losing streak formula

[boxcar]

Would appreciate it very much if one of the math cops on this board would again tell us what the formula is for determining what the probable number of consecutive losers would be based on any given win ratio. In my particular case, I'd be interested in knowing what the number would be for a hit rate of around 20%.

Thanks,
Boxcar

[GR1@HTR]

Don't have the formula but this is from an old B Meadow newsletter.



code:Highest number of consecutive wins/losses out of a series of one million bets:

Hit Rate Wins Losses
5% 5 220
10% 5 110
15% 6 74
20% 9 71
25% 10 44
30% 13 37
35% 13 30
40% 13 30
45% 18 27
50% 18 21

[FortuneHunter]

Very interesting. Thanks GR1.

I thing that strikes me is the big gap between 20% and 25% in the "losing streak". 71 to 44. Seems odd to me. I would have expected more of a linear progression.

Do you know which newsletter and how I might get a copy? I would like to know about the math.

IMO, the losing streak is a key factor, if not THE key factor, in investing in the mutuel pools.

I would rather bet 2 horses per race at 48% hit rate with an ROI of $1.15 (where $1.00 is breakeven) than betting 1 horse per race at 20% hit rate with an ROI of $1.18.

That's because of the losing streak (see previous post) is directly related to the bankroll needed. Off the top of my head, I would feel comfortable with a bankroll of 5 times the expected longest losing streak investment. Does somebody have a benchmark for bankroll vs. losing streak?

Balance between Hit%, ROI, and Losing Streak is the key to acceptable risk in the mutuel pools.

I plan to do a database analysis of the upcoming "Big A" Inner Track racing (starts 1st week in Dec) focusing on losing streak. We have 1245 races ('99/'00 & '00/'01) in the bank. I will post the analysis report here.

A contrarian view: Handicapping is not the key to making money at the track. The key is finding a consistent handicapping method (which IMO, can only to be done by computer, humans are not consistent). Keep it simple AND consistent, same method everyday. Find out the Losing Streak, HIT %, ROI of this Handicapping method and build a Money System with acceptable profit, say 20%??

Handicap for sport and entertainment. Take the Breeders Cup as an example. It was a lot of fun spending 8 hours handicapping 8 races. But I only have time to do that a few times a year.

Build a money system based on consistent handicapping method based on Losing Streak, HIT%, and ROI analysis, for serious investment in the horse racing mutuel pools. Handicap the racecard in 10 minutes after the late scratches, make your bets and get on with your daily life, and check your balance every night before bed.

And don't forget to go to the track a few times a year enjoy the "sport".

FortuneHunter
www.handicappers-datamine.com

[boxcar]

GR1 posted:

>>
Don't have the formula but this is from an old B Meadow newsletter.
Highest number of consecutive wins/losses out of a series of one million bets:
>>

Hit Rate Wins Losses
5% 5 220
10% 5 110
15% 6 74
20% 9 71
25% 10 44
30% 13 37
35% 13 30
40% 13 30
45% 18 27
50% 18 21

Thanks, GR1, for posting this. I 'd bank that in the real world, however, my system, that I'm nearly ready to put into use soon, won't encounter anywhere near 71 consecutive losses. For example, when was the last time anyone witnessed the smart and saavy public encounter 35 losses or so with their top betting choices? Could this happen? Sure, I suppose it could, but in my 30+ years of playing, I have never witnessed this occurring.

I've been charting my system for many moons now for over a course of thousands of races and haven't come anywhere close to 44 straight losses, let alone 71.

A good online buddy of mine (who has since passed away) worked his system for many years. His win ratio was very small -- in the 5 to 10% range, yet the longest losing streak he ever encountered (which he used to enjoy bragging about) was 81 straight losses. And he encountered that only once in his lifetime. If he had lived longer, could he have hit on a longer streak? Yeah, I suppose. Just about anything is possible -- but probably not probable. :)

Thanks again,
Boxcar

[BillW]

Boxcar,

Hopefully your system is better ... remember this is the "worst case" scenario.
I have no way of knowing if these numbers are accurate, but the statement is made that a streak like this will show up once in a string of 1,000,000 bets.

