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A different look at the odds

Frayed Knot Sep 26 2008 08:15 AM

With all due respect to the Baseball Prospectus project, which is terrific to follow in the final weeks because they take everything into consideration when you & I couldn't possibly boil it all down. But now the combinations of possible outcomes are so few that some smart guy can map them all out. Or even me. So there are (assuming everyone gets all their games in) 64 possible outcomes of this weekend for NL games that matter to us For ex: each team sweeps; or Mets sweep while Phils win twice and Brews get swept; or Mets win once while Phils win twice and Brews win once; etc. Now not all 64 of those are equally likely since 2-1 or 1-2 splits are more likely to occur than a 3-0 or 0-3. But if we assume that [u:e72fba76bf]the outcome of each game is a 50/50 possibility[/u:e72fba76bf], then of those 64: * 18 of them result in us winning the east outright, representing a 22.7% overall chance * in 10 we win the Wild Card free and clear - 14.8% * 22 results in us OUT of the playoffs - 30.5% * 8 put us into a Wild Card play-in game with Milwaukee - 20.3% * 3 put us into a one-game playoff for the NLEast, loser goes home - 4.1% * and 3 more throw us into a [u:e72fba76bf]double play-in[/u:e72fba76bf] situation (3-way tie) where NY & Phil fight it out for the East and the loser plays the Brews for the WC - 7.6% So that's: In = 37.5% Out = 30.5% Single Play-in game = 24.4% Double Play-in = 7.6% Enjoy the ride.

AG/DC Sep 26 2008 08:25 AM

My understanding from previous years was that, in a three-way tie among the Mets and the Phils and the Brews, the Mets and Phils have a one-game playoff for the division, and the loser --- since that counts as a regular-season game --- finishes with a worse record than the Brews and goes home. That seemed unjust from previous years so I hope it's not true anymore, if it ever was.

Benjamin Grimm Sep 26 2008 08:28 AM

Thank you for doing that! I was considering doing exactly what you just did and I'm glad you saved me the effort! Assuming no rainouts, (huge assumption, I know) we have a 37.5% chance of going to bed on Sunday night knowing we have NLDS action to look forward to. I would have taken that in a heartbeat way back when the Mets scurried out of San Diego with those four losses. But aren't there 512 possible outcomes? There are eight possibilities each of three days, and 8x8x8 is 512. 1. Mets, Brewers, Phillies win. 2. Mets, Brewers, Nationals. 3. Mets, Cubs, Nationals. 4. Mets, Cubs, Phillies. 5. Marlins, Brewers, Phillies. 6. Marlins, Brewers, Nationals. 7. Marlins, Cubs, Nationals. 8. Marlins, Cubs, Phillies.

Benjamin Grimm Sep 26 2008 08:30 AM

AG/DC wrote: My understanding from previous years was that, in a three-way tie among the Mets and the Phils and the Brews, the Mets and Phils have a one-game playoff for the division, and the loser --- since that counts as a regular-season game --- finishes with a worse record than the Brews and goes home. That seemed unjust from previous years so I hope it's not true anymore, if it ever was. They changed that. I think it was changed right after 1999, when the Mets would have benefited from that rule had they finished in a three-way tie with the Reds and the Astros.

Frayed Knot Sep 26 2008 08:34 AM Edited 1 time(s), most recently on Sep 26 2008 08:55 AM

]That seemed unjust from previous years so I hope it's not true anymore, if it ever was. That was briefly the case but was changed before it was ever used. ]But aren't there 512 possible outcomes? There are eight possibilities each of three days, and 8x8x8 is 512. 512 different possibilities yes, but only 64 different outcomes. IOW, if the Brewers WIN - WIN - LOSE the result is the same as if they WIN - LOSE - WIN So if you're betting on each game the specifics of how each comes out matters. But seeing as how we're only interested in the total weekend record it cuts down on things considerably.

Benjamin Grimm Sep 26 2008 08:36 AM

True. Good point.

AG/DC Sep 26 2008 08:42 AM

Frayed Knot wrote: [That was briefly the case but was changed before it was ever used. Excellent.

RealityChuck Sep 26 2008 08:54 AM Re: A different look at the odds

="Frayed Knot"]With all due respect to the Baseball Prospectus project, which is terrific to follow in the final weeks because they take everything into consideration when you & I couldn't possibly boil it all down. Uh, no they don't. As I've pointed out before, they are not calculating odds. They are showing the results of their simulation. But any simulation has a bunch of assumptions, any one of which, if changed, can change the result (note that AIG's computer simulations of the use of mortgage-backed securities consistently showed that there was no danger of them causing AIG to fail, and that NASA's flight simulations said that the loss of tiles on the Columbia would not put its crew in danger). If I were to assume, say, that the Mets bullpen wouldn't give up a run the rest of the season, it would lead to a different result than if we assume they'll always give up four runs. With all the assumptions built into the BP simulation, a change in any one of them would give different results. This is chaos, not a system -- small changes that result in different results. So, ultimately, the numbers are meaningless, even if they have decimal points. Further, there's no way to verify that the Baseball Prospectus odd mean anything other than "the team that's leading the division has a better chance of winning than any other team in that division." All that work to state the obvious. (But they have decimal points! So they must be scientific!) Your combination of outcomes is no more nor no less accurate than Baseball Prospectus, simply because they have no accuracy. Yours has the advantage of showing what combinations are favorable.

