If you start with a set of assumptions about how likely a particular event is, and you have some kind of logic programmed as to how one event effects another, you can use monte carlo simulations to simulate thousands of random iterations of these events and approximate the probability of a particular event happening.
Let's start with a simple example of a non real scenario with limited number of variables to remove a lot of complexity from the game.
In the game of football, we may have two playstyle's available to us to choose from or two players that influence the conversion percentage and we want to know what provides the best chance of producing a field goal. Let's just assume we are in over time and the other team has already punted so a fieldgoal wins. Let's also assume that if we punt or turn the ball over the game is over to eliminate complex decisions and turnover risks.
In fact, to further simplify, we aren't even going to look at 1st, and, 3rd and 4th down, we are looking at it as in a conservative strategy we either convert with 11 yards or we don't. In an aggressive strategy we either convert with 22 yards or we don't. The option A "small ball" we have to sustain a longer drive with a greater number of plays. The option B is an aggressive approach we have a lower conversion rate, but don't need as many conversions to get in field goal range.
We are hypothetically starting from the 20 yard line with 80 yards to go for a touchdown.
We will also say that for the short yardage approach we need 4 conversions which brings us about 44yards plus starting on the 20 puts us on the 36 yardline which is an over 50 yard attempt, but remember we also will gain short yardage plays until it's 4th down before we kick.
The aggressive approach means we only need 2 conversions, but we will have a slightly less makable fieldgoal if we don't convert as we will tend to either go incomplete or make a big play.
Now we can either do it backwards and determine how good one style has to be to be superior than another, or just make assumptions about the conversion rates.
Let's say we have a 70% chance per conversion using the "small ball" vs a 55% chance for the aggressive approach. We'll give an 85% chance of fieldgoal for the small ball approach vs an 82% chance for the aggressive approach. Which should we use?
Let's simulate:
Small Ball approach:
| Summary Statistics | |||||
| Average | 0.199 | ||||
| SD | 0.3991 | ||||
| Max | 1.000 | ||||
| Min | 0.000 | ||||
The result of the "small ball" approach is about a 20% chance of a fieldgoal based upon the assumptions made.
The aggressive approach:
| Summary Statistics | |||||
| Average | 0.248 | ||||
| SD | 0.4321 | ||||
| Max | 1.000 | ||||
| Min | 0.000 | ||||
The result of the aggressive approach carries with it about a 25% chance of a fieldgoal or better based upon the assumptions made.
This is a very basic simulation that requires acurate data and doesn't really model how much data changes.
[For a post about variable change and how blackjack and football are connected, check this post out by clicking here!]
So far these assumptions are only as valuable as the data, and only to a very specific situation.
One might think that if your conclusion is that the aggressive strategy scores more, it's better.
Not so fast! Football is a dynamic system of variable chaos. Everything impacts the system. The conservative approach leverages using time off the clock. Coaches also swear by "resting the defense" which is probably more related to actual time in real life than time off the clock, but time off the clock and time in real life tend to be correlated with number of first down conversions. Coaches also believe that more first down conversions wear out the opposing defenses, which should increase your chances of success later on. The high percentage strategy may be better at keeping the defense efficient throughout the game while also leaving a high efficiency for big plays in the future.
(In other words, a strategy that relies on fewer big plays early, the big plays work a higher percentage of the time later if you are losing and the risk of going 3 and out or punting is worth the increased chance of reward of a fieldgoal or better, or if you want to surprise them with a big play at any given point)
However, it's also true that a team attempting big plays more aggressively tends to loosen up the defense and open up the underneath routes as well as the run play will increase in effectiveness.. So over the course of the game it's difficult to say which is better without knowing ALL of the other variables including how your defense does against their offense and what strategy you anticipate your opponent could use.
Fortunately, this can be modeled in far more detail, far more accurately, although it may require a lot of data gathering and adjusting data based upon situations.
However, it's just another way to approach the problem if you like.
It also required a separate set of simulations after the punt and setting it up to calculate the back and forth without necessarily knowing the yardline. The idea was to simulate punts going 45 yards or ending as a touchback depending on field position, and fieldgoals would have to sort of complicate things.
Finally, the more accurate model requires a series of formulas of how things relate to another, and possibly even a series of basic playcalls and their expectations against other playcalls with those randomly selected weighted towards probability of usage in certain situations. THis would be a lot more work, but if you set everything up and modeled all decisions you could accurately model an entire game and play it out 10,000 times within less than 2minutes to determine how different strategies in certain situations compliment and effect the other.
I could go even more and set up infidividual players and personnel matchup that wear out at a particular rate per play run with them on the field and possibilities of injuries and effectiveness, but as you increase the accuracy it gets a lot more complicated to program the rules and situations and formulas.
I think if I were to run an NFL front office, I would get someone that programs and understands football enough to set up everything I'm looking for. I may look at # of defenders vs blockers "in the box" and try to estimate a distribution of all possible yards based upon every possible coverage and formation adjusted for the specific match up, but that's too much work for just a fan to do with limited programming skills without getting paid. But it's food for thought, and perhaps those trying to bet on vegas games would like to take the time to figure that stuff out.
For now it's useful to think about the process of optimization as looking at the odds, seeing how different pieces effect each other, and trying to make the best decision possible.
From my perspective, football analytics is not even in it's infancy yet, and most supposed decision trees are made based upon non football situations of "run or pass" without any information about how to run or distribute the ball or why or how it effects other specific players and changes probabilities of other plays working in the future.
Some may use it to look at college prospects, but to me that's the LEAST effective way to use analytics. The best way is understanding how peices fit into a system. For example, say someone always gets 2 yards and 2 yards only. That player is really bad if you just look at NFL averages, but that player is almost priceless if you only use him on 4th and less than 2, 3rd and less than 4 (with intention of going for it) or 3rd and less than 2 if you are not), and 2nd and 4 or less (or 6 or less if you plan on running on both 3rd and 4th down). This isn't remotely realistic, but the extreme demonstrates the principal. In this case, value of a player is dynamic and varies based upon the situation.
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