Placing 5 wagers a day, 5 days a week a streak like this would occur once every 769 years.


Here's to a long life!,

Bill

[Dave Schwartz]

BillW,

LOL - I gues I must be older than you guys. Some of these losing streaks look vaguely familiar.

Dave Schwartz

[FortuneHunter]

Originally posted by BillW
Boxcar,

Hopefully your system is better ... remember this is the "worst case" scenario.
I have no way of knowing if these numbers are accurate, but the statement is made that a streak like this will show up once in a string of 1,000,000 bets.

Placing 5 wagers a day, 5 days a week a streak like this would occur once every 769 years.


Here's to a long life!,

Bill


Just have to hope the one time it happens isn't at the start of the Big A Winter 2002 meet. lol

[BMeadow]

The losing streak figures that were posted on this thread came from research from Stefan Perry, printed in our June 1997 issue. They were based on random numbers for a one-million number sequence.

Nobody says you have to hit the negative (or positive streaks) that occurred in this one-million number run, but it COULD happen.

A more detailed list of possible streaks, based on math rather than an actual computer-generated run, is listed in Jim Bayle's booklet, Gambling Percentages and Probabilities. He calculated that for a 20% hit rate, there is a 0.74% chance of losing 22 or more in a row, for instance. Note that these are overlapping series, so that bet #3 out of 10,000 is part of series 1-20, 2-21, and 3-22, for instance.

[GR1@HTR]

FH,

Not sure what issue that is from. I just copied and pasted that info from an old HTR post I made a while back. Contact Mr Meadow at
www.trpublishing.com
and he will tell you. BTW FH, with all that dB stuff you do, you would really like BM Monthly since every month the King of dB analysis Jim Cramer runs all kinds of data that will make your head spin. Good stuff for us data freaks.

[tanda]

Maybe I am being too simplistic, but all you need to do is raise your loss rate (1-win%) to the power n. n is the number of bets in the losing streak.

So a 40% hit rate has a .60^20 chance of losing 20 or more consecutive bets. That figure is 36/10000 of 1%.

A 15% win rate has a .85^10 chance of losing 10 bets in a row. That chance is slightly less than 20%.

[Tuffmug]

The length of a losing streak for you is directly proportional to your pigheadedness in refusing to see that something has CHANGED!

[boxcar]

BillW posted:

>>
Hopefully your system is better ... remember this is the "worst case" scenario.
I have no way of knowing if these numbers are accurate, but the statement is made that a streak like this will show up once in a string of 1,000,000 bets.

Placing 5 wagers a day, 5 days a week a streak like this would occur once every 769 years.


Here's to a long life!,
>>


LOL! Well, this is certainly good news. But the bad news is that I'll now have to lay off the Eternal Life Juice formula I've concocted and have been taking religiously for years to prolong life. Ah...but what else is new? Everything else in this game has it upsides, downsides, tradeoffs, etc., so why should this be any different?

Boxcar

[ranchwest]

The fallacy here is that this assumes that every play has the same chance of winning. If we're assuming 20%, that means that we'd have to play a 4-1 horse in every race. Am I really to expect that in 71 races I'll be unable to find a 4-5 horse that can win, even when playing some 40-1 shots?

To really find out your tapout potential, you'd have to analyze your history at various odds levels and then randomly generate races with the same frequencies but in random orders.

[FortuneHunter]

Below is actual losing streak data taken on various selection algorithms

Sample Size: 1245 Races (AQU Winter Track '99, '00)

Race Played____HIT%__Avg.Losing__Max.Losing__Std.Dev.

