## The Odds Behind Seattle’s Losing Streak

Mercifully, the Mariners’ historically bad 17-game losing streak is over. Sure, Seattle didn’t play well for the last three weeks, but it found itself on the wrong side of probability on an incredible level.

If Seattle had a 50/50 chance to win every game, the chances that they would lose 17 games in a row can be calculated by using a probability chain. Taking 50-percent to the 17th power results in 0.0008-percent, or 1-in-131,072 odds.

However, the Mariners are not expected to win 50-percent of their games. In fact, they were only favored in two of the games during the streak. This makes the losing streak more likely to happen than the calculated 0.0008-percent, but by how much?

For those not up on their gambling lingo, a money line of +150 means that you would win $150 if you bet $100. The money line from each game can be transformed into a expected winning percentage. The aforementioned +150 line would translate to an expected winning percentage of 40-percent. Logically, if a better bets $100 10 times and wins four out of 10, he would win $600, but he would lose 6 out of 10, $600 total. Therefore, he would break even.

Taking the money lines for Seattle’s losing streak, converting those to an expected win percentage, and calculating the probability chain looks like this:

The bookmaker expected the Mariners to lose 15 of the 17 games individually, but the chances that they would lose **all** 17 is about 0.01-percent. Comparing that with the number calculated earlier, Seattle was about twelve times more likely to have a 17-game losing streak during that stretch than a .500 team.

The odds were 1-in-10,560, or about the same that a person will get hit by lightning in their lifetime. The good news is that the streak is over. Seattle no longer has to worry about becoming the sixth member of the 20+ club or, worse, passing the 1961 Phillies for the longest losing streak in history (23 games).

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When I saw a new article up on the site, I totally thought it was a Beltran trade reaction. No disrespect intended to the author but this was kind of disappointing.

why would you even post this comment?

he just wants to be thumbs downed 17 times. Poetic.

I see two potential problems with this analysis.

1. The article assumes that betting line are the same as the true expected winning percentages. I will give in that it is probably pretty close.

2. More importantly, money lines account for the bookie fees. Did this article account for that fact?

Biggest problem I see is that their losing streak was 17 games not 16 as of this writing. The rest of it I am ok with because it was written to be a rough estimate of their chances. But if we are to nitpick the remainder…

“Seattle was about six times more likely to have a 16-game losing streak during that stretch than a .500 team.”

This statement is also wrong because a .500 team wouldn’t win 50% of their games against the Sox, Rangers, and Yanks. They would probably be expected to win about 50% versus the BlueJays and Angels. Only the one game against the Athletics would a .500 team most likely be favored. That means that over this streak the Mariners were not 6 times more likely than a .500 team assuming the same home/away and pitching matchups. My guess would be something closer to 4 times as likely.

Still, I definitely agree that this streak was quite a feat, particularly when they roll out King Felix every 5 games.

FanGraphs Supporting Member16 games was a typo. Just fixed it, thanks for the catch.

Using the Vegas lines was one way I was trying to control for the competition. That’s what’s interesting to me, the line-makers only expected the Mariners to go 2-15.

No, their expected win total was a hair over 7. 7-10 was the most likely outcome. If a team has a .49 probability to win every game in a 10 game stretch, you cannot say they were expected to go 0-10.

The odds makers expected them win 41% of their games, not 2 of 17. If you roll a die 100 times, I would expect for each roll that it is not a six, but that doesn’t mean that I expect you to roll 1- 5 every time. I expect 1/6 to be sixes. This is a relative of the lottery paradox. (In that paradox, there is a lottery in which exactly one winning ticket will be drawn and hundreds of tickets. I expect of every ticket that it will not win, which seems to imply that I should expect no ticket to win, but that doesn’t make sense because, by hypothesis, one of the tickets will be drawn.)

I think this is being pretty nitpicky. He actually wrote, “The bookmaker expected the Mariners to lose 15 of the 17 games INDIVIDUALLY….” Which is basically true. I don’t think he was suggesting that any bookie, himself, or us should expect a 2-15 record (grammar, yikes!). He was just trying to point out that the Mariners were underdogs in 15 of 17 games of the streak. Perhaps better word choice was necessary, but I don’t think he meant it the way you suggested he did.

