The Kelly Criterion:

The following is a tutorial on the Kelly Criterion. I have given the basic formulas used and how I feel they are best applied. The Kelly Criterion was originally developed by an engineer by the name of John Kelly back in the 50's. Its original purpose was to establish optimum bet sizing and bankroll management for betting the "ponies". It is particularly well suited for that endeavor. It has since been adapted for various betting pursuits such as blackjack and sports betting. There is only one "rule" that is an absolute must to make it work. You must have a "positive expectancy" from your handicapping. In other words, if you flat bet any significant number of plays, you must be positive money after that series. In this example, the record stands at 199-159 or 55.6%. (I threw out all pushes) That is a respectable and repeatable record. I know that it is unverified for almost all of you, but it will do nicely for this example and will show you how to properly apply the Kelly Criterion. This sample size is a little bit small for advanced math wizards, but it is statistically significant based on my past experience.

Everyone knows how to define winning percentage or W. That is defined as the number of winning plays divided by the total of winning plays and losing plays. In my last 3 years W=199/(199+159) or W=55.6% or .556 Conversely, my losing percentage or L= 1-W or .444 These values will be used in following formulas.

The next thing you must figure out is your average payoff per winning bet. For point spread sports such as football, it is fairly easy. You take the amount won ($10) divided by the amount risk ($11). 10/11 is .909 So our average payoff or P equals .909 If you are laying 6/5 on totals or some other bogus thing, find yourself some new books! For variable payoff sports such as racing or baseball, it can be a little more complicated but can be explained fairly easily.

Now that we know P=.909, what is the next step. Hopefully, many of you know that you must win 52.4% of your bets to break-even in football or hoops. Do you know how or why that is? The formula is quite simple. The break-even point or BE is defined as BE=1/(P+1) or BE=1/1.909 or .5238 In a later article, I will show how you can use this formula to assess the break-even of parlays and other exotic bets. Understanding this formula is an absolute must if you desire to play a money line. Money line betting is STRICTLY an odds of winning versus rate of return comparison. Too many players play money lines and don't properly understand the price they are receiving. Please don't do it until you fully understand the odds!

Now the fun begins! We must now calculate our advantage over the odds. That's right, our advantage. If we can expect to win 55.6% and BE=52.38%, then we can expect to make money! Unfortunately, the vast majority of players do not make money at these numbers! Your bookie thanks you! Most players over-bet their advantage and went bust during a losing streak. Yes, EVERY player has losing streaks. In order to accurately calculate our advantage, we use the following formula: A=W-(L/P) In our example, that equates to A=.556-(.444/.909) or A=.068 This means that we should risk a maximum of 6.8% of our bankroll on each play. Note that this is the maximum to risk! That means that on a $2000 bankroll, we should play no more than $136 to win $123.60. It is no great sin to risk somewhat less, but a tragedy to risk more! You will see this in the next paragraph.

Let's recap our formulas so far:

Win % = W

Losing % = L

Avg. Payoff = P = .909 for football

Break-even Win % = BE = 1/(P+1)

Advantage = W-(L/P)

General rule - never risk more than your advantage or "A" on any wager. This is known as the optimum wager amount. When you bet more than your actual A value in the Kelly Criterion, your results diminish. Let's use our example number of A = 6.8%. If you bet only half of A or 3.4% per wager over the life of the sheet, most people would feel that your return would be half as much as when risking the 6.8%. That is absolutely true when looking at flat wagers. The nice thing about Kelly is that your return would be approx. 70%! Here are a few examples assuming a start with a $1000 bankroll. After 100 plays with a 56-44 record, someone risking 6.8% would have increased their bankroll to a little over $1300. Risking half as much (3.4%) would leave them with a little over $1200. Not bad huh? Cut your bets in half, yet win close to 70% of the money! That might make you think that the more you risk, the more you make. That is where you must be careful. If we bet 1.5 our A value or 10.2% on each wager, our ending bankroll is approx. $1250. That's right, increase our bet sizes by 50% and our ending bankroll was reduced by over 15%. Taking it one step further, if we risk 2A or 13.6%, our ending bankroll would stand at just over $1100. Bet twice as much and earn $200 less. Not a very appealing alternative. As you can see, betting higher than our actual advantage reduces our return substantially. Betting less than our peak advantage costs us money, but not nearly as much as over-betting our advantage.

Sessions 

We will now discuss the effect of sessions on this bankroll. Previously, we found that my record pegged our optimum risk at $136 based on a $2000 bankroll. I will adjust this down to $132 to win $120 since it is easier to look at plays on the even $10. That leaves us with 6.6% to win 6% plays. After our first day of wagers, our bankroll will stand at a little above or below $2000 since we will have won or lost for the day. Let's say we go 3-1 on the day on these $120 wagers. That would leave our bankroll at $2228. That means our 6% play would now stand at $133. I will again adjust this down to $143 to win $130. You would continue to do this after every session. The more sessions or adjustments, the better your Kelly chart will work for you. However, I strongly recommend you never split a day into multiple sessions! I look at each day as it's own session. During football season, all Thursday, Saturday and Monday plays are their own sessions. One of the advantages of the Kelly Criterion is that it allows "compound interest"; we allow our winnings to build on themselves. On the flip side, if we hit a cold streak (make that when!), we automatically cut back our unit size. The longer you stick with your Kelly sheet, the more you will see it work for you. Some of the bigger players I know have played to the same Kelly bankroll for several YEARS! A solidly constructed and well followed sheet will not let you down.

Setting Bet Proportion

Most bettors that have any sophistication at all have figured out that they must have a set bet amount to survive. You don't last long as part of the "Bet a Bunch on a Hunch" crowd. Many migrate to the Flat Bet. If it is not too large for your bankroll, you can do a lot worse! If you are betting 5% of your starting bankroll on each game and hit 55% of your plays, you should be OK. In fact, if you look strictly at the short term, flat betting will return a higher ROI than Kelly betting. The key comes in letting your Kelly sheet work over time. The longer you stick with a Kelly plan, the more dramatic the results will be. You will enjoy higher returns on the same bankroll risk and make the risk of going broke nearly impossible. The next question is: How do I set my bet amount? Advanced users of the Kelly use something they call a "slider" that varies the unit %. Simply put, the slider is adjusted based on their win %. In daily play sports such as basketball and baseball where you have several plays a day and 150 or more days of action over a single season, this works extremely well. I don't like the use of the slider in football unless you are using a multi-year sheet. Since I know most of you don't manage your bankroll that way and it only complicates matters, the Kelly sheet example I will be posting will be a basic one w/o slider. The important thing is to set a realistic bet proportion. Using my last three years experience of 55.6%, we can safely use an A value of 6.8%. Problem is that at this value, there is a good chance we might be slightly over our actual A value for the year. Remembering that it hurts much more to be over A than under, I will use 4.4% risk to win 4%. We only need to win 54.5% for the year to ensure that we don't exceed our A value. I am confident that I will be able hit that target.