1245 Races____46.9%______1.1________11_______1.44
_667 Races____45.4%______1.2________11_______1.63
_578 Races____48.6%______1.0_________7_______1.37
_233 Races____50.2%______1.0_________6_______1.33
_369 Races____42.3%______1.3_________7_______1.66

1245 Races____27.7%______2.6________13_______2.81
1245 Races____19.2%______4.2________22_______4.37
1245 Races____13.1%______6.7________45_______7.23
1245 Races____10.9%______8.3________39_______7.77

The Standard Deviation (Std Dev) is best explained by example:

Take row 6 where the HIT% =27.7%;
90% of the losing streaks will be between 0 and 6 races ( avg + - Std. Dev. Is 90% of occurances) 2.6-2.81 = approx 0; 2.6 + 2.81 = approx 6.

The Standard Deviation of the losing streak is a measure of the range of the losing streaks to expect for the majority (90%) of the time.

My conclusion is:

If you have a HIT% = 45% you are going to have losing streaks of 0 to 3 races and you better plan for one 12 race losing streak in your run

If you have a HIT% = 27.7% you are going to have losing streaks of 0 to 6 races and you better plan for one 18 race losing streak in your run .

[Lefty]

One thing I know about losing streaks:I can't seem to avoid them.

[Tuffmug]

All these losing streak calculations are flawed! They are a disguised version of the crap player's " I'm Due" fallacy.

Each throw of the dice is an event independent of all other throws. Each horse race is an event independant of all other races.

You are no more "DUE" for a winning streak or losing streak than a crap player is due to hit a seven on the next pass.

Statistics are a measure of past events. Betting on a horse race is NOT determined or controlled by the past. It is a unique event!

Statistics measure your PAST success or failure. They are a poor tool for predicting your future success!

[ranchwest]

>All these losing streak calculations are flawed! <

Well, I'm assuming that the conversation has to do with how large one's bankroll should be and the portion of the bankroll that can be safely played at one time. In that regard, there is probably some merit in holding the discussion. Even for that purpose, I see it as more complex than what is being presumed. After all, given the presumptions at hand, every time I play a 4-5 horse, I should have a 50% chance at ending the losing streak.

I think a whole lot of handicapping math is flawed. What good does it do to play an overlay that loses? What have I lost when I cash a ticket on an underlay? Who is to say what an overlay or an underlay is?

The question is how much money do I have at the end of the day. To come out with a positive ROI and not have long losing streaks, I just about have to hit on a variety of payoffs. Further, I can't hit the longshots because nobody else found that longshot that day, but simply because I found it and I must find it consistently and play it, regardless of what someone else is playing. Some days, you'll see a set of circumstances that will lead to a horse being 20-1 and the next day almost identical circumstances will lead to the horse being 5-1. Is one a better bet? I say no, if you like it, take the 20-1 today and take the 5-1 tomorrow and see what your bottom line is.

OK, so I'm a contrarian.

[BillW]

Tuffmug,

I'm familiar with statistics relative to independent events, but is horse wagering really an independent event, or would it be biased by knowledge gained from past wagers? (this is a real question directed at those more capable in statistics than I am, not a comment disguised as a question :-))

In any case, the greatest benefit to analyses such as these serve to prepare ones self to the realities of protecting ones bankroll, as stated above.

Bill W.

[Lefty]

I believe losing strk stats based on win pctg. are valid.
If stats don't matter then how come they can predict how many are going to be killed on the hwys any holiday weekend and get right in the ballpark a scary amt, of times? Losing strks happen.
When you cash a ticket on an underlay you've won the battle but are losing the war.

[superfecta]

Originally posted by ranchwest
The fallacy here is that this assumes that every play has the same chance of winning. If we're assuming 20%, that means that we'd have to play a 4-1 horse in every race. Am I really to expect that in 71 races I'll be unable to find a 4-5 horse that can win, even when playing some 40-1 shots?

To really find out your tapout potential, you'd have to analyze your history at various odds levels and then randomly generate races with the same frequencies but in random orders.

Thats the problem I have with data studies ranchwest,it seems sometimes people overanalize the numbers and can't grasp the fact that this treats every race in the study the same,and we know each race is different.