“I will give in that it is probably pretty close.”

I wouldn’t.

Betting lines are a good approximation of the public’s perception of true winning percentages. Not an approximation of the actual true winning percentage.

Vegas isn’t trying to predict who is going to win. They’re trying to set the odds so they have similar money on both sides.

I think it’s a quick and dirty way of putting the losing streak into context. To my knowledge there’s no absolute means of determining a team’s exact chance of winning or losing a game. If you know of one please email me and we’ll go take Vegas for all their worth!

That 0.01% chance is the probability that the streak will start again tomorrow, or on any given day. Given that there are ~140 games where the streak could start in a season, it greatly increases the probability of such a streak occuring. There are also 30 teams in baseball, so you are bound to see stuff like this every now and then. Unlucky? Yes. Outside of the realm of statistical likelihood? Nope.

I don’t think he said it was “out of the realm of statistical likelihood” he was just putting the crazy-rarity of such a streak into context.

Assuming their win probability over 162 games is 45%, their expected longest losing streak is ~6, so they blew by that number. Congrats Mariners

Why are you assuming Vegas odds are intended to be fair? the man who bet $100 on each game would break even if they won 4 times. who in Vegas has the goal of getting people to break even?

If 40% breaks even, they obviously expected them to win fewer than 40% of the games, because that makes them money.

In Vegas, the implied probability of the favorite + implied probability of the underdog is > 1. Thus if win expectations are fair and Mariners win 4 of 10 at 40%, Vegas makes money

“The aforementioned +150 line would translate to an expected winning percentage of 40-percent. Logically, if a better bets $100 10 times and wins four out of 10, he would win $600, but he would lose 6 out of 10, $600 total. Therefore, he would break even.”

As others have mentioned or implied, this is just plain wrong. Bookies would go out of business if those probabilities are correct, because if the bettors are breaking even, then the bookies aren’t making any money — and they do have expenses. That an obviously bankrupt business model, one which no sane bookie would follow — and therefore the probabilities are wrong.

The bookies are estimating that the bettor described above will win less than 4 out of 10 times, and will lose money overall. So the correct implied probability is … unknown, but certainly less than 40%. Probably less than 35%.

(And then there’s the additional complicating factor that others have mentioned: if bettors are systematically over- or under-estimating the probabilities, then even those figures are off. E.g. if diehard Mariner fans keep betting on the Ms regardless of their true probability of winning, then the betting line will reflect those diehard sensibilities, and not the true probability.)

Actually, you can calculate the “fair” line if you know the moneyline for each team, there is a simple formula. That said, Vegas books are probably not the sharpest books- might look online to Pinnacle.com for that. But they are probably close enough for these purposes.

“The aforementioned +150 line would translate to an expected winning percentage of 40-percent. Logically, if a better bets $100 10 times and wins four out of 10, he would win $600, but he would lose 6 out of 10, $600 total. Therefore, he would break even.”

This is actually right. An implied probability essentially means “if this game were played N, number of times, I would have to win pN to break even.”

The break even point for 40% implied probability (+150) is to win 4 games over 10 games. However, this does not mean if the other side wins 6 times they break even as well. Depending on the overround, their line would be around -165, implying 62.26% , rather than 60%, which is a loss of 2.26% that goes right into the hands of the bookie.

The article is fine. He’s just trying to put things in perspective using the Mariner’s market price.

So if I started with $100 and bet against the Mariners for every game of this streak, rolling the winnings from each game onto the next, what would I have ended up with?

I love fangraphs, but this is a terrible article. The probability analysis is completely flawed – as another commenter noted above, it calculates the odds of having a 17 game losing streak that begins right now (the wrong way to think about it), as opposed to having such a streak at some unknown point in time (the correct way to think about it).

Consider this – what are the odds under this methodology of the worst team imaginable (say 25% chance of winning on any given day) having a 20 game losing streak? That would be 0.03%, or about 1 in 315. So basically we should expect no team in MLB history to have ever had a 20 game losing streak. And yet there have been at least 3 such streaks in the post-war period alone (1961 Phillies, 1988 Orioles, 1969 Expos).

