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All posts by Neville Aga
Playoff probabilities via Monte-Carlo
I have added a product to the playoffPredictor.com site that visualizes the percentage chances a team has to make the college football playoff.
PlayoffPredictor.com was launched with the express belief that if you knew who was going to win future games, you could accurately predict the top 4 in the final poll. If you know (or can predict) that Alabama is going to beat Georgia in the SEC championship game, can you definitively predict if Georgia will still make the college football playoff? Yes, you can answer that if you know how all the other games pan out (like Baylor beating Oklahoma State for example, leaving that slot open for Georgia).
The next logical place to use that data would be to iterate through each future scheduled game and using the probabilities of each team to win, exhaustively calculating the probability of each team to win the college football playoff. Unfortunately exhaustive scenario modeling is virtual computational impossibility. If you tried to enumerate every possibility (just for wins and losses, not even for margin of victory) from week 8 till week 14, you have about ~450 games to model. Given that a game only has two possibilities for the winner, this works out to 2450 = 2.9*10135 scenarios to model. How big is 10 raised to the 135? Well, I have seen estimates of the number of atoms in the know universe anywhere from 1085 – 10110 , so 10135 is many orders of magnitude larger than the number of atoms in the universe, and would take trillions of years to compute.
So do we give up modeling future probabilities? No, we introduce Monte-Carlo simulations. The idea is that if we know percentage chances for an individual trial (say Ohio State beats Penn State 85% of the time), we simulate that trial and the other 449 games a large number of times, and calculate who actually made the top 4. This is much simpler because you only have to compute 450 * 1,000 = 450,000 = 4.5 * 105 computations, and that can be done in a matter of minutes.
So, the new product is on playoffPredictor.com. After week 6 I like how my calculated data matches with reasonable expectations. We have Ohio State and Clemson most likely to reach the cfp at ~65% (because the ease of their championship games), followed by Alabama and Georgia at ~50% and 40% respectively. Same boring top 4. The challengers around the ~25% mark are Mississippi, TCU, and USC, and then 13 teams under 20%, including Syracuse at 14%. Could Syracuse make it? Sure – imagine this scenario:
- Tennessee beats Alabama twice (week 7 and SEC championship
- Tennessee, Florida, and Mississippi State beat Georgia (weeks 9, 10 & 11)
- Texas Tech and Baylor beat TCU (weeks 10 & 12)
- UCLA and Oregon beat USC (week 12 and Pac12 championship)
You could end up with undefeated Syracuse, Ohio State, and Tennessee coupled with winners of the Big12 and Pac12 at 2-3 losses each, and a 2-loss Alabama. In that (unlikely) scenario, you put in Tennessee, Ohio State, Alabama, and Syracuse. And variations of that are exactly what the computer came up with 140 times out of the 1,000 simulated seasons.
Enjoy the new tool, compare it with ESPNs probabilities through the season, and drop me a line at @CiscoNeville if you have any thoughts on this new visualization.
Elo predictions for college football – base and divisor
Ever thought about chess ratings? The highest chess rating ever for a human is held by Magnus Carlsen at 2882. The lowest is shared by many people at 100. The United States Chess Federation initially aimed for an average club player to have a rating of 1500. There is no theoretical highest or lowest possible Elo rating (the best computers are at ~3500 and the negative ratings are theoretically possible, but those people will get kicked from tournaments, so they arbitrarily set 100 as a lowest possible rating).
This particular range of numbers from 100 – 3500 is a consequence of the base and divisor that Arpad Elo chose. The Elo rating system for chess uses a base of 10 and a divisor of 400. Why? According to wikipedia the 400 was chosen because Elo wanted a 200 rating point difference to mean that the stronger player would win about 75% of the time, and people assume that he used 10 as a base because we live in a base 10 world. Interestingly if he would have used base 9 then 200 points would exactly be a 75% chance of win, where base 10 is more like 76% :
1 /(1+9(200/400)) = .25
1 /(1+10(200/400)) ≈ .2402
But enough on Chess. I like the playoffPredictor mathematical formula that puts the teams between roughly 0 and 1 instead of 100 and 3500. But what base and divisor do I use with that system?
