[Doug]

I get the sexual reference. Discussion inspired by recent RX stuff. I present a version by a very good friend of mine, but don't agree with him.

Brian's take:

We have received numerous emails asking us for an explanation of unit betting and we will try to do our best here to explain it. If you are new to wagering it may seem complicated, however, it is quite simple.

A unit represents a percentage of your bankroll that you are willing to risk on each game. Once you establish the value of 1 unit it never changes. Never.

Lets assume that your starting bankroll is $500.00. Now let's assume that you are willing to wager 10% of your bankroll on each game. Thus, 1 unit = $50.00, or 10% of 500.00. If you are willing to wager 5% of your bankroll on each game, 1 betting unit would then = $25.00.

PLEASE NOTE!!! We are simplifying this system by using 10% as an example only. We do not recommend wagering 10% of your bankroll on one game. A more practical approach and the one we use is wagering 2.5 % of your bankroll on each game.


Again, once you establish how much a unit is worth, that never changes. The only think that would change is the amount of units you wager on each game. As your bankroll increases so does the amount of units per bet. For instance, if you doubled your bankroll to $1000.00 and are still willing to wager 10% of your money on each game then your wager would be 2 units instead of 1, or $100.00.

Simply put, all you need to do is decide what percentage of your bankroll you are willing to risk on a single game and convert that to a dollar figure. You now have the value of one betting unit and that value remains the same until you possibly raise your betting unit value.

When you see our record indicate that we are up 100 units on the year, the actual money figure is not relevant. What is relevant is the units won on the year and that is why we track it this way.





So what's a unit ?

[Doug]

I'd like Ganchrow's comment on this, since he's the best math dude, keeping in mind the author is not somebody I'm trying to fry, he's a valued friend ! Ganch is as good a math guy I've ever come across, and a fine addition to SBR.

[Ganchrow]

Thanks for the kind words.

The notion of a unit is certainly subjective and it’s up to the bettor to decide how he chooses to define it. A “unit”, however it’s specifically defined, is supposed to allow for comparison of results between handicappers who may not necessarily be betting similar amounts. If you learn that one player is up $50 after 100 bets at -110 and another is up $5,000 after 100 bets at -110, that doesn’t really tell you very much. If, however, the first player had been making $1 bets and the second $10,000 bets, then you’d be able to come to the legitimate conclusion that the first player’s performance was far superior to that of the second over that particular stretch. This is quite obviously true even though the first player had won only 1% of what the second player had won.

Another way of saying the same thing would just be that the first player is up 50 units over 100 bets and the second player is up 0.5 units over 100 bets. While this is functionally equivalent to what was said in the previous paragraph, it’s much more concise and doesn’t require one to reveal information regarding one’s personal finances.

The major problem with simply referring to “net units wons” is that if one is permitted to drastically vary one’s bet size it becomes exceedingly easy to falsify one’s results. To use an extreme example, let’s say that your goal is to be up 50 units after 100 bets. One easy way to accomplish this “feat” would be to use a Martingale strategy. Bet 50 units on the first game (or slightly more taking vig into account), if you lose, bet 100 units on the second game, if you lose that bet 200 units on the third game, etc. Assuming you eventually win (your chances of never winning are lower than 1 in 10^30), you immediately reduce your bet to some arbitrarily low unit size. This way, the vast, vast majority of the time you come out looking like a hero (“UP AN INCREDIBLE 50 UNITS AFTER 100 BETS!!!!! TRY OUR SATURDAY BUY ONE PICK GET ONE FREE!!!!! GUARANTEED WINNERS!!!!!”, or perhaps the more subtle non-tout forum version “I’m up 50 units so far this season, so my opinion matters more than yours!”) without actually having utilized any handicapping skill at all. (Note that this is in no way whatsoever an endorsement of the Martingale strategy. The only reason it “works” in this particular thought experiment is because there’s no real “cost” to a unit. Even if the exceedingly unlikely happens and you do lose those 100 bets in a row and wind up down 3.2 x 10^31 units, so what? You find yourself a new posting handle and just try again.)

Obviously, this is a very extreme example. It’s doubtful that it would continue to work on even the densest forums after a handful of consecutive losses (a 1,000 unit picks does tend to raise a few eyebrows). But it does illustrate the fact that unit records can be quite meaningless unless one knows the range of allowable bet sizes. One method which can be used to limit this effect would be to only permit wagers up to a certain maximum size. This is far from perfect, however, as it doesn’t sufficiently reward handicappers who may be more skilled at differentiating between stronger and weaker picks.