This article should be completely retracted.

Sorry, decimal error: that should have been 0.3%, not 0.03%. 1 in 315 is still correct.

A decimal error! Threw off your results by a factor of ten. Totally unprofessional and uncalled for. I DEMAND that your comment be retracted immediately. I think apologies are also warranted.

(See how easy it is to throw stones and generally be a douche?)

Yes, ha ha. Very funny. I threw no stones, I insulted no one, I cast no aspersions. I stand by my position that an analytical article which makes such a fundamental flaw in analysis shouldn’t be published, just like a news article that made unsubstantiated claims of fact (“Ichiro is on steroids”, etc.) would not be published. I understand the counterargument (see my exchange below with TangoTiger), but my only goal was to improve the quality of the content on Fangraphs. I apologize if I have offended the author in doing so.

Constructive criticism has its place, certainly. No author here is or should be above that, and it is a wonderful tool that can help them improve. However…

“this is a terrible article”

“This article should be completely retracted.”

Constructive? Even mildly useful? Not in the least. Douchenozzle factor? Off-the-charts.

You’re right. If I could edit my comment, I would take those two phrases out. I didn’t mean to sound so awful, but somehow I did. My main point (which I stand behind) is that the premise of the article is fundamentally flawed, not that the author sucks or deserves to be flogged. I was hoping the other 90% of my comment would be the focus, but I see that it isn’t. That’s the power of the written word I suppose. Unfortunately, there is no edit feature (as far as I know) so the comment will live on in its unintended over-harshness for all eternity.

Once again, I apologize.

No worries! I can tell from your later comments that you had some substance there, and were just genuinely trying to help. Sometimes our fingers move faster than anything else, and that’s generally more true when we disagree passionately with someone or something. No harm, no foul.

Another possible flaw, although I’m willing to be corrected on this, is that the odds at the start or at the end are simply wrong. At the start, they have a 48% chance of winning. By the end, they’re mostly down in the 20s and 30s. Did they really have less a chance of winning the game just because they had lost so many in a row? Perhaps, but I don’t think that it’s likely. More likely is that Vegas was overestimating the odds of the Mariners winning earlier before more information came in about exactly how bad they were, or underestimating their chances of winning based on the long losing streak. So even though the team doesn’t change, perceptions about the team’s strength do, which is why I think this may be useful in a rough sort of way, but still not completely accurate.

Don’t forget the opponent plays a big role, hence the win percentage going down in this case.

Fangraphs: good at statistics, bad at probability.

A lot of poepole have already pointed out the flaws: 1) calculating a streak occurring at an exact point in time for a specific team instead of at any time during the season for any team, 2) using Vegas lines as probability of winning. Not only are the odds built around the bookie taking a cut, but they are also based on how much action they expect to get on each team, i.e. based on which team bettors expect to win, not what the true probability is. Obviously this will be influenced based on what teams are popular in the general population.

Why not use ESPN’s AccuScore projections? You can get them just by clicking on the preview for each game. Seems like they’d be much more accurate.

“Why not use ESPN’s AccuScore projections? You can get them just by clicking on the preview for each game. Seems like they’d be much more accurate.”

If this were true AccuScore wouldn’t be releasing their info free on the ESPN sidebar. I’d say they are 50/50 long-term

You don’t think ESPN is paying them for that??

Seattle was a .500 team at the start of the losing streak. So the probability should be the same as a .500 team, b/c that is exactly what Seattle was.

Not against the teams they were about to face they weren’t. As I said above, the teams they faced(Sox, Yanks, Rangers, etc.) made the streak more probable.

Odds?? This is baseball where you get beat 10-2 one day and your pitcher throws a no hitter the next. It’s more about a series of bad days strung togeather, a point where all your hitters go cold just as the pitching takes a dive. Even really great teams have a losing streak sometime during a year, not 17 games but a streak that defies the odds. If this Vegas style betting odds were predicatable, there would be alot more rich sports betters.

