THE BOOK--Playing The Percentages In Baseball

Am I correct in reading this to mean what would happen if the actual 2009 Nationals players, the ones who lost a hundred regular season games, played the 2009 Dodgers in the playoffs?

This is a great question.  The question is what are the chances of the team with the worst record in the league winning a playoff series against the team with the best record.

Retrosheet indicates that in 2008, the Nationals won three games against the Dodgers and lost three.  I don’t know what the regular season record was in 2009 for the two teams playing each other.  I do remember that they swept the Yankees this year.

With a 0.25 probability to win each of the three series, a team would have ~65:1 odds to win it all.  To get to 100:1 odds win probability for each series would be around .215

If you think the Nats would have a 21.5% chance of winning each series, then you’d agree with the 100:1 odds.
vr, Xei

No way would the Nats be a 4-1 dog for each series.  They are not nearly as bad as their record was this year.  It is unlikely that the worst team in baseball, by record, ever is nearly as bad as their record, true-talent wise.

Heck, the Rockies are not a very good team.  If they played the Nats, they would probably be a 3-2 fave, 2-1 at best.  The Phillies, STL, and LA, would be a 2-1 to a 3-1 fave.  The Yankees would be a 4-1 fave or so, Boston and ALA maybe 3-1 and MIN maybe 2-1.

No way would they be a 100-1 dog to win the WS unless perhaps you assumed that their record this year equaled their true talent, which is very unlikely for two reasons.  One, as I said, if I told you that the team with the worst record in baseball was 59-103, you would have to put their true talent at something like 67-95 (a wild guess).  Two, if you actually look at the projections for their players, you would see that they are indeed not nearly as bad as their record, at least according to the projections.  Off the top of my head, I’d peg them as a .430 team.

MGL - You said it in the previous post as well so I’m curious why you are so down on the Rockies. BtB’s Power Rankings seem to like them a lot so I’m wondering what you see differently.

Thanks

http://www.beyondtheboxscore.com/2009/10/1/1064754/btb-power-rankings-10-1-09

The Nats won 2 out of 3 in Yankee Stadium earlier this summer.  Very few remember that now, if it happened during the playoffs, it would all be ARod’s fault. 

Patriot, for the purposes of his illustration, presumed them to be a .400 team.  It is irrelevant what they actually are, since he sets the illustration.

I don’t see the big deal to say that if you have a .400 team facing a .550 team, that the .400 team would have a 21.5% chance to win the series.

The single game win% would be .350.  Doesn’t it seem reasonable that a .350 team facing a .500 team would win a best 3 of 5 or 4 of 7 around 20-25% of the time?

My Monte Carlo shows in a five game series in order to have a 21.5% chance of winning the series, you’d need a win probability of 33.7% in each of the five games.  Of course in reality, each game would have different win probabilities.  I didn’t run the numbers yet for a seven game series, but does a 33.7% win probability seem realistic for the Nationals in each game of the NLDS?  The three road games would probably be lower than that and the two home games likely higher than that.  Of course it depends who they played against too, but I assume we are looking at a more macro level.
vr, Xei

As a follow up to my post above… for a seven game series the win probability for each game would need to be 35.9324% to come out with a 21.5% chance to win the series.
vr, Xei

Toffer, they just don’t have that great of a lineup offensively and defensively combined and they have one very good starter and a ho-hum bullpen.  Basically of all the playoff teams, they have the worst lineup and pitching.

No, the Nats as a .430 team would not be a 2-1 dog in every game on the average.

Whatever Patriot did, I’m sure it is correct given the inputs.  I am disputing the inputs, that’s all.  The Dodgers and STL are probably a .550 team.  Philly a .560 team.  COL a .520 team, and WAS a .430 team.  Those are just guesses, but pretty close I think.

In the AL, with the AL advantage, Boston and ALA are probably .600 teams, the Yankees .620 and MIN .550.

You do the math.

MGL--I spent a paragraph in my post pointing out flaws with the inputs, and I even said: “or better yet, we could look at projections for the team’s actual personnel rather than using aggregate season W%s.”

So I agree with your critiques.  I also agree with Xeifrank--it’s not correct to assume a constant W% for each game throughout the series.  What it does is makes the math straightforward, and the point of the post was not really to estimate the probabilities for each of the actual 2009 playoff participants--it was to discuss the high degree of uncertainty that comes with the playoff structure itself.

I agree that there’s no need to talk about the inputs because Patriot essentially used “.400” for illustration-purposes mostly.  So, that part is a non-issue.

And, a .400 team facing a .550 team will win 35% of its games.  A .400 team facing a .600 team will win 30% of its games.  Xeifrank’s number confirm that if you win 30-35% of your games, you will win 20-25% of the series.

So, all to say that there is no point of disagreement here!  The “Nats”, or a team with a true talent .400 team, are 100:1 to win the World Series if they were part of 7 other “normal” playoff teams.

We can talk about the Nats specifically, and we can talk about the precision of the numbers, but this if you read Patriot’s article to begin with, this is all besides the point.

