mrjames
Professor
Posts: 6062
Loc: Montclair, NJ
Reg: 11-21-04
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02-15-20 01:44 PM - Post#300109
Now that we're halfway through the season (and after tomorrow will have just six games to play), the Ivy Tourney picture is becoming a lot clearer and easier to break down. I've done this a bit in other places on these boards but figured I'd bring it all together here.
First, some overarching targets:
Ran some sims and at this point here are the number of wins needed for fourth -
9 - 16%
8 - 60%
7 - 23%
6 - 1%
Similarly, here are the percent of sims where the *fifth* place team has this number of wins -
9 - <1%
8 - 23%
7 - 53%
6 - 22%
5 - 1%
And the top combinations of teams (in any order):
Brown, Harvard, Princeton, Yale - 42%
Brown, Harvard, Penn, Yale - 25%
Harvard, Penn, Princeton, Yale - 20%
Brown, Princeton, Penn, Yale - 10%
Columbia, Cornell, Dartmouth - Given that from this group, at best, Cornell could be a game back of fifth with a huge hill to climb to flip tiebreakers, it's still safe to count these three out. It's even safer when you consider that the team most likely to finish sixth out of this group is the one that was winless until yesterday.
Penn - Tonight is one of those "statistical" must wins, even if it isn't remotely a mathematical must win. Either way, Brown-Princeton will be bad for Penn. A Princeton loss, and it's more likely that the battle for 4th would be between Penn and Princeton, and with that tiebreaker already gone, Penn would be down a game and the break with six to play.
A Brown loss, and Princeton is more solidified in the top three, and it's more likely that Penn-Brown could be the battle for the fourth spot. Penn's looking at tiebreaker #2 there (performance against top opponents) and a win against Yale that Brown doesn't have would give Penn the inside track to just needing a win at Brown. Otherwise, they both have a shot to win the tiebreak at Harvard OR Brown could do it hosting Princeton/Penn visiting Yale. The most achievable of those is Brown hosting Princeton, so advantage Bears.
A loss tonight to Yale means that real, mathematical "must wins" could be very close behind.
Brown - The Bears bought themselves a TON of outs with the win at Penn last night. Beating Penn at home and any combination of two other wins would likely be enough. A win tonight, though, could all but wrap a spot up, as Brown would essentially have two shots hosting the Ps to all but clinch a tourney spot.
A loss tonight makes things more interesting. The Harvard, Penn and Princeton group will take on at least two losses next weekend, so Brown will be in the race when it hosts the Ps regardless. That being said with the final two games at Harvard and Dartmouth, Brown really needs to focus on locking up a spot over the next five games. 3-2 would get that done, but 3-1 with a loss tonight would be daunting and seriously brings into play the need for a win on the final weekend.
Princeton - Weird to say "must win" for a 5-2 team that should feel it has a better shot at the title than missing the tourney, BUT...
A loss tonight would send a 5-3 Princeton team on the road to Harvard, Dartmouth, Yale and Brown where it will be an underdog in every game. Yes, that's backed up with a C's weekend that it should sweep (previous game in Ithaca notwithstanding), but if eight is the target, the easiest "eighth" win opportunity is tonight.
The good news for Princeton is that it is in good shape on tiebreakers (for now). Can't take the one against Penn away (which is likely the most valuable). And a win at Harvard would likely wrap up a tourney bid as well. BUT... if Penn gets hot, and Princeton loses vs. Brown tonight, that would mean the Tigers would likely *need* a win at Brown or at Harvard to keep their hopes alive.
Princeton is in really good shape, no doubt, but things can get out of hand quickly with two-straight road back-to-backs, just ask...
Harvard - First order of business is not stubbing its toe against the C's. Assuming it can avoid that, Harvard is left with a bunch of outs to make the tourney. So long as Yale keeps destroying folks, Harvard can pick up the tiebreak over Brown, Penn or Princeton by winning any of its home matchups with each. To some extent, then, the tiebreaker is implied, because if Harvard loses to all three at home, then it can at best go 8-6 and that would require beating Yale at home and sweeping the C's on the road, which is unlikely as a combination.
Most likely, Harvard is going to win a couple games it has to and lose a couple it shouldn't and end up 8-6 with enough of a tiebreak to get in.
Yale - The only way things get remotely interesting is if it loses tonight at Penn. Even then, that's really more to put the 1-seed in doubt than anything. The Bulldogs are likely 10+ favorites in their next four games, so even 9-3 heading into the final weekend would be a bit of a shock.