[ranchwest]

>When you cash a ticket on an underlay you've won the battle but are losing the war.<

I'm not in a war. I'm trying to win money. Since all tickets except maybe dead heats pay off more than they were purchased for, all winners put me ahead. I realize that I can't just hit 3-5 horses and come out ahead, but if I can have a day where I win on a good 6-5 horse and a good 15-1 horse and a good 5-1 horse in a 10 race card, then I figure I've done exceptionally well, regardless of whether somebody claims my horses were overlays or underlays. When I get a stack of Abe Lincoln's, they don't come to me with "underlay" stamped on them.

[Tuffmug]

ranchwest,

Good point! A winning ticket on an underlay is STILL a winning ticket. A losing ticket on an overlay is STILL a losing ticket.

BillW,

All of the above analases start from a flawed assumption that their hit rate in the future will be approximately the same as their hit rate in the PAST! They also are basing their projections on a rigid system of selection and betting as defined by their previous success and assuming those selection criteria and wagering strategies will be appropriate for future races.

Each horse race is an independant event. I believe each wager must also be tailored to that unique event and that the bettor has to continually refine his strategy and learn from past mistakes.
The world is nonlinear, chaotic, and ever changing. That is my FIRST assumption. Betting in this world requires a continually open mind and continual adjustment and refinement.
Too many handicappers believe (or should I say HOPE)the world is linear and ultimately perfectly predictable and can be made to fit their projections. They need to absorb the lesson learned by Long Term Capital a few years back.

[boxcar]

Tuffmug wrote in part:

>>
Each horse race is an independant event. I believe each wager must also be tailored to that unique event and that the bettor has to continually refine his strategy and learn from past mistakes.
The world is nonlinear, chaotic, and ever changing. That is my FIRST assumption.
>>

I think actuaries would take some issue with your first assumption, as would nature itself.

Boxcar

[karlskorner]

To steal a page from Ray Taulbot, think over the following:

"First let's examine the contrast between the thinking of the average racing fan and the professional turf speculator. The average fan is a day-dreamer who envisions quick riches acquired with small operating capital, very little effort, and a mode of play which permits him to indulge his peculiar whims. In short, he dreams of taking a $20 bill and piling up profits without emplying any degree of self-control.

His attitude toward turf speculation can best be summed up as "fun and games". He often resents any suggestion which derprives him of making the 101 blunders common to many turf enthusiasts.

The pro views his turf operation as a business, one upon which his livelihood depends. Therefore he never takes excessive risks. To us a poker expression "He plays 'em close to his vest"

Wheras the average fan has a fondness for long prices. which often leads him into taking excessive risks, price is of secondary consideration to the pro. Like all of us he prefers a good price, but he never permits price to become the decideing factor.

He knows that price is of no value if after the race he has to tear up his tickets. As John Barwell once remarked "Any price is better than a loser," a difficult agrument to refute. Thus, the pro places safety ahead of maybe".

Makes sense to me.

Karl

[ranchwest]

karlskorner, that's a great post.

The bottom line is that in every race, the best horse is the winner. We just often have a difficult time determining the best horse.

[Tuffmug]

Boxcar,
Actuaries often lose for precisely this reason! Ask any of them who set rates for hurricane insurance a few years back By the way, you will find them on the unemployment lines. Insurers took a wicked bath on that one.

Nature is chaotic and nonlinear. Read a few books on chaos theory. There is also a seminal paper on chaos and nonlinearity by Lorenz you might like to read. He was a meteorologist and started with the assumption that weather could be perfectly predicted if more and more data were compiled and the data were more and more accurate. Problem was that world didn't conform to his linear logic. His computer projections would unpredictably fail as time progressed. He realized that even the tiniest fluctuations in the atmosphere would eventually result in a chotic flux of the weather which could not be predicted. Made the analogy that "The beating of a butterfly's wings in Peking would affect the weather in New York 5 days later". (Hope I got that quote right)

[Tuffmug]

I misstated my position on overlay and underlay tickets a few posts back. I have never bet an underlay! I define an underlay as a TOTE price Less than MY ESTIMATION of the horse's odds.