Patriot, I know.  I thought it was a good post.  I was just pointing out that in reality, using projections for each of the teams, I am pretty sure that the Nats would not be such big dogs to win the series, which makes your point (that most people wouldn’t give them a 1 in a 1000 chance) even more salient.

In the 2nd half, the average expected winning percentage (as per the betting line) for the Nationals at home was 39.5%.

The avg exp. W% for the Nationals on the road was 31.4%

I’m gong to make these assumptions:
1. they got in via the wild card and do not have home field advantage in any series.
2. vs NL I’ll assume the avg. betting line numbers above.  Nats = 39.5% at home, 31.4% on the road.
3. Since those betting lines were only against NL teams, I’ll assume they’d be - on average - 2% worse if they got to the World Series against the AL team

In the NLDS, they’d have a 22.9% chance of winning.
In the NLCS, they’d have a 19.7% chance of winning.
In the WS, they’d have a 16.5%

Putting it all together, that comes out to 0.7% or greater than 100 to 1.

You could say the betting lines were wrong, so the argument may be that using the betting lines were not a good approximation.  However, if you believe that, then you would have been happy betting on the Nationals in the 2H versus those playoff teams right?  (Yes, I know there is selection bias here since the playoff teams actually made it to the playoffs, thus they were likely to have won a nice share of games against the Nats).  And you would have gone 2-13 and lost a nice chunk of change. 

My thinking is that if the Nationals, as they were constituted at the end of the season, were shifted in the wild card instead of Colorado, 100-1 to win the World Series would not have been a slam dunk bet, I’d pass on it thinking there’d be a good chance it was a negative expectancy bet.

"Yes, I know there is selection bias here since the playoff teams actually made it to the playoffs, thus they were likely to have won a nice share of games against the Nats).  And you would have gone 2-13 and lost a nice chunk of change.”

yes, of course huge selection bias.  Not even close to a fair fight.  Your picking a team that we know to have a terrible record including the 2nd half against teams that we know to have been good enough to make the post-season.

Anyway, I’m really not sure what I think the true odds would be and of course no on knows.  It doesn’t really matter.  There is no argument here.  Patriot uses a reasonable back of envelope method of assigning a true WP for each team and then correctly (I assume) figured the odds of them winning the WS assuming those values.

It was a fun post by him and his point was well taken.

King: I *love* the idea that you took the Vegas odds to figure out the expected win % for the Nats.  That is really the very essence of the “true talent” level.  Fantastic. 

Can you do the same for every team?  Here’s my request (unless you just want to give me the data, and I’ll do it):
- for intraleague games only, figure out the Vegas win% odds, for the whole season, by team
- for interleague games only, figure out the odds, by league (just one number)

Great stuff.

Tango, I’d rather give you the data
I’d be thrilled to see what you come up with.  All the data for 2009 is at covers.com.  I do have data from previous years in Excel form, if you don’t care about the year and want to do a broader study, email me and I’ll send you the sheet.

Here is the page for all the different teams:
http://www.covers.com/pageLoader/pageLoader.aspx?page=/data/mlb/teams/teams.html

Click “Past Results” under each teams and you’ll get every game this season.  The Nats page is here:

http://www.covers.com/pageLoader/pageLoader.aspx?page=/data/mlb/teams/pastresults/2009/team2972.html&t=0

(P.S., wow, the Nationals won 7 games in a row to end the season? )

Two notes:
I agree with MGL it wasn’t a fair fight to use the selection bias, but at least I mentioned it instead of pretending it didn’t exist, right? 

I did “cheat” a little, in that I only used the WAS line, but there is a vig incorporated in the line that covers.com reports.  For example, in the last game, they show WAS vs ATL with a line of WAS +160, but the ATL page shows ATL -168.

King: broader study is better for me, so you can email me what you have.  Thanks!

tom~tangotiger~net, and replace the ~ appropriately.

While the Vegas line is a “fair line” it is a little like using the method that Patriot used, in that it is fair on the average but not necessarily accurate.  I am claiming that WAS is a better team than the “wisdom of the crowds” (the Vegas line) thinks and therefore better than a Vegas line would have them if they were playing in the post-season.  Sure, Vegas might have them at 120-1 to win the WS based on individual Vegas WAS lines.  I would bet against that line if I could.

As I said, there is no controversy in this thread.  Whatever you think the true talent of the Nats is versus the true of the other teams, you take those numbers and do the math.

I’ll agree that it would interesting to take the Vegas lines to do the math as that is probably the best estimate of each team’s true strength, notwithstanding what I think.

MGL, do you think there’s a systematic bias, or do you think fans simply are missing the boat on the Nats?

That is, is it the case that fans overemphasize current streaks, and therefore, if a team goes 15-2, that team will be favored more than their team talent dictates?

Similarly, when the Royals started tanking after their big April run, did the odds start shifting greatly?  Ideally, the odds of the Royals winning (notwithstanding the starting pitchers) should be the same for any 5-game time period, correct?  Did this happen?  If you group the Royals games in, say, 15-game chunks, were their odds the same (after accounting for opposing pitcher/team)?

Or, did the fans try to follow the Royals wave?