an actual mathematical theorem. Baseball, at it's most basic, yet most accurate, is a game whose outcome is determined by how many runs the teams score. This has two four points: runs scored by both teams and runs given up by both teams. The obvious: the team with more runs after 9 innings wins. So, he combined the idea of the pythagorean theorem that you all probably still remember (and aren't you glad that's so--I'm sure you've used it to determine the long side of a right triangle given the two short sides recently!): a² + b² = c²

Now this has led to countless important discoveries, not the least of which couldn't have happened without it, Algebra and Trigonometry. So James' basic idea was that there was some correlation between runs scored, and runs given up, and somehow coming up with wins. I don't recall the details now (I first came across this in the late '80s). But the formula that he came up with (which I've detailed elsewhere before) is:

P WP = R² / R² + RA²

P WP = Predicted Winning Percentage

R = Runs Scored (batting)

RA = Runs Given Up (pitching)

So as an example, let's compute this for the Cubs this season. Cubs scored 854 and gave up 668 runs.

P WP = 854² / 854² + 668² = .620

This is the number that was used to compute the predictive standings. But for the Playoffs, I get more granular, since the games encompass playing 3 at home and 2 on the road. For that, I consult ESPN, but this time, get their extended team stats and sort by home and away runs/runs-against.

So the Cubs then end up at:

Home: P WP = 854² / 454² + 339² = .649

Away: P WP = 854² / 401² + 332² = .563

So this is where we want to see what their chances of winning a home game and winning an away game are against their opponent, the LA Dodgers. This is when we bring in James' second discovery which he called Log5 probability (I won't go into the details of the name, that's totally straining your staying power!). Log5 allows you to take the winning percentage of any team, multiply it by their opponent, and come up with a probability of victory (or defeat, as the case might be). Now, because actual winning percentage can sometimes be a function of luck or other external factors, I use the pythagorean or predicted winning percentage.

To do this, I also need the same information for the opposing team, in this case the Dodgers. I'll use the same method and come up with their home and away winning percentages, which are .637 and .454, respectively. So the formula will then look like this:

One Game Win Probability (Cubs home advantage)

 = CHPWP - (CHPWP x LAAPWP) / CHPWP + LAAPWP - (2 x LAAPWP x CHPWP) where

CHPWP = Cubs Home Predicted Winning Percentage

LAAPWP = Dodgers Away Predicted Winning Percentage

With the numbers just given, the formula and result look like this:

Cubs Win Probability = .649 x .454 / .649 + .454 - (2 x .454 x .649) = .690 or 69%

LA Dodgers Win Probability = 1 - Cubs Win Probability = .310 or 31%

The next step is the one I outlined briefly early this week and referenced in the Diamond Mind article of Monday's post, where you assemble all the potential probabilities of the different scenarios in a 5-game series: sweep 3, lose first and win next 3, lose first 2 win next 3, etc. Each one of these is associated with a probability. So, as an example, how do we calculate the probability of a 3-game sweep for these two teams? We simply use the multiplicative property of probabilities. The Cubs have a probability of winning each of the first two home games of .690. The already calculated chance following the above Log5 method for the Away games are .454. The formula and result:

Probability of 3-game sweep for Cubs = .690 x .690 x .454 = 22%

For the Dodgers, the chance of a sweep is only 5%. But since the Cubs lost the two games at home, the chance of a sweep for the Dodgers went up:

Probability of Dodgers Sweep with two victories = 1.00 x 1.00 x .546 = 55% 

(1.00 represents a victory or probability of 100% of winning that game which we know they won)

Hopefully, this has been properly explained. Now to go back to the Red Sox vs. Angels game!

White Sox Vs. Twins in One-Game Playoff Tomorrow--Who Wins?

Based on the fact that White Sox are at home tomorrow, where they sport a lofty 0.643 pythagorean winning percentage, and that the Twins will bring their less-than-stellar 0.450 pythagorean road winning percentage, the Sox have a 69% chance of facing the Rays on Thursday, using the log5 win probability.

Today's Win Probabilities for the Mets, Brewers, White Sox and Twins

It all comes down to one day, one game, to determine two divisional races.

The Mets have a 54% chance of winning their game; the Brewers only a 42% of winning theirs (based on log5, as explained yesterday). For the Brewers to win the Wild Card today, we multiply their odds of winning to the odds of the Mets losing, then vice versa for the Mets to win it:

Brewers, 42% x (1-54%) = 20%

Mets, 54% x (1-42%) = 31%

Tie Today, either by both winning or both losing, (42% x 54%) + ((1 - 42%) x (1 - 54%)) = 49%

As of now, the Mets and Marlins are tied 0-0 in the 3rd, while the Cubs have taken 1-0 lead in the first.

As for the Twins and White Sox, their situation is a little different. Two things have to happen for the White Sox to win the division--they have to win and the Twins lose, then play a one-game playoff. Whereas the Twins just need to hold serve:

Twins, 74% chance to win division (based on log5 win probability to beat the Royals)

White Sox, 70% x (1 - 74%) = 18% (Sox win AND Twins lose) just to tie for the NL Central

As of now, Sox lead 3-1 over Cleveland in the 3rd, and Twins/Royals 0-0.

Who do the odds favor to reach the post-season, then? Well, Twins and Mets have the better chances to outlast their opponents, though it will be much harder for the Mets.

And just a side note to Mets' fans--this team has lost Billy Wagner, John Maine and Ryan Church for extended portions of the season, long enough to have probably cost them the division. That they are even in this situation is a testament to the team (players and manager) in overcoming these obstacles. With those three playing the full season, they are about equal to the Cubs in performance.

UPDATE and OOOPS!: With the White Sox win today, they force their remaining game to be played--I hadn't taken that into account. So the Twins are done, and now have to wait until tomorrow to see if the tie happens or they win.

Mets Win, Chances to Tie/Win Go Up

The chances of a one-game playoff between the Mets and the Brewers just went up to 82% with the Mets' victory. Brewer's chance to win outright drops to 56%.