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.

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%

According to Hoyle...

Odds for the Phillies making it to the Series have gone up sharply with their two victories, and winning the first game has made a world (series) of difference for the Red Sox, who now are most likely to win the series. The Dodgers home winning percentage probably means that they should be able to win at least one at home, but the Phillies are no slouches on the road.

ALCS	H PWP	A PWP	Win	Sweep
Rays	0.628	0.515	30%	0%
Red Sox	0.652	0.534	70%	16%
NLDS
Phillies	0.598	0.561	82%	18%
Dodgers	0.637	0.407	18%	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%

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!

Rays and Red Sox Increase Their Odds, Things Look Bad For Angels and White Sox

The Angels and the White Sox have basically a 1 in 4 chance of making it to the ALCS. Looks like I might not be able to spin out my long-awaited probability of the Cubs meeting the White Sox in the World Series.

The Phillies are playing right now and beating Sabathia badly. The question on the Hot Stove circuit will certainly be "Is it too many starts on 3-days rest down the stretch or is he just not a 'clutch' or capable playoff pitcher?" Last year in the playoffs, his ERA was 9.00...

ALDS	H PWP	A PWP	Win	Sweep
Angels	0.539	0.556	24%	0%
Red Sox	0.652	0.534	76%	30%
Rays	0.628	0.515	74%	25%
White Sox	0.644	0.441	26%	0%
NLDS
Cubs	0.649	0.593	42%	0%
Dodgers	0.637	0.454	58%	17%
Phillies	0.598	0.561	69%	24%
Brewers	0.635	0.522	31%	0%

I Guess That Answer's Last Night's Question; Now Updated Playoff Odds

No real changes except that we now have the actual contestants and final runs/runs against. Basically, I still think the Red Sox will beat the Angels (57% chance to do so); Rays will beat the White Sox (61%--Sorry, Chicago, no subway series); Cubs will beat the Dodgers (68%); and even though the Phillies have a 53% chance to beat the Brewers, that is really a toss-up.

ALDS	H PWP	A PWP	Win	Sweep
Angels	0.539	0.556	43%	10%
Red Sox	0.652	0.534	57%	15%
Rays	0.628	0.515	61%	17%
White Sox	0.644	0.441	39%	6%
NLDS
Cubs	0.649	0.593	68%	22%
Dodgers	0.637	0.454	32%	5%
Phillies	0.598	0.561	53%	14%
Brewers	0.635	0.522	47%	10%

And if each of the teams predicted to lose the series wins the first game, it changes the odds to plus 60% for all of those teams, except one, the Cubs. They would no longer be favored, but the odds would be just under 50/50 for them to pull it out anyway.

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.

White Sox Have Good Chance to Tie for the NL Central Title Tomorrow

The White Sox have a 67% chance of beating the Tigers tomorrow and taking this into a Tuesday one-game playoff with the Twins. Very cool.

Playoff Prediction or Fun With Pythagorean, Log5 and Probabilities: Cubs, Phillies, Red Sox Will Advance

Alright folks (all 60 of you now!), you'll hear it here first: the Red Sox will upset the Angels. The Red Sox have an almost 60% chance of taking the series, mostly on the strength of better record on the road, and an unbelievable record at home.

The Rays will almost certainly beat whoever they play, be it the depleted Twins or depleted White Sox.

The Cubs, on the strength of an excellent road record, also have a great chance to proceed to the NLCS, 67% (the most of any of the post-season aspirants). Their home record vs. the road record of the Dodgers is very big, and their excellent road record can almost nullify the great home advantage of the Dodgers. On the other hand, should the Dodgers steal one at Wrigley, that would probably have a significant effect on the outcome.

Phillies should beat the Brewers (57% chance), and that might be more true considering how much Milwaukee's staff was battered and overworked in the last week (except when CC Sabathia pitched).

ALDS	H PWP	A PWP	Odds to Win Series	Odds to Sweep
Angels	0.525	0.554	41%	9%
Red Sox	0.658	0.536	59%	16%
Rays	0.628	0.514	x%	x%
Twins/WS	0.xxx	0.xxx	x%	x%
NLDS
Cubs	0.642	0.596	67%	21%
Dodgers	0.637	0.456	33%	6%
Phillies	0.588	0.561	58%	16%
Brewers	0.558	0.522	42%	9%

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.

Fun With Probabilities: Brewers/Twins have best shot at postseason

I'm sure every one of my 34 regular readers (according to Google Analytics!) went immediately to their trusty Texas Instruments TI-35 calculators and used my probabilities from yesterdays' posts to calculate overall odds of making the post season for their favorite teams.

You mean you didn't?