1. The Vegas money line is fairly solid. Certainly, for the purposes of this article, it’s an excellent thing to use. The point here is to be fairly illustrative. You can argue for Pinnacle or Bodog or whatever, but the end-result will be reasonably close.

Those arguing against this are being very nitpicky.

2. But, you have to account for the vig! I’m not a bettor, but if I see a line that is +105 on one side, I’m going to presume it’s ALSO +105 on the other side! That makes the odds 50/50 and not 49/51. So, the author of this piece should have put a bit more effort into getting truer odds than just presuming that if he sees +105 for one team, that it means -104.8 for the other team.

This is not being nitpicky in my opinion, so the readers who pointed this out are correct.

3. As for the argument about odds the streak existing at all at any point in the season (meaning that the streak was preceded with a win, and followed by a win or end of season, and that this streak could start at any point from game 1 through to game 145, and you have 30 such teams), that is definitely valid.

It doesn’t take away from this article. It just limits the answer to what the author actually did.

4. Readers upset at the article should demand a refund immediately. What I see is the author putting an inspired thought and a decent amount of effort to produce a somewhat interesting article.

Clearly this is the kind of article that would benefit from constructive criticism.

Readers should be demanding more articles from Jesse, not less. The cynicism exhibited by some is disheartening. You need to encourage guys like Jesse, not only for him, but to potential future writers. These guys need to be cultivated, otherwise we are left with, well, whoever ESPN and Fox Sports decides is worth paying.

I suppose Fangraphs can take it as a compliment that such an article is considered by some to be below acceptable, because of the high expectations the rest of the site produces.

To expand on point #3: what is the chance that the average team will win two games in a row? Well, you’d say it’s 50% x 50% = 25%.

But, what is the chance that we will see some team, at some point in the season, win two games in a row? The answer is going to be 0.999999999999… (I don’t know how many 9s, but I’m sure it’s even more than I’m showing).

Similarly, the readers are right when they talk about “this one team at this one point in time” versus “some team at some point”. It may seem nuanced, but it’s not.

I’m pretty sure the probability of a team having a two win streak is exactly 1.0 because schedules would have to work out just so. Imagine if 16 teams play on Monday and so 8 win and 8 lose. Then on Tuesday, 14 teams are playing, all of whom played on Monday and 8 of them won on Monday and 6 of the lost on Monday. Then on Tuesday, at least one team has to have a two game streak when the day is done.

#3 was the point I would have commented on as well

#4: even more important. thanks tango

Re: point 4, criticism is not the cynical action, silence is. I would love to see more (and better!) work from Jesse. He will not improve as a writer and an analyst unless he learns from his mistakes. He won’t learn from his mistakes unless he recognizes them. He won’t recognize his mistakes unless diligent readers flag them.

This is a site which is dedicated to furthering intellectual discourse on baseball. I consider the role of commenters to be not dissimilar from peer reviewers in scientific journals. If I could discreetly voice my (very serious) objections to this article I would. Alas, the only mechanism I have is a public comment. What you interpret as cynicism I interpret as my duty to the advancement of intelligent discussion of baseball.

There’s constructive criticism, and then there’s “This article should be completely retracted.”

You made a valid point in your argument (i.e, my #3). Instead of then recognizing that the author’s conclusion should be limited as I said it, you then come down heavy-handed as you did.

The column doesn’t need to be retracted so much as it needs to be enhanced. The core of the article is fine, and therefore does not need to be “completely retracted”.

Otherwise, I agree with your basic sentiment that this forum provides peer review.

I guess this is where we disagree, and I apologize if I seem too heavy-handed. I was just trying to be helpful and honest. I didn’t insult the author, I didn’t say things like “Fangraphs sux”, I just provided valid criticism in a civil tone and said the article should be retracted, which I believe to be true. There is no malice in my comment. I just happen to believe this is more than a minor blip in an otherwise interesting article – in my opinion the article is wrong in its very premise (title: “The Odds Behind Seattle’s Losing Streak”) and would be better off being taken down and rewritten after the author has reconsidered his approach to the probability analysis.

