Welcome to another instalment of Dear Plus EV! I’ll be answering questions I get from the community on the analytics and mathematics of betting. Got a question that you would like to have answered? DM me on Twitter @PlusEVAnalytics, or email me at [email protected]. Some questions may be lightly edited for clarity. Let’s get right to it!
Are there any reasons to play a teaser instead of parlaying alt point spreads? – Twitter @AmberGambling
I’m going to answer this using a restaurant analogy. You’re hungry to increase your win probability by moving the spread in your direction, but you want good value for your money. Where’s the best place to eat?
Alt point spreads are like an a la carte menu, you can order whatever you want and everything has its own price. Buying through the five (from -5.5 to -4.5 or from +4.5 to +5.5) is going to cost less than buying through the three (from -3.5 to -2.5 or from +2.5 to +3.5) because a final score margin of three happens more frequently than a final score margin of five.
Teasers are the buffet. You can pick whatever you want and some items are more valuable than others, but you pay the same price regardless of what you take. Teasing through the five? That’s a hamburger. Through the three? Filet mignon. Through the seven? Lobster. Through zero? That’s a dinner roll.
Now, there’s nothing wrong with being hungry for hamburgers and dinner rolls, but if that’s what you want and you go to a $50/plate buffet to get them, you’re wasting your money. But if you want surf and turf that would cost you $70 off the a la carte menu, then the $50 buffet is a great deal! The thing about teasers is that the price is the same regardless of which numbers you’re “buying.” So use teasers for expensive numbers and alt spreads for cheaper ones. Surf and turf!
What is your favorite distribution for counting events (like goals, touchdowns, fouls, etc)? Are there any better alternatives to Poisson? - FoG_BLoG via email
This is a simple question with a very complicated answer. I’ll hit the highlights here, and I’ll invite anyone who wants to go (MUCH) deeper to check out my course on the Art of Sports Betting Analytics at https://analytics.bet/art/.
The Poisson distribution is an essential part of every analyst’s toolkit. In order to use Poisson, the thing you’re modeling has to obey two well-known rules that everyone talks about, as well as one super secret rule that nobody talks about.
Well-known rule #1: The thing must be a count of the number of times that some event happens. So yay to passing touchdowns, nay to passing yards, yay to three pointers made, nay to basketball player points, etc.
Well-known rule #2: The event must have a probability of occurring at each moment that is both a) equal to the probability at every other moment and b) independent of what’s happened in every other moment. Sometimes this rule gets bent a little bit; for example, Poisson is commonly used for hockey goals even though goals are more common late in close games due to goalie out and overtime scenarios. Unless you’re modeling something super specific like “how many goals will be scored in the last two minutes of the third period,” the error in your model from minor violations of this rule usually isn’t big enough to worry too much about.
Poisson is very easy to work with because it only requires one parameter, the mean. If you know that Tom Brady touchdown passes in next week’s game are Poisson distributed with a mean of 1.5, that’s all the information you need to compute the exact probability of Brady throwing no TDs, one TD, two TDs, three TDs, etc.
Here’s the knock on Poisson: it often underestimates the variance of the distribution. If you fit a Poisson model to a set of data and then compare the actual outcomes to what Poisson would have predicted, you’ll likely find that extremely low and/or extremely high values are more common in the real world than in the Poisson estimates. Which brings us to our super secret rule:
Super secret rule: For Poisson to work, that one parameter, the mean, must be KNOWN. I’m not talking about estimated from data or estimated from a market number, I’m talking about KNOWN known, as in, “we know that the probability of two dice rolling snake eyes is 1/36” level of known. “But Matt,” you say, “in sports, we estimate everything from data and/or markets. Nothing is ever KNOWN known.” And I say to you: Precisely.
Here's an example. In Scenario A, Brady’s touchdowns per game is Poisson with a known mean of 1.5. In Scenario B, Brady’s touchdowns per game is Poisson with an unknown mean that could be either 1.0 or 2.0 with 50% likelihood of each.
Both scenarios have a mean of 1.50, but the probabilities of the more extreme events (zero and 4+) are quite a bit higher in Scenario B. The real world tends to look like Scenario B, which math geeks like me call “overdispersed Poisson.”
Fortunately for us, a distribution exists which is an overdispersed version of Poisson. Which brings me back to my answer to the question. My favorite distribution for counting events is something called negative binomial. Don’t be thrown off by its weird name, or by Googling it and finding that its original purpose had to do with counting the number of failures before a given number of successes. None of that matters. For our purposes, negative binomial works exactly like Poisson but it contains an extra shot of variance to account for the overdispersion. The cost of that extra accuracy is that negative binomial has two parameters instead of Poisson’s one.
Confused? If so, you’re not alone. This stuff is taught very poorly in schools, even in advanced university statistics courses. It took me 15 years of practice to fully get it. The nice thing is that once you do get it, it opens up lots of opportunities – my NFL Season Win Totals analysis is based on an overdispersed Binomial distribution.
Do you buy back when you have an in-game arb? If so, what is the calculation to figure out when and where? – Twitter @AmberGambling
I’m assuming that “in-game arb” refers to the situation where, for example, you have a pregame bet at +200 and you can take the other side in-game at -150 to lock in a profit. Is this a good idea? I’ll borrow a line from a classic Simpsons episode where Flanders asks Rev. Lovejoy if God is punishing him: “Short answer: yes with an if, long answer: no with a but.”
The short answer: Yes, IF the amount of money at stake is life-changing. The math of hedging with live bets is the same as the math of hedging in general, the only difference being that live bets usually come at the cost of higher vig than pregame bets. One of the most common mistakes made by amateur bettors is that they too often use -EV hedge bets to reduce their risk. It’s a weird psychological quirk that our “let’s gamble!” attitude that prompts us to make the bet in the first place goes out the window as soon as there’s the possibility to lock in a few pennies of profit. Don’t. Let it ride!
The long answer: No, BUT the cost of hedging can be greatly reduced if you can find a good number on your in-game hedge. Assuming you’re not originating your own in-play numbers, the way to find a good number is by line shopping. If the market in-game line is -150/+120 and you hedge at -150, you’re paying an extremely steep price to lock in your profit. If the market in-game line is -160/+130 and you can find a book that offers -150, your hedge is still -EV but not by as much. If the market in-game line is -170/+140 and you can find a -150, that hedge is neutral EV and if you feel like taking it, you can do it guilt-free.
You can line shop for live lines in the same way as you line shop for pre-game lines, with the obvious caveat that there’s a lot more time pressure when you’re betting live. To give yourself a bit more time, and to help avoid the book freerolling you with the dreaded “spinning wheel,” I recommend doing your live betting during commercial breaks.