OK, then, let's take a look from the spreadsheet. The beauty of probabilities, statistically speaking is that they can be added, subtracted and multiplied to come up with odds of combinations and odds of mutual exclusivity, among the many other possibilities. Here, we'll really look at the combinatorial property.

Before I delve into this, I want to point out that the best description of what I'm doing comes from DiamondMind Baseball. I first posted my playoff version of Bill James Log5 theorem in 2005. What I will be doing in the playoffs is exactly what they describe. You can also find my original description on BigShouldersSports, where I used to occasionally contribute. In essence, I take the home team's winning percentage at home vs. the away teams road winning percentage, all using the pythagorean expectations formula as used during the season, to compute a probability of victory in each game of the series. I then use the combinatorial mathematics to come up with the odds of sweeping, winning two games, or winning just one for each team. As you will see in the playoffs, this also will take into account all five or seven games.

For now, though, we've already had one game, so the odds have changed a little. Looking at the numbers for the Brewers, they have a 49% chance of beating the Cubs twice (since they won last night). The Mets have only a 29% chance of winning two games. The Brewers also have a 33% of winning one game, Mets have a 50% of doing so, facing easier competition. If both teams win one game or both teams win two games, then they end up tied, so we add up both of those probabilities for each team and multiply to get the odds of this happening, which is 64%.

But unfortunately, for the Mets, because they lost yesterday, they do not have the ability to sweep their series and will therefore have to hope that the Brewers will lose at least one game. Otherwise, the chances of the Brewers winning the Wild Card are 59% (odds of sweeping plus odds of winning two games plus odds of winning one game while the Mets lose two plus Mets losing one plus Mets being swept). Those same odds in reverse, i.e. for the Mets to win the WC, are 41%.

If you're wondering why some of those numbers don't total one hundred, it's because these possibilities are mutually exclusive, meaning they exist on their own (this is something I'm sure my regular visitors already know, but I include it in case I get some new visitors that might not). That is not true, though, for the Mets probability (P) of winning, that is exactly 41% because it is calculated 100% (Mets OR Brewers win P) minus 59% (Brewers win P).

Calculating the same for the White Sox and Twins, we get, respectively, 43% and 57%. Best way to check a probability is to do a gut-level check: Twins are playing the Royals, who are the worst team in the league, whereas the Sox are playing the Indians, which are in third place in the division. So the Sox have a tougher schedule.

Updated, and Now, AL, too

Updated probabilities, plus I've finally included the White Sox and Twins. So how does it look for our finalists, some of whom will go home with consolation prizes (a higher draft pick next summer?).

Important places to look below: the Brewers have an 18% chance to sweep the Cubs, but even if they win only two, their chances of winning two now is almost 50/50. That is in stark contrast to the Mets who have only a 50/50 chance of winning ONE game. The Phillies have practically clinched, so they're not even in the equation anymore. If the Brewers win one more game, that will probably knock the Mets off (sorry, Mets fans).

I think I have to say sorry to White Sox fans also: they have to win the next two games to guarantee a tie, whereas the Twins, winning two games, will win the division. In the immortal words of The Jam, "Here Comes The Weekend"!

	sweep	2-wins	1-win
Cubs	0.0%	33.1%	48.9%
Brewers	18.1%	48.9%	33.1%
Phillies	45.4%	43.9%	10.6%
Nationals	0.0%	10.6%	43.9%
Mets	0.0%	28.6%	49.8%
Marlins	21.6%	49.8%	28.6%
White Sox	0.0%	48.2%	42.4%
Indians	9.3%	42.4%	48.2%
Twins	0.0%	55.2%	38.2%
KC	6.6%	38.2%	55.2%

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Final Weekend: National League Version

The table below is the Log5 probability (I will explain this in a following post) of the possible results in this weekends NL games with Playoff implications. The three columns are probability of a sweep for each team, for getting two wins, and getting one win.

The Brewers and Mets need to win 2 games and the Mets have the best chance of doing that. The numbers absolutely favor the Phillies winning at least one game and very likely two, and the Mets are second most likely to win. Of course, will the Cubs bring their A-Team this weekend? Given what I saw last night in Shea Stadium, they probably won't. Of course, the B-Team sure didn't disappoint too badly.

	sweep	2-wins	1-win
Cubs	19.3%	42.3%	30.9%
Brewers	7.5%	30.9%	42.3%
Phillies	30.6%	44.4%	21.5%
Nationals	3.5%	21.5%	44.4%
Mets	15.2%	39.8%	34.8%
Marlins	10.1%	34.8%	39.8%

Ed note: My original post incorrectly showed the Cubs as the home team, and they are in fact the visiting team in Milwaukee. The numbers changed slightly.