Staking Plans v's Even Bets

[becareful]

Ok - here goes nothing! I will try to keep this as simple as I can - if anyone has questions or constructive comments I will be happy to try to answer them.

Please note: throughout this example I have used Equine Investors strike rate, average div and staking plan as an illustration (basically because he has posted his figures here) so it is based on place bets - but it would apply equally to the systems proposed by Bhagwan, etc and also to win or exotic bets as well.


STAKING PLANS v EVEN BETTING

First a couple of basic definitions:
STRIKE RATE: How often you have a winning bet (as % of bets placed). Eg If you place 100 bets and have 56 winners then the strike rate is 56% or .56. An important note here is that you cannot place 10 bets, have 8 winners and conclude your system has an 80% strike rate - you must have at least a hundred bets to get something close to an accurate strike rate and preferably several hundred or even several thousand (the more bets the more accurate your strike rate calculation will be).

AVERAGE DIVIDEND: The average dividend you have received on your WINNING Bets. Simply add up the winning divs, divide by the number of winners and you get your average dividend.

EG. Lets say we have 2 winning betting sequences of 10 bets each:

1. 1.80, 1.80, 1.90, 1.80, 1.80, 1.90, 1.80, 1.80, 1.90, 1.80
2. 5.00, 1.10, 1.30, 3.20, 1.20, 1.20, 1.80, 1.00, 1.20, 1.30

If you add both of these up they total $18.30 so the average dividend is $1.83

Now before I go any further lets have a look at the idea that "good dividends" somehow give better return than average dividends. In the sequences of divs. above the first consists of divs of around the average only - the second has 2 "good divs" of 5.00 and 3.20, one average div of 1.80 and the rest pretty ordinary divs of 1.10-1.30. However if you add them up you end up with the same total dividend of $18.30 (or 183.00 with $10 bets, 1830 with $100, etc). Therefore it makes no difference whether we have 10 1.83 divs, 10 divs of around 1.80 - 1.90 or a range between 1.10 and 5.00. The important thing is the AVERAGE.

THE STAKING PLAN
Lets have a look at EI's staking plan - for those of you that missed it he bets 1 unit, 2 units, 6 units then 18 units (place betting) - if he does not hit a winner after the 4th bet (18 units) then he stops and goes back to 1 unit. Now he has given his long term average dividend as $1.83 and his long term strike rate at 56%. Multiplying these two figures together gives us the projected return on his system -

So we have $1.83 * .56 = 1.025 or a 2.5% profit on investment.

Now lets look at how it goes with his staking plan. Lets assume we will bet his system for 100 sequences (ie. we will start the betting sequence 100 times and continue until either we hit a winner or we have placed 4 bets).

Out of the 100 single unit bets we place we expect 56% to win so we will get 56 winners on the first bet and 44 times we will have to continue the sequence and place a 2 unit bet. Out of the 44 2-unit bets we again expect 56% to win - this should give us around 25 winners and 19 times we will have to continue to the 6 unit bet.
Out of the 19 6-unit bets we again expect 56% to win - this should give us 11 winners and 8 times we will have to continue to the final 18-unit bet
Out of the 8 or 9 18-unit bets we again expect 56% to win - this will give us 4 or 5 winners (for the purposes of the calculation we will call it 4.5 - sometimes you will get 4 and sometimes 5) and 3 or 4 times we will "strike-out" and lose our money.

So in summary we have placed 171 bets (100+44+19+8=171) and the total number of units bet is 100 + (44*2) + (19*6) + (8.5*18) = 100+88+114+153 = 455 units

Now what about the dividends?
We have 56 single unit winners @ 1.83 (ave div) = 102.5
We have 25 2-unit winners @ 1.83 = (25 * 2 * 1.83) = 91.5
We have 11 6-unit winners @ 1.83 = (11 * 6 * 1.83) = 120.8
We have 4.5 18-unit winners @ 1.83 = (4.5 * 18 * 1.83) = 148.2
So the total dividends are 463 units

So our return on investment using this plan is (drum roll please) 463/455 = 1.02 so we have a 2% profit on investment (by the way the difference between this and the 2.5% forecast is due to the rounding errors in the calculation above - if you do it without rounding it comes out to exactly 2.5%).