Too many people use the morning line as their basis for comparison to determine what is an overlay or underlay. This is a fatal mistake!

[BillW]

It makes my teeth hurt when I hear talking heads on race b'casts reference tote/ML < 1 == underlay. Of course I guess I should be thankful that they are spreading such ignorance. My other pet peeve, along the same lines is the mis-use of the term value (see second sentence above).

Bill W.

[boxcar]

Tuffmug wrote in part:

>>
Actuaries often lose for precisely this reason! Ask any of them who set rates for hurricane insurance a few years back By the way, you will find them on the unemployment lines. Insurers took a wicked bath on that one.
>>

With all due respect, that is utter nonsesne. Insurance companies frequently cry poverty over losses after a big catastrophe. The truth of the matter is that Insurance Companies (as whole) are among the wealthiest industries in the world. And they would never be able to enjoy such wealth if the world were anywhere near as chaotic as you make it out to be. Those actuaries win far more often than they lose!

>>
Nature is chaotic and nonlinear. Read a few books on chaos theory.
>>

Forget books on chaos theory. Read what the bible says about nature and then take some time out to observe it around you. Daily we witness the overall order in the universe. The planets hold their orbits around the sun, the sun rises in the east, and always sets in the west, night always follows day, rainy seasons usually follow dry seasons and vice versa, birds always migrate in their season, most animals observe a mating season, we could set our clocks by the tides, etc., etc., etc. This is not say that "chaos" is never interjected into the ordered world in which we live. But it is a huge mistake to think that the world is, generally, chaotic when "isolated" events we perceive as chaotic occur.

We humans tend to emulate the same order imposed upon the universe by its Creator. We order and structure our own little world by establishing schedules, routines and priorities. A society would not be able to exist and function apart from these elementary protocols being securely in place.

We have seen that such a seemingly chaotic event as a horse race even has structure and order about it. Year in, year out the public's first betting choice will, uncannily, win around 1/3 of the time. And as Barry Meadow pointed out, EVEN money shots will more often than 6/5 shots, and 2-1 shots more often than 3-1 shots, etc., etc. These facts clearly suggesting that there is a good deal of predictability and order about the game -- something we would not expect to find if the game were truly "chaotic".

Finally, permit one more racing illustration. Many years ago, I profiled longshot winners, and walked away from my extensive study with several good "longshot angles". To this day, all of those angles continue to produce longshot winners -- and at about the same hit rates as they did when I conducted that study. Very consistent producers -- very reliable longshot predictors. This tells me many things -- among them that racing mirrors life itself. History tends to repeat itself over and over and over again. Stated differently, the public is prone to making the same mistakes over and over. -- year in, year out.

Bottom line: Statistical studies are very useful for making pretty accurate generalized statements. But stats have limited predictive power in telling us when something will actually occur. This because every single event is indeed independant of all the others that have preceded it. Therefore, each race should be evaluated on its own peculiar merits in order to derive maximum benefit from any method of play, angle or whatever. I would no more blindly play any of my longshot methods than play every favorite in every race, if I were a chalk-oriented player.

Boxcar

[Lefty]

ranchwest, if you consistently bet on underlays you cannot have a +ROI. You can cash a ticket, everybody cashes tickets: but most lose money. I can cash about 48%of time playing pass or don't pass at craps but I can't make any money cause every bet is an underlay.

[ranchwest]

Lefty, some of my selections you would likely consider overlays, some underlays. I'm not saying I bet short odds horses. What I'm saying is that I have difficulty with the whole concept of overlays and underlays.

First, we spend a major portion of this thread discussing the macro analysis of the odds board being a strong indicator of the statistical probability of a horse winning. Then, some say we should micro analyze and come up with our own line and compare our line to the live odds. Well, we already know that in a macro sense the odds on the board are right.