Frayed Knot Sep 26 2008 09:04 AM

Well, what I'm doing is different than what they've been doing. Yes, theirs is a simulation based on assumptions but so is mine. I'm assuming, for instance, that each game is a 50/50 shot. But is Hamels against the Nationals really 50/50? What BP is doing over and above what I am is factoring in things like future opponents, RS/RA ratios, etc., and doing so when the total future outcomes are still so massive that I couldn't possibly attempt them.

AG/DC Sep 26 2008 09:05 AM

They're likelihoods. You continually insist that likelihoods are meaningless if they don't guarantee outcomes. They're not supposed to. If you want to assume and bank on at this point on the Mets bullpen giving up no runs, that's fine. They're not meaninless.

HahnSolo Sep 26 2008 09:18 AM

Paging Dr. Ian Malcolm.

Frayed Knot Sep 27 2008 04:57 AM

So after a triple-crappiness night, we're reduced to this: 27 possibilities left * 17 of them result in us OUT of the playoffs with a 67.2% chance of that happening * 1 which results in a double play-in game where we play the Phils for the East and the loser meets the Brewers for the WC (3.1%) * 5 where we enter a play-in game for the WC (21.9%) * 1 where we enter a loser-goes-home play-in game for the East Division (1.6%) * 2 where we win the Wild Card outright (4.7%) -- {Mets win 2, Brews lose 2, Phils win 1 - OR Mets win 2, Brews lose 2, Phils win 2} * and 1 where we win the division outright (1.6%) -- {Mets win 2, Brews lose 2, Phils lose 2} So that's: OUT = 67.2% IN = 6.3% Single Play-in = 23.5% Double Play-in = 3.1% IOW, nearly 1 chance in 3 that we're playing beyond Sunday

Frayed Knot Sep 27 2008 02:37 PM

The different starting times for today's games gives us a rare chance at doing a mid-day update for the playoff possibilities chart. With only FIVE total games remaining - 2 today plus 3 tomorrow - we're down to [u:66e34af5d4]18 possible outcomes[/u:66e34af5d4]. Of those: * 8 result in us out of any playoff scenario (46.88%) * 1 throws us into a Play-in game for the division (3.13%) * 1 throws us into a Double Play-in system where we play Phils then the loser plays the Brews (6.25%) * 5 of which mean we host a Play-in game with Milwaukee for the WC (31.25%) * 2 where we win the Wild Card free and clear (9.38%) * and 1 where we win the East free and clear (3.13%) So that's: OUT = 46.88% - Down from 67% this morning IN = 12.51% - Up from 6.3% Single Play-In = 34.38% - Up from 23% Double Play-In = 6.25% - Up from 3.1% IOW: * as of now, we are [u:66e34af5d4]slightly more likely than not[/u:66e34af5d4] to be playing past Sunday * there's approx 1 chance in 8 that we'll have clinched a spot w/o a Play-in by the end of Sunday Plus, throw in the early Cub lead and all the above odds improve ever so slightly.

Nymr83 Sep 27 2008 03:03 PM

As usual, OutOfTuneWith-Realitychuck doesnt understand that probabilities aren't certainties. Pocket Aces doesn't beat 7-2 offsuit every time, but that doesn't mean you can't assign a % chance to your winning that matchup pre-flop.

Frayed Knot Sep 27 2008 05:22 PM

Well this project is now dead as there's nothing complicated to the season anymore. With the Philly game now irrelevent there are 4 choices left: * Mets win, Brews lose = Mets as Wild Card * Mets lose, Brews win = Brews as Wild Card * Mets win, Brews win = Play-In Game * Mets lose, Brews lose = Play-In Game Sticking with the 'All outcomes equally likely' theory there's a 25% chance of either team winning outright and a 50/50 shot at a Play-In game. If you want to temper those odds by thinking that Sabathia going tilts things towards the Beermakers then go ahead, but we've got a nearly 3-1 shot at playing past Sunday. Bottom line, if we win tomorrow it's not our last game. That's a helluva lot better situation than when we all woke up this morning.

Benjamin Grimm Sep 27 2008 05:31 PM

Frayed Knot wrote: Bottom line, if we win tomorrow it's not our last game. That's a helluva lot better situation than when we all woke up this morning. Exactly. While we'll still be hoping for the Cubs to beat the Brewers tomorrow, the Mets can control their fate by winning the next two games, if it comes to that.

TransMonk Sep 27 2008 05:37 PM

Frayed Knot wrote: That's a helluva lot better situation than when we all woke up this morning. It's the exact same situation we woke up to a year ago on the last day of the season. I'm banking on the hope that Perez is on tomorrow.

Benjamin Grimm Sep 27 2008 05:37 PM

Frayed Knot wrote: If you want to temper those odds by thinking that Sabathia going tilts things towards the Beermakers then go ahead, but we've got a nearly 3-1 shot at playing past Sunday. Sabathia's taken a few turns through the rotation on three days rest, hasn't he? Here's hoping there's a cumulative effect. (I just looked it up. This will be his third consecutive start on three days. He's lost two of his last three starts, including September 16 against the Cubs in Chicago, his last start on four or more days of rest. Sean Marshall is listed as the starter for the Cubs, but he pitched yesterday in relief. (3 batters, 11 pitches.)

TransMonk Sep 27 2008 05:39 PM

Cubs.com has Zambrano pitching, but just to get some work in. Not sure that he'll actually go, though.

Benjamin Grimm Sep 27 2008 05:43 PM

If he does I wouldn't imagine it would be more than two or three innings. They'll be starting him on Wednesday, I'm sure.

AG/DC Sep 27 2008 10:08 PM

Worth remembering that we went through this for a few years under Bobby Valentine also.