EVEN BETTING
The return from even betting is very easy to calculate as it is just the number of bets multiplied by strike rate multiplied by average dividend (multiplied again by your stake amount).

In this example we have 171 bets, strike rate is 56% and ave div is 1.83.
If we multiply these together we get 171 * .56 * 1.83 = 175.25
Of course given we were betting up to 18 units at a time in the staking plan we wouldn't only be betting one unit with even betting. Lets say we bet 3 units per time. This means our total dividend would be 175.25 * 3 = 525.75

So betting up to 18 units with our staking plan we get a return of 463 units less our 455 investment leaves 8 units profit.
Betting 3 units with even betting we get a return of 523 units less 513 units gives us a 10 unit profit.

Of course if you miss 4 consecutive bets on the staking plan you are down 27 units, miss 4 on the even betting plan and you are down 12.


WHY DO PEOPLE BELIEVE STAKING PLANS WORK?
This is a good question and I don't really know for certain. I suspect it is because in the staking plan your losses are effectively "hidden" in the rare 4-miss scenario (with this particular plan) than only happens around 3.5% of the time. So if you are starting 3 or 4 "sequences" of bets per day then you could go for weeks without hitting a bad patch - therefore you seem to be making higher profits (which, of course, largely get wiped out by your bad day so that you are back to the 2.5% profit again). With even betting you probably see each bet as an individual occurance and hence you feel like you are losing nearly half the time (with the 56% ratio) - with the staking plan you don't look at the individual bets as much but rather each sequence. This means that you feel like you are winning about 96.5% of the time and only losing 3.5% of the time - that has got to be better than only winning 56% of the time. Of course the problem is that your losses, when the happen, are much larger and so you end up in the same place overall.


Sorry for such a large post but some people expressed interest and I thought it would be useful to some of you. I hope I have explained myself well enough for you to follow it - if there are any questions I am happy to try to answer them.

:smile:

[Equine Investor]

Very thorough explanation there becareful but the effectiveness of the system is where you get an above average return on your third or fourth bet. That is where it kills level stakes.

[mr magic]

becareful,
Congratulations on an excellent and common sense post. It is a shame there aren't more intelligent and factual posts here rather than the usual "if it works for you, good on you mate and stick it up the non believers" drivel that occurs.
To me the most important point you make which is seemingly lost on progressive stakers is that each bet is an isolated occurance. Oliver's chances of riding a placegetter on Falvelon after 3 misses are the same as his chances of placing on Falvelon after 30 places in a row. Despite progressive staking planners protestations that is a fact that is impossible to refute. Does tails have a better than even money chance after 30 heads are spun? Of course the answer is no.
Keep up the thought provoking posts becareful, it is very refreshing reading.

[Bhagwan]

Thanks for your detailed detailed post , it was well explained.

Progressive staking has to be treated with respect & caution , for the simple fact that the 20 outs in a row or more is always lurking in the shadows if win betting .

It`s always a better idea to stop betting after a pre-determined series of loosers E.G. 8 loosers in a row, then start again once one of your selections gets up, only this time you half the amount to be recovered, once thats done, you can the recover the other half & so on .

Its based on the well known observation , that where there is a run of outs , there`s also a run of ins.
I beleive staking plans can work, it`s knowing when to stop once your ahead is the tricky bit.
If you had a selection plan thats always picked a winner within 20 bets based over 300 races ,you would possible make a fortune ,depending of course on the average dividends , you would also have to work out what size bank you would need based on the average divided stuck over your past results , to sustain 20 outs in a row.Its also an idea to have 2 banks of the same amount so your are not betting with frightened money . This where most punters judgement gets clouded & they start changing their plan of attack .Thats when the most used sentence in the world is heard "IF ONLY I....."
Once you have that figure you can make that you min. divisor you`ll go to ,if the price on offer is less than this & you still wish to bet that horse .Personally I will not bet my selection unless I get a min. dividend of at least $3.30 for the win.The min.divisor I would use no matter how short priced the horse, is 3.0 if it falls over the out lay is not as great , if it gets up I recover most of my losses, & then keep going.