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mrjames
Professor
Posts: 6062
Loc: Montclair, NJ
Reg: 11-21-04
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Re: Breaking It All Down
02-16-20 11:40 AM - Post#300353
In response to mrjames
Here's how those overarching targets have changed this morning:
Ran some sims and at this point here are the number of wins needed for fourth -
9 - 24%
8 - 65%
7 - 12%
6 - <1%
Similarly, here are the percent of sims where the *fifth* place team has this number of wins -
9 - 3%
8 - 33%
7 - 48%
6 - 15%
5 - 1%
And the top combinations of teams (in any order):
Brown, Harvard, Princeton, Yale - 35%
Brown, Harvard, Penn, Yale - 34%
Harvard, Penn, Princeton, Yale - 19%
Brown, Princeton, Penn, Yale - 11%
Brown, Harvard, Princeton, Penn - 2%
Last night was pretty damaging to Brown for a few reasons. First, its own loss. Second, Penn's win. Third (and related), now the bar for fourth is potentially higher. More often than not, the fifth-place team doesn't get to 8 wins, but if it does, there's no guarantee that's going to be enough. Unless you've banked particular tiebreakers (Yale over Brown, Princeton over Penn), your target needs to be nine wins.
Brown has the toughest road to get there with zero games in which it is projected to be more than a one-point favorite. It does, though, have the chance to nab tiebreakers against Penn and Harvard with a win.
Penn and Princeton are in the much better boat of hosting the C's to close. They both have a chance to secure the tiebreaker from Harvard this weekend. But Princeton will likely end up with the tiebreakers over both Penn and Brown, which combined with the game in hand, makes it far more secure.
Harvard has the most high variance weekend ahead. Sweep the Ps, and it likely picks up two important tiebreakers and can focus on the title chase. A split would be enough to feel good about where it stands but would add some pressure to split the C's weekend and beat Brown. Getting swept would essentially make its next three games all must wins.
Yale is pretty safe and would have to get swept this weekend to feel any real danger.
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SomeGuy
Professor
Posts: 6404
Reg: 11-22-04
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Re: Breaking It All Down
02-16-20 12:03 PM - Post#300356
In response to mrjames
Don’t your numbers indicate that Brown has a much higher chance than either Penn or Princeton? Looks like Brown has an 81% chance, while the Ps are both around 35%. Or am I reading wrong?
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HARVARDDADGRAD
Postdoc
Posts: 2691
Loc: New Jersey
Reg: 01-21-14
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02-16-20 12:22 PM - Post#300358
In response to SomeGuy
If you aggregate, odds to make the tournament seem to be:
Yale - 98%
Harvard - 89%
Brown - 81%
Princeton- 66%
Penn - 65%
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mrjames
Professor
Posts: 6062
Loc: Montclair, NJ
Reg: 11-21-04
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02-16-20 01:08 PM - Post#300365
In response to HARVARDDADGRAD
I copied and pasted from yesterday, so let me check and make sure. I might not have flipped the order of the team pairings. From what I remember at the top level, Brown and Princeton’s odds should be flipped exactly, so I bet I didn’t change the order of the pairings.
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mrjames
Professor
Posts: 6062
Loc: Montclair, NJ
Reg: 11-21-04
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02-16-20 03:23 PM - Post#300373
In response to mrjames
Yep - flip number two and three, and those are the right numbers.
FWIW, Luke Benz does this work as well (used to do it for Yale Undergrad Sports Analytics Group, but now is still doing it post-college). His is always a half-step better than mine because his tiebreaker code is more robust than mine (he also uses different rankings as his baseline, but that should produce only very small differences).
His calcs like Harvard and Princeton more to make the Ivy Tourney. Penn is basically the same, and Brown eats almost all of the loss.
My guess as to why this is happening is that Harvard is slightly more likely to have the right tiebreakers than my model thinks. And Princeton likely has wrapped up both the tiebreaker with Brown (in scenarios relevant to there being a tie) and with Penn.
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Tiger69
Postdoc
Posts: 2814
Reg: 11-23-04
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02-16-20 04:10 PM - Post#300380
In response to mrjames
Thank you, MRJ. I was just pondering how the Tiger chances had worsened from 75 to 67% by BEATING Brown Saturday.🤔 Now, I’m 81% happy.ðŸ…
Have you cal’d each team’s chance of winning the real prize?
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HARVARDDADGRAD
Postdoc
Posts: 2691
Loc: New Jersey
Reg: 01-21-14
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02-16-20 04:14 PM - Post#300383
In response to Tiger69
Do you mean flip 3 (Brown) and 4 (Princeton)?