Last year I went with base equal to the week number (1-17) and a divisor of .4. The reason for the week number is because bases 2-3-4 don’t exponent out to crazy scenarios, so in week 2 when there is very little data it does not make such drastic judgements. The divisor I picked empirically, it seemed to fit the data and it was also a callout to Elo’s 400.
Really though I have been doing some fiddling and I think a base of 1000 and a divisor of 1 will work better. Here are some spreadsheet results.
To read the above table, look at the row for 1000. This reads so if a team is better by .2 (like computer ratings of .9 and .7 for the 2 teams) then the .9 team as a 79.9% chance of winning. I need to model these against real life, but I feel this is a start.
Further for choosing a base and divisor the following are all equivalent pairs:
So 1000 and 1 give the same result as 10000 and 1.3333, or 100 and .6666. In the same way 1000 and 3 give the same result as 100 and 2, or 10 and 1. Log math.
So I’m going to move to a base of 1000 and a divisor of 1. The divisor of 1 make sense — take that out of the equation. Then, what base should you use? Empirically 1000 seems to fit well. I need to backtest with data from week 13-14 when ratings are pretty established to see how the percentages mesh with Vegas. To do.
At a base of 1000 and divisor of 1, a team with a rating +.16 more than an opponent will have a 75% chance of winning. So in this sense +.16 corresponds to 200 points in chess Elo.
In my rating the teams will be normally distributed with a mean at 0.5 and a standard deviation around 0.25. Meaning teams that are separated by 1 standard deviation, the better team has a 85% chance at success. For example, the following teams are all about 1 sigma apart:
- #1 Georgia (~1)
- #20 BYU (~.75)
- #70 Illinois (~.5)
- #108 Tulane (~.25)
- #129 1AA (FCS) (~0)
So Georgia has a 85% chance of beating BYU, BYU has a 85% chance of beating Illinois, Illinois has an 85% chance of beating Tulane, and Tulane has a 85% chance of beating a FCS school. Is that right? Not sure
Keeping with the logic, Georgia would have a 97% chance of beating Illinois [1/(1+1000^(-.5))]. BYU would have a 97% chance of beating Tulane. Are those right? I think so. Would need to check against Vegas.
tldr; PlayoffPredictor.com used to use week number and .4 for the base and divisor, but now uses 1000 for the base and 1 for the divisor.
Just how fast was Secretariat?
I’m a fan of Secretariat. I’m not sure why, but a lot of people are fascinated by this horse. I think that when you see greatness – something that is just clearly apart from all others, it just brings emotions out. Even Jack Nicklaus cried watching Secretariat win the Belmont in 1973, that should tell you something.
You can google quite a lot about how fast Secretariat was (37.7 mph / 2:24 flat for the Belmont), or even how big his heart was (22 pounds, when the average horse heart is about 9 pounds, and the next biggest horse heart on record is ~15 pounds), but those numbers, especially the speed numbers, are clinical. They don’t give the context to let you appreciate. Enter statistics:
It is a very easy statistical problem to look at all the Belmont winner times since 1925 (ever since the track was at its current 1.5 mile length). Secretariat is the record holder at 2 minutes and 24 seconds flat. The next closest horse is 2 minutes and 26 seconds flat. There are about 90 horses between 2:26 to 2:33. Here is the list:
YEAR HORSE time (seconds) Z score percentage 1973 Secretariat * 144.00 -3.01 99.870% 1992 A.P. Indy 146.00 -1.83 96.674% 1989 Easy Goer 146.00 -1.83 96.674% 2001 Point Given 146.40 -1.60 94.515% 1988 Risen Star 146.40 -1.60 94.515% 1957 Gallant Man 146.60 -1.48 93.080% 2015 American Pharoah * 146.70 -1.42 92.263% 1994 Tabasco Cat 146.80 -1.36 91.373% 1978 Affirmed * 146.80 -1.36 91.373% 1985 Creme Fraiche 147.00 -1.25 89.370% 2021 Essential Quality 147.10 -1.19 88.250% 1990 Go And Go 147.20 -1.13 87.049% 1984 Swale 147.20 -1.13 87.049% 1968 Stage Door Johnny 147.20 -1.13 87.049% 2004 Birdstone 147.40 -1.01 84.400% 2009 Summer Bird 147.50 -0.95 82.950% 1999 Lemon Drop Kid 147.80 -0.78 78.102% 1983 Caveat 147.80 -0.78 78.102% 2006 Jazil 147.90 -0.72 76.325% 1991 Hansel 148.00 -0.66 74.472% 1972 Riva Ridge 148.00 -0.66 74.472% 2018 Justify * 148.20 -0.54 70.549% 2003 Empire Maker 148.20 -0.54 70.549% 1987 Bet Twice 148.20 -0.54 70.549% 1982 Conquistador Cielo 148.20 -0.54 70.549% 1948 Citation * 148.20 -0.54 70.549% 1943 Count Fleet * 148.20 -0.54 70.549% 1975 Avatar 148.20 -0.54 70.549% 2019 Sir Winston 148.30 -0.48 68.489% 1965 Hail To All 148.40 -0.42 66.370% 1964 Quadrangle 148.40 -0.42 66.370% 1959 Sword Dancer 148.40 -0.42 66.370% 2016 Creator 148.50 -0.36 64.197% 2014 Tonalist 148.50 -0.36 64.197% 2005 Afleet Alex 148.60 -0.30 61.977% 1979 Coastal 148.60 -0.30 61.977% 1953 Native Dancer 148.60 -0.30 61.977% 1950 Middleground 148.60 -0.30 61.977% 1937 War Admiral * 148.60 -0.30 61.977% 2007 Rags to Riches (f) 148.70 -0.25 59.717% 1997 Touch Gold 148.80 -0.19 57.424% 1996 Editor's Note 148.80 -0.19 57.424% 1969 Arts And Letters 148.80 -0.19 57.424% 1967 Damascus 148.80 -0.19 57.424% 1962 Jaipur 148.80 -0.19 57.424% 1998 Victory Gallop 149.00 -0.07 52.770% 1981 Summing 149.00 -0.07 52.770% 1976 Bold Forbes 149.00 -0.07 52.770% 1955 Nashua 149.00 -0.07 52.770% 1951 Counterpoint 149.00 -0.07 52.770% 1974 Little Current 149.20 0.05 48.078% 1961 Sherluck 149.20 0.05 48.078% 1942 Shut Out 149.20 0.05 48.078% 1934 Peace Chance 149.20 0.05 48.078% 1947 Phalanx 149.40 0.17 43.412% 1938 Pasteurized 149.40 0.17 43.412% 2002 Sarava 149.60 0.28 38.836% 1977 Seattle Slew * 149.60 0.28 38.836% 1966 Amberoid 149.60 0.28 38.836% 1960 Celtic Ash 149.60 0.28 38.836% 1940 Bimelech 149.60 0.28 38.836% 1939 Johnstown 149.60 0.28 38.836% 1931 Twenty Grand 149.60 0.28 38.836% 2008 Da' Tara 149.70 0.34 36.601% 1993 Colonial Affair 149.80 0.40 34.411% 1986 Danzig Connection 149.80 0.40 34.411% 1980 Temperence Hill 149.80 0.40 34.411% 1956 Needles 149.80 0.40 34.411% 2017 Tapwrit 150.00 0.52 30.189% 1936 Granville 150.00 0.52 30.189% 1963 Chateaugay 150.20 0.64 26.217% 1958 Cavan 150.20 0.64 26.217% 1952 One Count 150.20 0.64 26.217% 1949 Capot 150.20 0.64 26.217% 1945 Pavot 150.20 0.64 26.217% 2012 Union Rags 150.40 0.75 22.532% 1971 Pass Catcher 150.40 0.75 22.532% 1935 Omaha * 150.60 0.87 19.159% 2013 Palace Malice 150.70 0.93 17.595% 1954 High Gun 150.80 0.99 16.115% 1946 Assault * 150.80 0.99 16.115% 2011 Ruler On Ice 150.90 1.05 14.718% 2000 Commendable 151.00 1.11 13.405% 1941 Whirlaway * 151.00 1.11 13.405% 2010 Drosselmeyer 151.60 1.46 7.207% 1930 Gallant Fox * 151.60 1.46 7.207% 1995 Thunder Gulch 152.00 1.70 4.495% 1944 Bounding Home 152.20 1.81 3.487% 1926 Crusader 152.20 1.81 3.487% 1927 Chance Shot 152.40 1.93 2.672% 1933 Hurryoff 152.60 2.05 2.023% 1932 Faireno 152.80 2.17 1.513% 1929 Blue Larkspur 152.80 2.17 1.513% 1928 Vito 153.20 2.40 0.815% 1970 High Echelon 154.00 (mud)
Its trivial in Excel to compute a mean of this data set (149.12 seconds) and a standard deviation (sample) of 1.699 seconds. From there you can see a Z score of each winner. I left out 1970 as the track was filled with mud (you can see that race here) . Leaving 1970 out moves Secretariat from a -2.93 to a -3.01, a true -3 Z score event. How rare is that? basic statistics says 99.7% of all data is between -3<Z<+3. So there is .3%, spread .15% in each tail — or that Secretariat happens less than .15% of the time. 99.87% of all Belmont winners will be slower. Put that in perspective with days: 1/0.13% is 770 — or it will take, on average, 770 years for a horse to eclipse Secretariat