This is where the diciplin thing comes into it & also the frustration of only winning a small amount to outlay, but that`s the attitude one has to be resigned to if one is insistant on progressive betting.

[becareful]

Mr Magic - thanks for your comments - glad to see at least one person understands what I am saying!

EI - I thought I had covered that point - it does not matter if you get a good dividend on the 3rd or 4th bet - in the long run this will even out (yes it will "kill" the even stakes system ON THAT DAY but the next day when you get a good div on one of your 1st bets and a poor div on the 3rd or 4th bet then the even stakes system will be better - it is all the same IN THE LONG RUN). If your long term average for your 18 unit bets is $1.83 then the fact you get a $5 div one day is balanced by all the 1.20 and 1.30 divs which bring your average back to the 1.83. As per my post there is no difference between the $1.80-$1.90 sequence of dividends and the $1.00-$5.00 sequence, they both average the same amount.

[Equine Investor]

Mr.Magic, I don't agree...if a jockey has a strike rate of 56% and has a losing sequence of hypothetically 20 unplaced runners..the odds of him placing at the next run are still 56%...I'll take those odds anytime. As his average is maintained in the longrun.And past results reflect a winning system, and so do current results which is the true test of any system.As for the future,unless the strike rate and average dividend drops below expectation, I can only see profits. I am aware however that should a jockeys consistency fall below par for a long period ,then I may change my jockey list in the future - which I said at the beginning of my system about reassessment.But for the time being I am happy.Even though Munce and Prebble had shocking days on Saturday, I watched their losing rides carefully and was still very impressed.Sure enough they bounced back on Sunday.
Becareful, see what you are saying but the profits from an extra good day maintain the bad times. If I got a run of 4 sets of outs in a row,that's 16 unplaced runners in a row!!!(never had it to date and statistically improbable, but not impossible) I would still be ahead even on yesterdays results without eating into previous profits and this is what maintains the system.
You are not taking into account the very low strike rate of a run of four losses in a row.
It has occurred once in the last 76 bets.

However, I must add this...becareful you are the only person that has put some effort into logically explaining your point of view, and provided mathematical statistics to back up your argument. Congratulations because you are not outright bagging the system and are openminded enough to be interested how it all works and anxious to see more results.

<font size=-1>[ This Message was edited by: Equine Investor on 2002-05-13 11:36 ]</font>

<font size=-1>[ This Message was edited by: Equine Investor on 2002-05-13 11:40 ]</font>

<font size=-1>[ This Message was edited by: Equine Investor on 2002-05-13 11:46 ]</font>

[becareful]

EI - You are free to disagree with Mr Magic but from a statistical point of view he is right. As he says each race is a seperate occurance and the chances of a placing after 20 losses are the same as after 20 wins - just like with tossing a coin (or betting red/black at roulette). With coin tossing the average is fixed but calculated over millions of occurrances - 20 heads or tails in a row makes no difference. With horse racing, on the other hand, the average is not necessarily fixed - your average at the moment is 56% but that does not mean that it will not change in the future to 50% or to 60% - so if you have a run of 20 losses it does not mean you "must have some wins soon to restore the average" - it could mean that your average is changing. I suspect that this point is pretty irrelevant anyway. My guess is that if one of your jockeys had 8 straight losses you would probably drop him from your list temporarily until he returned to form?

Of course with this particular system I suspect you may find that you are more likely to get sustained winning and losing streaks than the statistics would suggest purely because jockeys are people and therefore they have days when the are feeling good & confident and days when they are not so good (maybe had a fight with the wife, got a cold, hangover from night before, etc). On their good days you are probably more likely to get 4 straight winners than the odds would suggest, on their bad days more likely to get the 4 straight losers - could be an interesting statistical analysis! Of course would be hard to incorporate this into any betting system (unless you know the jockeys personally and can get an accurate "how do you feel" rating each morning) :smile:

With regards to your other point I am not saying that your system will not maintain a profit (it will if the strike rate/divs are maintained) - merely that in the long run I would expect the profit to be about 2.5% of your investments. I think I have said before that it is possible that your system does give better results if, for some reason, your strike rate/ave. div is different depending on the bet size. In this case it would be a good idea to try to work out WHY this is so - you could use it to improve your overall profits.

