What win rate do you think an ac­tive trad­er needs to be suc­cess­ful in the stock mar­ket? Most peo­ple guess that it’s some­thing dra­mat­ic and ex­pect the im­age of a mar­ket gu­ru who calls it right al­most every time.

This col­umn isn’t about sug­gest­ing you be­come an ac­tive trad­er, be­cause the odds are very much stacked against the av­er­age per­son who tries. But I do want you to know and ap­pre­ci­ate the math be­hind re­al, sus­tained trad­ing suc­cess be­cause it is rather counter in­tu­itive.

The truth is a trad­er who is right just slight­ly more of­ten than wrong, ap­plied across a large num­ber of in­de­pen­dent de­ci­sions, can turn mod­est cap­i­tal in­to a very large sum. We are not talk­ing about be­ing right 6, 7 or 8 out of 10 times but rather a per­cent­age win rate of 51 per cent, which is just mar­gin­al­ly above break even and the ran­dom­ness of a coin toss.

Sup­pose you make a bet where you ei­ther win $1 or lose $1. If you win 51 per cent of the time in­stead of 50 per cent, your ex­pect­ed prof­it is 2 cents for every $1 you wa­ger. That’s a triv­ial look­ing num­ber. You prob­a­bly wouldn’t be con­cerned or even both­er to play be­cause it’s so triv­ial. It can still be seen as ran­dom and of no con­se­quence.

But make that same bet thou­sands of times while al­ways risk­ing a small, con­sis­tent slice of your grow­ing pot rather than bet­ting every­thing on one out­come, and two things hap­pen. First, the more times you re­peat the process, the more your ac­tu­al re­sults con­verge on that av­er­age, so a two per cent lead stops be­hav­ing like a coin toss and starts be­hav­ing like a near cer­tain­ty.

Sec­ond, be­cause you are rein­vest­ing your win­nings each time rather than spend­ing them, your pot does not grow in a straight line. It grows ex­po­nen­tial­ly, the same way a small in­ter­est rate com­pounds in­to a large sum over many years. A triv­ial edge, mul­ti­plied by enough rep­e­ti­tions and rein­vest­ed at every step, be­comes a for­tune.

This is why pro­fes­sion­al trad­ing op­er­a­tions ob­sess over con­sis­ten­cy and vol­ume rather than the size of any sin­gle win. A hedge fund does not need one bril­liant trade a year. It needs a small ad­van­tage it can ap­ply thou­sands of times, sized so that no sin­gle loss can wipe it out, and ap­plied with enough dis­ci­pline that the edge is nev­er aban­doned out of fear or greed halfway through a los­ing streak. The in­di­vid­ual de­ci­sions look al­most bor­ing but the ag­gre­gate re­sult can be quite spec­tac­u­lar.

The edge

None of this works with­out a gen­uine edge in the first place. You can’t ac­com­plish this with a poor trad­er in an in­con­sis­tent sys­tem. In stock mar­ket trad­ing, the edge can come from many dif­fer­ent places. Some­times it is speed: be­ing frac­tion­al­ly faster than oth­er par­tic­i­pants at re­act­ing to new in­for­ma­tion, so a trade is placed be­fore a price has ful­ly ad­just­ed. Some­times it is in­for­ma­tion pro­cess­ing rather than in­for­ma­tion it­self: two traders can see the same pub­lic da­ta, an earn­ings re­port or cor­po­rate news, but the one who process­es it faster and con­verts it in­to a prob­a­bil­i­ty cap­tures the edge be­fore the price catch­es up.

Some­times the edge comes from sim­ply pro­vid­ing a ser­vice, a mar­ket mak­er who quotes a price to buy and a slight­ly high­er price to sell, cap­tur­ing that small spread over and over across enor­mous vol­ume, tak­ing on very lit­tle risk on any sin­gle trans­ac­tion. Some­times it comes from the knowl­edge that in­vestors pan­ic sell dur­ing down­turns and chase eu­pho­ria dur­ing ral­lies in fair­ly pre­dictable pat­terns; a dis­ci­plined trad­er who has stud­ied those pat­terns can po­si­tion against them, not be­cause they know the fu­ture, but be­cause they know how fright­ened or greedy peo­ple tend to act un­der pres­sure.

From our dis­cus­sion, a fur­ther source of edge, is sim­ply spread­ing a small ad­van­tage across many un­re­lat­ed bets rather than con­cen­trat­ing it in a few large ones. A thou­sand small, in­de­pen­dent trades each car­ry­ing that same 51 per cent edge be­have very dif­fer­ent­ly than a one off. Again, this is why large trad­ing op­er­a­tions prize hav­ing many small, un­re­lat­ed po­si­tions over a hand­ful of large, con­vict­ed ones. It is not cau­tion for its own sake. It is the math­e­mat­ics of av­er­ag­ing work­ing in their favour.

What all of these sources of edge share is mod­esty. None of them pre­dicts the mar­ket. None of them is right most of the time about any sin­gle event. They sim­ply shift the odds a lit­tle, con­sis­tent­ly, in a re­peat­able sit­u­a­tion, and let rep­e­ti­tion and dis­ci­plined siz­ing do the rest of the work.