Your friend Brian has chosen to hold the size of a single unit constant while allowing the number of units wagered per event to vary with stake size. I’m sure I don’t need to point out this is fundamentally no different from holding constant the number of units wagered per event (or per event tranche if you allow bets to vary based on the strength of your forecasts) and instead varying the dollar value of each unit.

The major advantage to the latter method is that allows for simple and straightforward record keeping. For example if I tell you that over some time interval out of 1100 units wagered at -110 I’ve won 99, then, as long as I’ve kept constant the number of units wagered per event (and you know what that number is), you have a pretty good idea of my performance. The relative size of a unit is irrelevant as is the order in which the wins and losses occurred. Furthermore, whether your unit size is $1 or $1,000, 1% of your bankroll or 10%, you know precisely how you would have fared had you been mirroring my picks.

Now contrast this with using the same record keeping alongside Brian’s method. If Brian tells you that out of 1,100 units wagered at -110 he’s won 99, then while you do know how much you would have won had you followed Brian’s picks, you really have no idea how good a handicapper Brian. The reason for this is because implicit in Brian’s method is the idea that number of units wagered per event is not kept constant. If Brian had started off with a winning streak and his initial were sufficiently high relative to his bankroll, then it’s conceivable that those 1,100 units wagered might represent an extremely small number of actual discrete bets.

Another way of putting this is that in the former example making 1 units bets, we know that my winning percentage is 57.1% (57.1% * 1000 - (1-57.1%) * 1000 *1.1 ≈ 99 units) while in the latter example, even given that Brian started off with a 1 unit bet, we simply have no way of knowing Brian’s winning percentage.

[slacker00]

I'm glad someone brought this up. I've been agonizing about the philosophy of betting more than 1 unit per play since reading this article last night:
http://www.professionalgambler.com/debunking.html

J.R. Miller seems kinda controversial on some other forums that I searched, but he kinda makes sense to me. He says that it's useless to bet more than 1 unit per game, e.g. Kelly betting. Instead, one needs to establish a unit size in accordance with desired risk and use that unit for all bets. If it's deemed a profitable bet, one should risk the maximum amount (adjusted for risk) on that bet.

Now, if someone gave an obscure coinflip scenario where a mysterious stranger wants to pay 10 to 1 if heads is flipped on a fair coin, then Miller may soften a little on his units philosophy. Thing is, in the real world, even the best sharps don't find an opportunity that exceeds 60% on a supposed 50-50 wager. (Or am I mistaken?) The point is that betting 1.1 units rather than 1.0 units when an edge is perceived at 54% rather than 53% may maximize BR utility while maintaining the same risk level, but how many people who vary their units are calculating out risk and know their perceived edge down to single percentage points? Fact is, unless one is extremely rigorous mathematically and sharp, there is zero reason to vary from 1 unit play.

ganchrow, does any of this make sense to you, mathematically? I haven't worked out the numbers, because I'm not sure of some of my assumptions, plus I don't know how to examine risk mathematically, much less know how to approach how units should change as I "understand" my edge to change from 53% to 55% to 57%. My gut instinct is that Even if I risk one unit for a 53% edge, then "maybe" a 60% edge would be a two unit play. Then there's the argument that no sharp worth his salt could ever evaluate anything as being over a 60% edge, because the bookies just aren't that stupid.

[Ganchrow]

I wrote briefly of this (including Miller's silly rantings) in this post.

I'd say the only reason for an advantage bettor not to use at least a pared-down, simultaneous bet version of Kelly would be if he were unable to make accurate determinations of individual bet expected win frequency. This isn't a small point. Many fairly successful handicappers simply don't approach their 'capping in such a manner. But that's not a good thing. IMHO what sets a good 'capper apart from a truly great 'capper is the ability to handicap his own handicapping. The ability to determine not just whether or not you like a bet but how much you like that bet is an essential skill to learn. Now I'm not saying that one can reasonably be expected to determine one's expected profit down to 5 decimal places, but if one's even able to successfully distinguish between a couple of expectation tranches then that person's got a big leg up on the competition.