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mrjames
Professor
Posts: 6062
Loc: Montclair, NJ
Reg: 11-21-04
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02-16-20 04:56 PM - Post#300387
In response to HARVARDDADGRAD
Technically was referring to the second and third sets of four teams, but if you’re looking at the odds, then yes, it’s 3 and 4. Either way, flip Brown and Princeton.
FWIW, Luke Benz does the tiebreakers even better than my model can (because he builds up rather than approximating like I do), and he believes that Princeton’s over 10pp more likely and Brown is over 10pp less likely, presumably because a more detailed run through of the tiebreaks has Brown edged out more often than I have them.
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SomeGuy
Professor
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Reg: 11-22-04
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02-16-20 06:13 PM - Post#300396
In response to mrjames
When I look at Pomeroy, it looks like if each game went to the current favorite the rest of the way, the finish would be:
Yale 12-2
Harvard 10-4
Penn 9-5
Brown 8-6
Princeton 8-6
Some of that depends on Dartmouth not giving up. Right now, they would be the slimmest of favorites at home against Brown and Princeton, but not against Penn.
These are razor thin in regard to probabilities though, so the Dartmouth home games seem like they will all be 50/50, and how they come out could swing this whole thing.
Of course, this Penn team seems like a perfectly reasonable bet to lose at Dartmouth and then come right back and win at Harvard.
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penn nation
Professor
Posts: 21193
Reg: 12-02-04
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02-16-20 07:09 PM - Post#300397
In response to SomeGuy
When I look at Pomeroy, it looks like if each game went to the current favorite the rest of the way,
I've mentioned this before, but that has been a risky proposition this year.
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TigerFan
PhD Student
Posts: 1885
Reg: 11-21-04
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02-16-20 07:15 PM - Post#300398
In response to SomeGuy
MRJames is the statistician of record here and can explain this far better than me but just because Princeton may be the underdog in each of its 4 remaining away games does not mean it is expected to go 0-4. It has a certain probability of winning each of those games and in the aggregate I’d think would be expected to go 1-3 or maybe even 2-2. I’d say the Tigers have a reasonable chance of finishing 9-5 or better (although they could certainly end up 8-6 or even tumble further if the ball bounces the wrong way).
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iogyhufi
Masters Student
Posts: 680
Age: 27
Reg: 10-10-17
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Breaking It All Down
02-16-20 08:16 PM - Post#300400
In response to TigerFan
Right, you can get this by calculating the expected value. Essentially, this is found by multiplying the probability of an event happening by the payoff you get if it happens. So if Princeton had a 40% chance to win 4 games, its expected record would be 40% times 1 (the "payoff" of one win) times 4 (the number of games), which gets you 1.6 total wins. This tells you that Princeton should expect to win at least one game of those 4 and is more likely than not to win a second, despite the fact that they aren't expected to win any of the games individually. You can think of this like the fact that even though you're more likely to not roll a 1 on a regular die than to roll one, you would expect to roll a 1 eventually if you rolled the die enough times.
Edited by iogyhufi on 02-16-20 08:17 PM. Reason for edit: No reason given.
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mrjames
Professor
Posts: 6062
Loc: Montclair, NJ
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Re: Breaking It All Down
02-16-20 08:55 PM - Post#300402
In response to iogyhufi
All correct interpretations.
The way I like to do it is just to add up the win odds over the number of games you’re looking at. That gets you expected wins over that span. The math is a bit more complicated if you want the odds of specific records (eg going specifically 3-1 in a four game stretch), but just to get expected win totals, adding up the probabilities works! Adding up the projected wins and losses is usually overstated to the extremes.
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mrjames
Professor
Posts: 6062
Loc: Montclair, NJ
Reg: 11-21-04
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Re: Breaking It All Down
02-21-20 06:02 PM - Post#301011
In response to mrjames
Had a post I was working on here with all the different (relevant) permutations of outcomes and the associated Tourney Odds, but never got around to finishing it. So, I'll give some high-level takeaways here:
- Weirdly, the most important set of games for Tourney Odds this weekend is Brown at the C's. That's because if Brown gets swept this weekend, the results for Harvard, Penn and Princeton don't matter nearly as much. And if Brown sweeps, it puts any of those three teams that gets swept this weekend into a HUGE hole.
- It's arguable which game is more important for Harvard. Beating Princeton would likely bring the tiebreaker too, whereas beating Penn wouldn't necessarily bring the tiebreaker with it. That being said, beating Penn would help with any (very possible) three-way tiebreakers with Penn and Brown.