Now this data is not perfect, normally you need 200 data points to have a good sample (What Carter Worth taught me). However, it is quite good. I’m sure we can bring in the 2nd and 3rd place finishers to get ~300 data points and still have about the same mean and standard deviation, but I’ll leave that exercise for someone else. Note this data is normally distributed, period. The central limit theorem states that no matter how horserace speeds are distributed, when I pull samples those are normally distributed.
For comparison here is how the top 45 finishers fare – note the 2:26 horses are a 1 in 30 year event. We will see 3 of those in our lifetime. But unless you are sticking around for the year 2750, you are not going to see Secretariat’s record taken down.
Losing my pinball machine
My parents moved us in 1981 from Pittsburgh, PA to Birmingham, AL. I was not pleased at the time to move again and lose my friends, so my parents bought me this pinball machine, that I played with for 40 years.
It was finally time to let it go, I sold it in an estate sale for my parents last month. The player 1 did not keep accurate score as the 1,000 wheel was broken, but the player 2 side did keep accurate score. Here is my last time flipping those flippers — 129,070. A very good score! At 150,000 it lit the special for the free extra play. In general any time I played and got over 100,000 I was happy
The room / area I like to stay at the grand Hyatt kauai
6034
2021 holiday letter
Dear Friends & Family, Christmas 2021
2021 has been a year I’ll remember for the Aga family. Life is good, and we continue to watch with wonder as our kids grow into the young people God has in store for each one of them. But 2021 was also a year of a missed opportunity for me.
Austin (23) is turning into a world explorer. He spent May in Italy with the OU in Arezzo program, and subsequently graduated from OU in June with his degree in advertising. He took advantage of the work-from-home trend and decided to start his career by moving to Seattle, Washington where he teleworks for Global Gear, an OKC based apparel company. On weekends he is exploring Seattle and the Pacific Northwest and hopes to continue his career with a northwest agency in 2022.
Evan (20) is in his second year at OU, which feels like a first year since last year as a university freshman all his classes were virtual with closed buildings. This year the OU campus feels open again, and Evan is living in an apartment east of campus, with a pair of roommates he has known since kindergarten. He bikes to his classes for engineering a couple times each day, which is giving him great exercise. He has grown well over 6 feet tall, and is easily the tallest Aga. He likes to take quick sprints (he does a half-mile in under 3 minutes ), and he spends weekends with the OU academic bowl team, including tournaments in Oklahoma and Texas.
Addison (14) is in her 10th year of dance at Massay’s, and her 2nd year of cheer at Whittier Middle School.
Emerson (14) is playing point guard for the WMS 8th grade varsity basketball team. She has a great team and group of friends, and she practices and gets better each day.
Addison and Emerson came with Shelli and I to Portugal this summer, where we got to explore Lisbon and Porto. We rented a car for a week and made it to the mountains that separate Portugal from Spain.
Neville’s parents Hoshi and Nergish decided to move from Birmingham to Norman to be closer to their grandkids. They have settled into a senior living center in Norman and Neville gets to drop by throughout the week. It is a very different dynamic than having them 700 miles away. They have gotten to see one of Emerson’s basketball games and weekly lunches with their kids and grandkids.