BTW - a small point but your profits yesterday would only sustain just over 3 "strike outs" - and you don't need 12 consecutive losses to give those strike outs, 3 seperate lots of 4 would do it) Of course you can lose money without striking out (eg. div of 1.20 on 18 unit bet give 21.6 unit divs but you have invested 27 units up to that point).

[Equine Investor]

I think we have to agree to disagree as said before and let FUTURE results speak for themselves.I will however post the past results so you can get an idea over a longer number of bets and timeframe.
I do see the problem with staking plans ....if the unthinkable happens, and yes sometimes it does. That is why I limited to staking only to four bets, other staking plans require you too increase your bet to a winner, whenever this occurs. That staking system is Dangerous as it could eat away all profits and your bank.
And yes, if a jockey is out of form for a number of outs,he would be replaced until I decided he was riding CONSISTENY up to his regular standard. This is not a change of rules as I said this at the very start.
Sorry, it is very time consuming going through my old sheets and separating the result, and then compiling them in excel, but bear with me I will post previous results true to my word.

[supersoul]

Hi Mr Magic
I see that you place absolutely no value on the abilities of a Jockey? You equate a SELECTED, consistent performing Jockey's chance to win to the flip of a coin? Sorry, but there is a flaw in your logic. As we have seen, a consistent performing Jockey also gets offered the best rides, etc.

You cannot compare such a jockey's chances to statistical "chance". If it was there will be no diff in any prices in a race, and no Jockey Premierships either.

Come on...

Becareful, I also suspect a slight problem in your statistical analysis, although I cannot define it exactly. It just seem outside my grasp... instinct?

The average of 1.83 as stated by EI can be misleading, as one would have to be more detailed about this: The actual divs of the strikes of the 6 and 18 WILL make a diffs.

Take your example of two x10 runs: A win of 18 units on $5 would certainly influence the average... The diff being between the losses and the wins- NB: Lose at 18 units= 18 units "down", but win at 18 units "equals a run of 18 straight (single unit) wins AT THE PRICE"! Does this make sense?

You cannot lose more than the units you bet, but you can win a hell of a lot more than the amount/units bet.

I think the way you examined the 56% strike rate is also a bit suspect: 100 bets = 56% strike rate. You cannot then ADD more winners to the 44 losing bets as "secondary winners" at $2 and $6 and $18... increasing to 171 bets in total... this is wrong, as the original 56 bets within 100 bets MUST include the higher amount bets(2/6/18)!

Your assumption regarding losses looks like this: 56 straight wins(have to be!) ie 44 out of the first 100 lost;

then 25 2 units out of THIS 44 equals 50 losses (somewhere) again...??? Because this is second tier bets!

also 11 6 unit = 11x2 losses = 22 losses

and lastly 4.5 x 3 = 10.5 losses

our losses out of 171 must be 44+50+22+10.5=126.5 which is no longer 56% strike rate out of 171...

THUS the 44 "original"losses must include some of the other second and higher tier losses- which means that the 56 winners are not all plain 1 unit winners, etc etc etc.

My stats are no good, I know, but as far as I can determine, there are a few logical flaws in your stats too.

Please- I am not shooting anybody down here- I am merely pointing out some mistakes in the reasoning of the answers. The dividends might average 1.83 but because of the staking plan, this cannot be used as with flat betting.

I admit I am too stoopid to come up with the correct interpretation myself, but I can only say I "feel" EI's system deserves a bit better scrutiny before filing it in file 13...as with all systems which relies on the user for some discretionary input.

To pick this Jockey or that, that is the question...!

[becareful]

Supersoul,

I think you will find that Mr.Magic's point about the coin toss was that in theory the chance of a particular jockey winning/placing on a particular horse is a particular percentage (say 33%) and this is not related to how many rides he(she) has had since their last win/place. Just because a jockey has not won for 20 races does not mean they suddenly have a much better chance of winning just to maintain their win/loss ratio.