What I'm saying is that rather than looking for a micro analysis of beating the odds of a specific race, I look at the macro analysis of what is likely to constitute a good play in the macro sense and I expect my good plays to sometimes pay well and sometimes pay fairly short odds. Now, when odds get too short, I get leary, say below 4-5.

Unlike some of those who are agreeing with me about overlays and underlays, I am very much in tune with statistical analyses and I depend on historical data to reveal advantages. In other words, I try to find tendancies, in the macro sense, that will yield an advantage. Nearly always, these are what you would find to be overlays, but I don't worry about the odds unless the odds are very, very short. If my analyses have validity, then I'm going to get the price I'm looking to get.

I know some of you will find my notions to be heresy. After all, I'm not a pace handicapper, either.

[Lefty]

ranchwest, your last post makes a lot of sense.
I think we're pretty much in agreement, after all.

[smf]

From what I've seen at the track, the people most enamored with longshots are "contest players". Making money at wagering isn't a prioirty for them (hey, it's their choice to do as they please- nothing wrong w/ that) . Handicapping is either a fun hobby for these guys, or their "goal" is to be a contest whiz of sorts.

Imho if you want to make money at "the window" you have to pick/ scope out winners and bet them hard to make a decent profit.

[PaceAdvantage]

Originally posted by ranchwest
I know some of you will find my notions to be heresy. After all, I'm not a pace handicapper, either.


Heresy? Not in the least...I look to learn from everyone...ESPECIALLY if they do things I don't normally do...


==PA

[Rick Ransom]

Fortunehunter,

One standard deviation (plus and minus) should contain about 68% of the occurrences (not 90%) in a normal distribution. Of course when you have a fixed lower bound of zero, it can't be a normal distibution anyway (maybe lognormal), but that's another story.


This has been an intesting discussion to read and everyone has some good points. My approach would be to try to estimate my lifetime number of plays and estimate the probability of losing streaks of varying lengths. Let's say for instance I get 1000 plays per year and play for 40 years. Then I'd have 40,000 lifetime plays.

Say I have a 25% win rate and I want to know what the chance is that I'll lose 50 in a row sometime in my life. There are 40000 - 50 + 1 = 39951 groups of 50 plays in 40000 total plays. The probability of not having 50 losses in an individulal group is 1.0 - (0.75)**50 = 0.999999433.

Now take that number and raise is to the 39951 power to find out the probability of not having 50 straight losses in the 40000 total plays. That would be 0.9776. Subtract that from one and you get the chance of having 50 straight losses anytime in the lifetime 40000 plays. So I have about a 2% chance under those assumptions of losing 50 in a row. That would probably be acceptable to me.

If I play for longer than that, the probability will be greater than that (but not by a lot). The bigger risk is in overestimating my win %. For example, if my win % is only 23% instead of 25%, the chance rises to about 8%. A 20% win rate gives you about a 43% chance of 50 losses! As usual, it's always best to be conservative. I don't think you can count on win percentages being stable over long periods of time.

[ranchwest]

Rick,

I'm still not accepting that one can assume that an overall percentage of 25% correlates to a 25% chance on each race. If I hit 25% overall, do I also always play 7/2 horses? The first time I play a 4/5 horse, I have a 50/50 chance of ending my losing streak, statistically speaking. Do we accept some statistics and disregard others? Or am I just not very good at math?

[BillW]

Ranchwest,

Your assertion is entirely correct. It would be a misuse of statistics to try and determine the outcome of a single event based on the statistics of a collection of events. As a matter of fact, it is flawed to assume that a 4/5 horse has a 5 out of 9 chance of winning a given race. In the long run a 4/5 horse will win 5 out of nine (plus or minus takeout) but it is the job of the handicapper to find those instances where the public has made a mistake and overvalues a given horse (an overlay). This is the basis of profit in this game.

Bill W.