Shelli’s parents have had a challenging 2021 with Donnie getting a cancer diagnosis, but the great news is that reasonably early detection has given him a good prognosis, and he is feeling better now than he has felt at any time this year.
Shelli is active daily in her local yoga studio, fit and strong as ever. She is practicing headstands and keeping our family on track with all the events, activities, and homework of the girls.
As for me, after running what is likely my final half-marathon in October, I found out I have a broken heart (literally, not figuratively) and will need surgery in 2022 . I will finish up my night MBA program from OU this summer. Work at Cisco is humming along fine, I am in my 13th year of architecting networks at OU/OSU and school districts around the state. I did have an opportunity to move to the beach in Daphne, AL. Really a dream job for me at this career stage — Cisco security in commercial covering Alabama, Mississippi, and Louisiana. Looking back now I am very upset with myself for turning it down. I think about that bungled opportunity daily. I thought I was putting my girls needs ahead of my needs, but in reality I did not show the leadership and vision that the head of a family should show. At least now I know what was the biggest mistake of my life. One day soon I do want to get back to Alabama and the beach.
We hope this letter finds you well and thriving. Best wishes for a joyous holiday season and an exciting 2022.
Neville, Shelli, Addison, Emerson, Austin and Evan
Cisco Catalyst 9300 RFID identification
New Cisco switches come with a RFID tag. Need to do inventory? No need to move the switch all around looking for serial numbers, just use a scanner and read them in as you enter the room!
I bought a sub $100 scanner on Amazon (Thincol RFID reader) . It works as a keyboard — when it comes into contact with a RFID tag it energizes the tag and types out the info on the tag. This particular scanner works only with windows (or in my case a windows VM via virtualbox).
I was trying to RFID a switch with this serial:
| FCW2141L002 |
And when I used the RFID scanner, it outputted this info:
| 36142D8D4000B1E343AEC98B4633183064000000000000000000 |
So, how in the world do you get to the serial from that hex gobbledygook? Read on!
There is this article on cisco.com on RFID tag identification. It seems to be the only article out there. It has some good info in it, mostly behind the theory, but lite on practicality. What is output from the scanner is only the Electronic Physical Code (EPC) at 208 bits. The tag ID and user memory portion are not read/output (at least I could not get anything there). Of those 208 bits:
- Bits 1-8 are for the EPC header and say ’36’ in hex (0x36)
- Bits 9-11 are for the filter and read ‘0’ in hex (0x0)
- Bits 12-14 are for the partition and read ‘5’ in hex (0x5)
- Bits 15-34 are for the GS1 company prefix (whatever that is) and read on my switch ‘0B635’ in hex (0x0B635). Note this is different than the example given on cisco.com which is 7 characters: 0746320
- Bits 35-58 are for some item reference (again, whatever that is) and read ‘0002C7’ in hex (0x0002C7)
- Finally bits 59-135 are where the serial number is
This is very non-intuitive (hey, it’s Cisco, not Meraki). Speficially if you look at the first 2 bytes that come back on the scanner (3614) – the 36 maps exactly to 36 for the EPC header, but the next byte (14) the “1” maps to all bits 9-11 for the filter (all zeros) and 1/3 of the bits 12-14 for the partition (specifically the first 1 in 101). The first half of the “4” maps to the rest of the filter 01 and the last half of the “4” maps to the first part of the GS1 company prefix (00). Confused? Yes you are.
Now the simple thing to do is put the string you get back from the RFID scanner in a HEX to binary converter like this one. Then on the resulting string back will be 206 bits long, like this
11011000010100001011011000110101000000000000001011000111100011010000111010111011001001100010110100011000110011000110000011000001100100000000000000000000000000000000000000000000000000000000000000000000000000
Why 206 bits and not 208? There are 0 leading zeros you have to put in for the ’36’ on the EPC header. So add in 2 leading zeros and you get:
0011011000010100001011011000110101000000000000001011000111100011010000111010111011001001100010110100011000110011000110000011000001100100000000000000000000000000000000000000000000000000000000000000000000000000
Now that you have 208 bits, you want to grab bits 59-135 (because you want 77 bits starting at position 59). Getting that out gives you:
1000110 1000011 1010111 0110010 0110001 0110100 0110001 1001100 0110000 0110000 0110010
(spaces added every 7 bits for readability)
Then you take those bits (with the spaces every 7 characters) and put them into a binary to ASCII converter: and you get: FCW2141L002.