I have no doubt the author is capable of doing better analysis if he puts more time and thought into it. If I had done bad work, I would personally welcome the suggestion that it be taken down – I would then take it as an opportunity to correct an error and republish.

There are some articles around the web that should be retracted, because they offer nothing.

Most offer something, and so, you just need to have a rider attached to the article.

The most helpful thing the reader can do is offer constructive criticism, focused on specific points, things that the author can address, tackler and refine.

The overall decision to publish or not publish is an editorial discretion best left to the editors. Your summary opinion of “safe or out” is not needed. At best, the article is a gray area, so leave it as that.

I understand what you are saying. I may not fully agree, but I understand, and in any case I am not at all qualified to opine on editorial issues (and only slightly more qualified to opine on matters of probability :) so I will leave it there. Thank you for your thoughtful responses.

The vig argument is really the one that is obvious. ESPN has some bad stuff – I agree, but missing that Vegas lines don’t go down to some mythical -100 is something that any other sports site editor would have caught.

I guess that shows my thinking that FG has a higher standard, but if anyone posted that on TheBook, they would have been demolished. You must know this. These reply posts of yours TT seem to me to be a subtle condescension of FG.

Of course, articles superior to this were actually found on ESPN back in the “uneducated” years of 2003!

http://sports.espn.go.com/mlb/columns/story?columnist=neyer_rob&id=1506830

Of course, I will submit that these types of articles are the ones ESPN no longer felt are worth paying for.

if accuscore was a better predictor of the score than the Vegas line, their information would literally be a money printing machine and they wouldn’t release the info to the public. since this is obviously not the case, the Vegas line is a better predictor (ar at least as good) as Accuscore

the Vegas line really is just very close to the wisdom of crowds, which is very hard to beat

Nope! For the very reason that a number of people have pointed out: the bookie charges a fee to place the bets (in effect.) This means that AccuScore has to out perform Vegas odds by so much that you make up the cost of the bookie’s fees.

right, accuscore would need to be right (vs betting lines) about 53% of the time. which it can’t do

And because of this reason (fees), Vegas lines get a bit more complicated because their goal is not to establish a breakeven point given JUST w/l probability, it is to predict crowd behavior and entice people at the margin (who think the line is just wrong enough) to bet so Vegas can collect the fee.

To illustrate, if “Vegas” decides that the crowd uses Accuscore’s 58% chance the Yankees will win tonight, Vegas’s thinking would be:

if we set the money line to 59%, we lose X dollars in probability of loss and gain Y dollars in fees

if we set the money line to 60%, we lose X dollars in probability of loss and gain Y dollars in fees

if we set the money line to 70%, we lose X dollars in probability of loss and gain Y dollars in fees

and the new curve becomes: how far do we move the line before the number of bets I get does not make up for the lost dollars in loss probability.

Still, I agree with Tango’s point above- this digresses to the very netpicky. For the purposes of this article the Vegas line is a fine assumption to use.

I doubt if the wisdom of crowds, which exists and is important, applies much to sports betting. Most people will bet on their favorite team to an irrational extent.

For several years, I made a little money by betting against popular teams and for unpopular teams in NFL games.

I should make it clear: that was betting in Nevada casinos, so I had to overcome the bookies’ odds. I used a statistical system to pick the games, but it always amounted to betting on an unpopular team against a popular team.

then you should be a pro sports bettor.

and the same goes for anyone who says “people just bet on their favorite teams”.

but I’ll save you the trouble of moving to Vegas and trying this out: you’ll probably go broke, b/c the crowd is a lot smarter at setting the line than you are.

Ken, you have no idea how good at analyzing a game he is. So don’t assume the crowd is a lot smarter than him. He could BE one of the “crowd” for all you know. Idiot.

“The odds were 1-in-10,560, or about the same that a person will get hit by lightning in their lifetime.” Sure, but what Seattle has done with their franchise is the equivalent of someone strapping a 50 foot metal rod to their ass and standing at the highest point of the prairie with a severe thunderstorm overhead. Odds get a little better that lighting will strike.