With regard to your point on the different divs on the different bet sizes - yes that does make a difference when you are looking at a few days worth of winners - but in the LONG RUN (say thousands of bets) it makes no difference unless there is a higher average dividend on those bets. You may have seen I posted an analysis of Beadmans winners for last 4 months in another thread which indicated that he did have higher divs & higher strike rate on the $6 & $18 bets which makes EI's system work better than even stakes FOR THIS RIDER. I can't explain why this is (it may just be a statistical anomoly which will dissappear over a longer period of time). What it probably does show is that you have to be careful with any statistical analysis of horse racing - sometimes your gut feel may be more reliable!

Finally I don't believe your criticism of my analysis of the 56% strike rate is valid - I simply started with 100 $1 bets as it made it easier for people to follow the maths. It doesn't matter whether the example has 100 bets, 171 bets or 3276 - the percentages all work out. As for your loss analysis can I just ask how you get 50 2-unit losses when we have stated there are only 44 2-unit bets? The total number of losses in my example is 74.5 which is roughly 44%.

In summary I think you will find my analysis is technically correct but I agree that it does not mean you have to throw away EI's system. Personally I think his jockey selection has merit but if I were to use it I would change the staking plan to something like 0,3,5,7,6,6 (for BEADMAN - you would need to work out the best one for each jockey) - this gives you the higher bets on the better paying rides, skips the first ride from a win which statistically loses money, and allows you to go up to 6 rides instead of 4 without increasing your maximum loss.

[supersoul]

Hi Becareful
Regarding Mr Magic- I see what you/him are saying, only I still say that there is a better than even chance for a next win given a losing streak- BASED ON PAST PERFORMANCE. That is the thing about racing- it is not an open-ended system like coin tossing. It is a closed system- a champion jockey does not, at the end of a long career, break even with the "mean" winning average of all jockeys... He has his own average at a relatively higher than average level- otherwise he would retire as a mediocre jockey! So the average should be over a closed range, and thus MUST achieve higher than "chance" scores throughout! Three out of ten stuff, not three thousand out of ten thousand...

Quote:
"As for your loss analysis can I just ask how you get 50 2-unit losses when we have stated there are only 44 2-unit bets? The total number of losses in my example is 74.5 which is roughly 44%."

You have me stumped! LOL! I think my logic left me there- I have no idea how I got there in the first instance... I might have got mixed up with units lost? I was convinced then, though your stats makes sense now. Apologies all over...

[becareful]

Supersoul,

I agree that different jockeys will have different strike rates and therefore the chances of a particular jockey winning the next race is based on their strike rate (not the overall strike rate for all jockeys). So Beadman's chance of riding a placegetter is say 60% while an apprentice may have only a 10% chance. Of course in reality it is more complex than that and the chances for a particular race are not going to be the same (eg. Beadman riding a favourite has a better chance than Beadman riding a long-shot).

What I was saying was that if Beadman has had 5 misses in a row then the chances on the sixth horse are still say 60% - they do not go up to 80 or 90% just so he can maintain his average for the week. My point is that whether a jockey wins/places in a race can be treated as a "chance" outcome with a probability determined by THEIR skill level (which you should be able to work out from THEIR past strike rate).

Hope this clears it up.

[mr magic]

becareful,
You have explained my reasoning well.
A jockey may achieve a seasonal strike rate of 50% by riding 100 placers from 100 rides and then missing with his next 100. This is an extreme example but it makes a point.
I know Equine Investor drops jocks who are out of form but the subjectivity mixed with the mechanical system is messy. Surely the reasoning of the progressive stakers is that the jockeys will come good sooner or later and that is why the bets are increased accordingly. So why drop Munce for example because he has ridden poorly for a couple of meetings? He was selected in the first place because he is a leading jockey with an excellent strike rate. Bets slide upwards on the basis that the longer he goes without a hit the closer he is getting. So why drop him in the first place? Doesn't the placegetters theory mean he is about to gave a great day?
I think the real problem I have with the whole concept is that the Progressive staker would be secretly hoping that Oliver's first 3 mounts that are paying $1.10 a place all miss so that his 4th mount which is paying $5 a place will lob with his $1800 on board.
If the first 3 lobbed and he picked up $100 x 1.10 he wins $30. The other way he drops $1200 on the first 3 (100,300,800) then cleans up with a $7200 win on bet 4. If you secretly hope the horse you are on loses then there is something wrong.