Voila! FCW2141L002 from 36142D8D4000B1E343AEC98B4633183064000000000000000000
Final weekend – CFP chances
Heading into Saturday morning here are the playoff chances for each team:
Georgia – 100% – lock
Alabama – 83% – In with a victory vs Georgia, or any Michigan, Cincinnati, or OK State loss
Cincinnati – 70% – In with a win over Houston
Michigan – 65% – In with a win over Iowa
Oklahoma State – 51% – In with win over Baylor EXCEPT if Alabama, Michigan, Cincinnati all win, or in with Georgia, Michigan, and Cincy all lose.
Ohio State – 17% – In with Georgia & Michigan win, Cincy & OK State loss, OR Georgia win, Michigan & Cincy loss, OR Georgia & Cincy & OK State loss, OR Georgia, Michigan, Cincy and OK State all lose.
Baylor – 13% – In with: Baylor beats OK State, Iowa beats Michigan
College Football week 11 probabilities
I have been messing around with playoffpredictor.com. Still have a long way to go, but I thought I would look at the data for this weeks games and see how it compares to betting available at Draftkings money line. I am looking to exploit situations where the moneyline payout is misplaced compared to the predicted winning probabilities from playoffpredictor.com.
When the expected value on a moneyline bet is greater than 100%, I want to bet that game/team. In this weeks top 11 games, there are 6 games that the computer believes you can make a bet and get an expected payout in excess of 100% of the bet.
The most appealing, from the computer standpoint, is taking Purdue to beat Ohio State, with an expected payout of $2.89 on a $1.00 bet. This intuitively makes sense as Purdue is ranked #19 by the computer (and also #19 by the committee), and #19 beating #4, especially when played in #19 stadium, is very reasonably possible. Probable? no, but the payout at +750 is a huge incentive to bet on Purdue.
The least appealing bet by the computer is Penn State over Michigan, with an expected payout of 57 cents on a $1.00 bet.
Georgia vs Tennessee
Georgia (-1250) Total return on $1 bet if bet is successful (Georgia wins) = $1 * 1350/1250 = $1.08 P(Georgia wins) = 91% Expected return of $1 bet on Georgia = $1.08 * 91% = $0.98 Tennessee (+750) Total return on $1 bet if Tennessee wins = $1 * 850/100 = $8.50 P(Tennessee wins) = 9% Expected payoff of $1 bet on Tennessee = $8.50 * 9% = $0.765
Georgia – Tennesse is what is expected — each bet is expected to have a negative return — the house wins both ways.
But sometimes the computer spots something it likes
New Mexico State vs Alabama
No moneyline offered on New Mexico State vs Alabama
Cincinnati vs South Florida
Cincinnati = $1.01 South Florida = $0.36
Michigan vs Penn State
| moneyline odds (DraftKings) | unbiased probabilities (playoffpredictor.com) | Total expected return on $1 | ||
| Georgia | -1250 | 0.91 | 0.98 | |
| Tennessee | +750 | 0.09 | 0.77 | |
| Alabama | 0.98 | |||
| New Mexico State | 0.02 | |||
| Oregon | -630 | 0.78 | 0.90 | |
| Washington State | +450 | 0.22 | 1.21 | |
| Ohio State | -1250 | 0.66 | 0.71 | |
| Purdue | +750 | 0.34 | 2.89 | |
| Cincinnati | -2200 | 0.97 | 1.01 | |
| South Florida | +1100 | 0.03 | 0.36 | |
| Michigan | -115 | 0.71 | 1.33 | |
| Penn State | -105 | 0.29 | 0.57 | |
Oklahoma vs Baylor
Mississippi State vs Auburn
Northwestern vs Wisconsin
Utah vs Arizona
Purdue vs Ohio State
Minnesota vs Iowa
Southern Miss vs UTSA
Maryland vs Michigan State
Texas A&M vs Ole Miss
Notre Dame vs Virginia
NC State vs Wake Forest
Arkansas vs LSU
TCU vs Oklahoma State
Washington State vs Oregon
Nevada vs San Diego State
Results will be posted next week!