r/statistics • u/2ForEachofYou • 16d ago
Discussion [Discussion] Did anyone catch the stats error in the Thurs Night Football game, post game recap?
Tony Gonzales (love him), pointed out that teams that start out 0-3 have a 2.9% chance of making the playoffs (when talking about the Texans). He then asked what are the chances of doing it two years in a row, which he pointed out is 0.08%. That's correct (0.029)^2. He went on to say because of the even lower odds, i.e. 0.08%, he didn't think they'd make the playoffs this year. But last year's results are irrelevant now. Their chances of making the playoffs this year with an 0-3 record are still 2.9%. Am I wrong?
33
u/RobertWF_47 16d ago
That's right, Tony fell victim to the gambler's fallacy (assuming the two events are independent).
26
u/Great_Northern_Beans 16d ago
The difference is that the two events typically aren't independent.
The team roster generally doesn't change much year to year. If the reason that they're off to shit starts is endemic to the line up, i.e. due to major injuries at key positions, mismanagement of talent, or even just a generally poor roster; then you would continue to expect poor performance going forward.
And because of this, you would also expect lower odds of this team making the playoffs than your "average" 0-3 team that's just incidentally off to a slower season start.
2
u/RobertWF_47 15d ago
True, althought I'm not sure Tony was reasoning through all of these conditions.
8
u/MrKrinkle151 15d ago
They aren't independent, but that also means the overall probability isn't just P(Y1)*P(Y2)
7
4
u/DigThatData 15d ago
He then asked what are the chances of doing it two years in a row, which he pointed out is 0.08%. That's correct (0.029)2.
This assumes independence, in which case "Their chances of making the playoffs this year with an 0-3 record are still 2.9%" is still accurate.
But last year's results are irrelevant now.
sports performance is highly correlated YoY, so I'm not sure this part is accurate. The numeric analysis above assumes a forgetful distribution, but the team is largely comprised of the same players and the same is true of the other teams. I propose that the bad assumption here is the independence assumption, and rather than estimating the likelihood as (0.029)^2, you'd be better served at looking at the historical record to find cases where teams started 0-3 two years in a row. I bet their playoff likelihood is worse than the independence-assuming case estimates.
1
u/bzc91 15d ago
this comment has a lot of interesting ideas imo. I agree with the idea that yoy correlation should be quite high- I think you're right that we're really interested in the p(miss playoffs year T+1 | 0-3 starts in {T, T+1}), if we for some reason wanted to just address the data quoted by gonzales (which your methodology would cover).
However, to properly conduct this current discussion (i.e., how likely is it that the texans make the playoffs this year?) it'd make more sense to use all the info that we have from last year (texans going 12-5): they're probably "better" than an 0-3 team (I say this without knowing about any material offseasons moves by them). At the very least, the Gonzales comment is odd in ignoring a bunch of information, for no real reason that I can detect.
I do wonder if there's somehow more merit to considering the "two seasons of 0-3 starts" vs "last season 12-5, then an 0-3 start here" for the actual purpose of "what is currently the texans playoff probability." My (strongly felt) guess is no, though I realize it's being brought up to align with Gonzales's comments- which I think are basically riddled with errors (everyone else correctly pointing out gambler's fallacy, plus for some reason just throwing away a bunch of info, the rest of their 25-26 season).
Ultimately Gonzales's statements fail on the gambler's fallacy (he was, intentionally or not, embedding independence in his discussion, which is ALSO likely flawed, but, even presuming independence, he proceeds to a more fundamental error), but more importantly on the "throwing out a bunch of data" count, imo.
2
u/itsactuallynot 15d ago
If we're going that deep into the weeds, it should be pointed out that last year's team that started 0-3 was playing a first place schedule (Texans won the AFC South in 2024) while this year's team has a second place schedule (they finished second in the division for 2025). So that would increase the chances of them making the playoffs this year.
1
1
u/Gravbar 15d ago
He's not right, because P(E1)*P(E2) isn't the right thing to calculate, since E1 already happened.
He wants to calculate P(E2 | E1), which if they're independent, would just be P(E2), but in this case, since they're not independent, would be P(E2,E1) / P(E1), but we don't know P(E2,E1) so we can't calculate it without going through the data.
the number he gave for 2 years probability is just 2.9%2, which implies that it was calculated assuming seasons are independent, instead of looking at season N and season N-1 for all seasons > 1
1
u/WittgensteinsPoker-2 15d ago
The process that generates your measured outcomes here (a sports team winning a season or another season ) typically does not have winning one season as INDEPENDENT of winning the next.
Whatever justifies your assignments of probabilities is going to be your underlying process / causal model of HOW season-wins are generated.
Having a "winning team" relative to the others in one season and then NOTHING ELSE changing in other teams of YOUR TEAM prior to the next season will mean there might be a HIGHER probability of you winning the next season.
It's hard to say without creating a VERY COMPLICATED empirical model.
I don't think we should treat probability claims in scenarios like this as rolling independent dice or something. Very different outcome generating process!
1
u/Successful-Bug920 16d ago
this season alone
it's like flipping heads on a coin, the odds of two in a row are 25% but if you just flipped heads the next one's still 50/50. stats guy should know better
4
u/johndburger 15d ago
It’s not like flipping a coin at all. The two seasons aren’t independent - most of the players are the same, the coach is probably the same, etc. (TV guy is still wrong though.)
-3
u/Berstuck 16d ago
Correct. Their odds from before last season would not have any impact on their odds now.
If you’re rolling a six sided die, your odds to roll a six two times in a row is 1/36. That’s (1/6)^2. If you’re starting out after that first roll of a 6 though, your odds of getting a six again is still 1/6.
8
7
u/shwilliams4 16d ago
I didn’t watch this but for football, stocks, etc. what happened last season absolutely plays into this season. The events are not independent.
1
u/2ForEachofYou 16d ago edited 16d ago
Be that as it may, Tony’s reasoning/calculations were still incorrect.
1
u/2ForEachofYou 15d ago edited 15d ago
Lol why did this get downvoted? I never disagreed that the events are not independent, after initially treating them as independent events. I was pointing out that Tony's math assumed they were two independent events, by squaring the probability of an 0-3 team making the playoffs two seasons in a row. That's wrong even if they were independent events, let alone the fact that they are not. That's Tony, not me. Don't shoot the messenger, folks.
-4
u/efrique 15d ago
stats error in the Thurs Night Football game
Ah, it appears we have found this week's candidate for /r/USdefaultism/
22
u/TheJavoClown 16d ago
I agree with the other answers, but I think it's also worth noting that two consecutive seasons are most likely not two independent events...