- Princeton basically secures its bid by beating Harvard tonight (not mathematically, but statistically).
- Penn can get really close to securing the bid (statistically) this weekend with a sweep, but likely will still need one of two things to happen: 1) win at Brown, 2) sweep the C's at home.
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PennFan10
Postdoc
Posts: 3584
Reg: 02-15-15
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02-21-20 07:49 PM - Post#301023
In response to mrjames
Love this time of the year. Thanks Mike!
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rbg
Postdoc
Posts: 3050
Reg: 10-20-14
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Breaking It All Down
02-21-20 10:34 PM - Post#301169
In response to PennFan10
After 2/21/20 games -
Men
Yale 7-2
Princeton 6-3 (2-1 vs Harvard and Brown)
Brown 6-3 (1-1 vs Harvard and Princeton)
Harvard 6-3 (1-2 vs Brown and Princeton;best win vs Yale)
Penn 5-4
Dartmouth 3-6
Cornell 2-7
Columbia 1-8
Women
Princeton 8-0
Penn 6-2
Yale 6-3
Columbia 5-4 (1-0 vs Harvard; best win vs Harvard)
Harvard 5-4 (0-1 vs Columbia; best win vs Penn)
Cornell 2-7
Dartmouth 2-7
Brown 1-8
Edited by rbg on 02-21-20 10:34 PM. Reason for edit: No reason given.
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iogyhufi
Masters Student
Posts: 680
Age: 27
Reg: 10-10-17
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Re: Breaking It All Down
02-22-20 12:55 AM - Post#301183
In response to rbg
If Harvard and Brown win tomorrow, things would look bleak for the Quakers, who'd be two games out of the playoffs with four to play.
If Penn wins tomorrow, I think all heck will break loose, since you'd have at least two and possibly three teams tied for the last spot with four games to go. Penn would have the inside track on Harvard in such a case, since they'd own the tiebreaker. Would make the last two weekends must-see TV. I'd be interested to see what the simulations would say in such a case.
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mrjames
Professor
Posts: 6062
Loc: Montclair, NJ
Reg: 11-21-04
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Re: Breaking It All Down
02-22-20 02:51 PM - Post#301235
In response to iogyhufi
Here's where we stand:
Wins needed for fourth -
10 - <1%
9 - 24%
8 - 65%
7 - 10%
Percent of sims where the *fifth* place team has this number of wins -
9 - <1%
8 - 33%
7 - 56%
6 - 10%
And the top combinations of teams (in any order):
Brown, Harvard, Princeton, Yale - 61%
Harvard, Penn, Princeton, Yale - 27%
Brown, Harvard, Penn, Yale - 7%
Brown, Princeton, Penn, Yale - 3%
Dartmouth, Harvard, Princeton, Yale - 1%
Brown, Dartmouth, Harvard, Yale - 1%
Tourney Odds:
Yale >99%
Harvard 97%
Princeton 92%
Brown 72%
Penn 37%
Bid Odds:
Yale 44%
Harvard 36%
Princeton 11%
Penn 5%
Brown 5%
Saturday Night Scenarios (all assume Yale wins)
Brown W, Penn W, Princeton W
Yale 99%
Princeton 96%
Harvard 87%
Brown 71%
Penn 48%
Brown L, Penn W, Princeton W
Yale >99%
Princeton 99%
Harvard 93%
Penn 59%
Brown 49%
Brown W, Penn W, Princeton L
Yale 99%
Harvard 92%
Princeton 77%
Brown 73%
Penn 56%
Dartmouth 2%
Brown L, Penn W, Princeton L
Yale 99%
Harvard 95%
Princeton 88%
Penn 63%
Brown 51%
Dartmouth 4%
Brown L, Penn L, Princeton L
Harvard 100% (it's not, but only ran 1000 sims)
Yale >99%
Princeton 94%
Brown 65%
Penn 34%
Dartmouth 7%
Brown W, Penn L, Princeton L
Harvard 99%
Yale 99%
Princeton 90%
Brown 82%
Penn 26%
Dartmouth 4%
Brown L, Penn L, Princeton W
Yale >99%
Harvard >99%
Princeton >99%
Brown 62%
Penn 39%
Brown W, Penn L, Princeton W
Yale >99%
Princeton >99%
Harvard >99%
Brown 76%
Penn 26%
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Bryan
Junior
Posts: 231
Loc: Philadelphia
Reg: 11-21-04
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Re: Breaking It All Down
02-22-20 07:34 PM - Post#301258
In response to mrjames
This is great stuff! Thanks very much for developing the model and sharing the results,
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