Ap­ply­ing the log­ic

This idea of small com­pound­ing bets can al­so be used to de­sign a sys­tem where “the house” al­ways wins. Such sys­tems don’t an­nounce them­selves through one dra­mat­ic act. They work through some­thing small­er and hard­er to see: a slight, re­peat­ed tilt, ap­plied of­ten enough, un­til an out­come that looks like chance turns out to have had a di­rec­tion all along.

Now take the trad­ing log­ic and ap­ply it some­where else en­tire­ly: to a foot­ball tour­na­ment, where as I point­ed out last week, the ref­er­ee and the VAR pro­duce a se­ries of sub­jec­tive de­ci­sions stacked on top of each oth­er.

To be clear this is not a claim that any tour­na­ment has been ma­nip­u­lat­ed. It is a demon­stra­tion that the math­e­mat­ics be­hind a 51 per cent trad­ing edge is not on­ly a fi­nan­cial mar­ket con­struct. It can be ap­par­ent in any en­vi­ron­ment that re­quires a re­peat­able de­ci­sion, made un­der un­cer­tain­ty, many times over.

Foot­ball, at the elite lev­el, is of­fi­ci­at­ed through hun­dreds of small judg­ment calls across a match and a tour­na­ment: a foul giv­en or waved away, a card shown or with­held, a mar­gin­al off­side, a hand­ball ruled de­lib­er­ate or ac­ci­den­tal. Most of these are gen­uine­ly close calls, de­fen­si­ble ei­ther way. That is pre­cise­ly the con­di­tion in which a small, re­peat­ed skew could op­er­ate with­out ever pro­duc­ing one in­de­fen­si­ble mo­ment. No­body needs to fix a re­sult out­right. It would be enough for un­cer­tain, mar­gin­al de­ci­sions to be re­solved in one di­rec­tion slight­ly more of­ten than the oth­er, spread across many match­es, nev­er ris­ing to the lev­el of an ob­vi­ous, prov­able er­ror on any sin­gle oc­ca­sion.

The ef­fect of such a skew would not need to be dra­mat­ic to mat­ter, be­cause it would be giv­en to elite, high­ly skilled foot­ballers who can con­vert small op­por­tu­ni­ties in­to large ones, the foot­ball equiv­a­lent of the ex­pe­ri­enced, dis­ci­plined trad­er.

Mar­gin­al de­ci­sions that hand a top lev­el side an ex­tra half yard of space, or spares their best de­fend­er a card that would have lim­it­ed how hard he could chal­lenge for the rest of the match, is not wast­ed on play­ers of that cal­i­bre the way it might be on a weak­er side. The play­ers sup­ply the fin­ish­ing that turns these op­por­tu­ni­ties in­to goals. Peo­ple will fo­cus on the out­come and the per­sis­tent skew be­comes part of the de­bate that can nev­er be test­ed.

Ap­pre­ci­ate that a sin­gle mar­gin­al de­ci­sion does not stay con­tained to the mo­ment it oc­curs. A team that con­cedes an ear­ly goal, it might not have con­ced­ed, is forced to com­mit more play­ers for­ward, which opens space in be­hind for the oth­er side to ex­ploit. A team giv­en a slight­ly favourable whis­tle can re­tain more pos­ses­sion, man­age the game, forc­ing its op­po­nent in­to greater risk. A play­er cau­tioned or sent off changes the shape of his en­tire team for what­ev­er re­mains of the match and im­pact­ing the re­main­der of a tour­na­ment. None of these con­se­quences re­quire an out­ra­geous­ly bad de­ci­sion.

A tour­na­ment is a con­tin­u­um, where small de­ci­sions com­pound. A re­sult shaped in part by a se­ries of mar­gin­al de­ci­sions changes points and goal dif­fer­ence, which changes which group a team fin­ish­es in, which de­ter­mines its op­po­nents, its trav­el, and its re­cov­ery time in the next round. A card shown in one match po­ten­tial­ly re­moves a play­er from the next one en­tire­ly.

None of this re­quires the vol­ume a trad­ing strat­e­gy need. A tour­na­ment has rel­a­tive­ly few match­es com­pared to a trad­ing book with thou­sands of po­si­tions, so what sub­sti­tutes for vol­ume is lever­age: a small num­ber of mar­gin­al de­ci­sions, land­ing in a par­tic­u­lar di­rec­tion can re­shape paths with­in and across match­es.

At the end of the day ap­pre­ci­ate that it’s easy to in­ter­vene in a sys­tem. How­ev­er, au­dit­ing the out­come of those in­ter­ven­tions is an­oth­er mat­ter al­to­geth­er. Small bets are all you need to skew a win. It has pro­duced doc­u­ment­ed re­sults in stock mar­ket trad­ing. It is dif­fi­cult to prove or dis­prove else­where when da­ta and in­for­ma­tion flows are not as trans­par­ent.

Ian Nar­ine is a fi­nan­cial con­sul­tant who is watch­ing a World Cup of small bets. Please send your com­ments to ian@ian­nar­ine.com