In Joseph Buchdahl’s canonical Fixed Odds Sports Betting: Statistical Forecasting and Risk Management, Buchdahl uses Monte Carlo simulations to determine risk/return characteristics for 6 different staking strategies while varying player edge, unit size (with a “unit” be differently defined under each staking strategy), and average odds level (from large dog to large fave). The staking strategies Buchdahl examined were:

1. Level staking
2. Percentage staking
3. Fixed profits staking
4. Martingale staking
5. Pyramid staking
6. Kelly staking

The results are certainly illuminating and I can definitely recommend this book. One important point Buchdahl makes is that from a risk perspective it makes considerably more sense to use fixed profit wagering as opposed to fixed stake wagering. This conclusion can also be extended to include percentage-style wagering -- rather than betting X% of one's stake per event, betting the amount such that one would stand to win X% of one's stake per event. (I'll point out that this functionally equivalent to using Kelly with all bets assumed to have equivalent expected profit.) The implies that a bettor will find himself risking larger amounts on favorites than on underdogs with equivalent expectations. The net result of this when compared to fixed stake wagering (assuming a fixed stake equivalent to the average stake under fixed profits) over a given number of bets is: lower standard deviation in finishing bankroll; lower probability of not achieving a profit; and lower probability of bankruptcy. What's more, all these benefits are obtained without any real degradation in expected profits.

So equivalent expected return with lower risk. To me that's quite a compelling argument.

[Santo]

I agree with Ganchrow.. if you're betting because "I think they'll cover" then fixed unit is acceptable.. if you have some computer model that gives you a calculated edge, and you believe the model is accurate, then Kelly is substantially better.

[Doug]

I should have added that Brian keeps the bets very similar in size, almost flat-betting like Miller, and he's not a tout, he gives his picks for free. Now if he won a bunch of units over some time ( say a few hundred over several years) his flat bet would be too small, right ?

I hesitate to link his site, but I'll PM it to Ganch, so he can see it.

[Mudcat]

I don't think of my unit as a percentage of my overall bankroll. I guess I could think of it that way but it would be equal to 0.1% or something like that. Most of my bankroll is dedicated to arbing/scalping/middling. The bets I place on both sides of an arb are much bigger (ideally) than what I'm willing to risk on a straight bet.

Sometimes I tell myself, 'Okay so let's say that only a portion of the bankroll is set aside strictly for gambling and the unit is 2% of that.' I could look at it that way - it would be convenient for the sake of discussions like this - but that is really just playing word games with myself.

Basically, my unit for straight betting is just a round number that I am comfortable with. I don't vary it from bet to bet (or place multi-unit bets). I just plop down a unit when I see a bet I want.

I do re-evaluate my unit size periodically. (Every ~3 months.)



I frequently curse myself for not having my unit size 5 or 10 times larger. Instead, I conservatively focus on arbing, scalping and, to a lesser extent, middling. I tell myself I am focusing on the "sure money" but I have been winning so consistently at straight betting for so long, it really has to be considered sure money as much as anything. But somehow I can't quite look at it that way and loosen up with the unit size. I focus on the sure money for that given day instead of taking the long view.

I battle my own psychology (or, more accurately, I surrender to my own psychology). I wonder if anyone can relate to this.

[BuddyBear]

I bet 2% of my bankroll on every game....

[not mofome]

ganchrow were you a straight `a` student?

[slacker00]

Thanks for the links and the write up ganchrow.

I've got Fixed Odds Sports Betting : Statistical Forecasting and Risk Management on my Amazon.com wishlist now. Sounds like it addresses exactly what I'm trying to figure out.

[Patrick McIrish]

My unit is 1% of bankroll. As for what is better, Kelly or flat it depends on the individual and how experienced they are. I personally recommend a very conservative flat betting style for newer players, at that point their main concern is bankroll protection (whether they realize it or not). Unless you stay in the game you can't win, nor can you learn much if you are back on the rail quickly. Either 1/1.5/ or a maximum of 2% of bankroll on any one play and try not to risk more than 8% on any one given day. Later as you are able to recognize and identify what sort of edge you have then Kelly or some form thereof is best. Just my opinion of course.

[Ganchrow]

My unit is 1% of bankroll. As for what is better, Kelly or flat it depends on the individual and how experienced they are. I personally recommend a very conservative flat betting style for newer players, at that point their main concern is bankroll protection (whether they realize it or not). Unless you stay in the game you can't win, nor can you learn much if you are back on the rail quickly. Either 1/1.5/ or a maximum of 2% of bankroll on any one play and try not to risk more than 8% on any one given day. Later as you are able to recognize and identify what sort of edge you have then Kelly or some form thereof is best. Just my opinion of course.

This of course still leaves open the question of whether one chooses to risk x% of his bankroll or bet to win x% of his bankroll.