Forgive me, I’m putting forth a mathematical case study here. One that I don’t know the answer. Maybe somebody can set me straight.
Say you’re doing a replay of a 162-game season for just one team. During the course of the season, the team you are playing as well as the other teams rack up wins and losses and therefore a winning percentage. However, this is a replay of a simulated season and even though you aren’t playing them, theoretically, the other teams do play each other and not just your team you are playing.
My question… is there a way to extrapolate an accurate won-loss percentage based on only games that you’ve played against the team you are replaying?
For example, let’s say I’m doing a dice replay of the 1976 season but I’m only playing the games of the 1976 Reds. For simplicity’s sake, let’s say the Reds have played each team in the West Division six times (let’s pretend the East Division doesn’t exist for this scenario) and the Reds went 4-2 against each team. Theoretically, that would mean every team in West has played each other roughly the same number of games. That gives the Reds a 20-10 record and every other team (including a pretty good Los Angeles Dodger team) a 2-4 record in my replay.
Now in real life though, Los Angeles, who went 92-70 in real life, would have also been playing teams like Atlanta and San Diego and most likely won a few games against them. It’s just that you had decided not to replay those games.
Now what if LA had gone 3-3 against the Reds in our example? Would there be a formula or method to show that their team must have in theory done pretty well in the first 30 games of the season? Since they went 3-3 against a 20-10, their projected record would certainly be better than .500, wouldn’t it?
Is this something other replayers worry about when they do a single team season replay? Is the answer smack dab in front of my face? Or am I just too over-concerned about something that really doesn’t matter in the long run?
I’ve been doing APBA and Strat-O-Matic replays for a couple years now and I use Whatifsports.com website to sim the games I’m not playing. It does add some time to your simulation, which is why I typically only play a 72-game shortened season (that and I do seasonal sims for hockey, football, and basketball as well), but I find it to be highly accurate. I reccomend checking it out when you have some time.
Not sure if this will help or may be even relevant. Somewhere in the 2000/2001 timeframe someone on ABTL posted a link to download “Fastplay Charts” for various seasons. Each team was given a rating between 11 & 66. If you decided not to play the game entirely you could roll the dice and based on the result determine who won the game. Here is an example from 1953 AL:
StL vs NYY (H)
New York’s rating against the Browns was 54 so if you rolled the dice and the result was 54 or less then the Yankees won the game. Had the result been 55 or more than the Browns won. Now had the Browns been the home team their rating was 22 against the Yanks. Had the dice roll been say 16 then the Browns won the game.
I believe the gentleman who created this took into account win-lose records for each team against the other seven teams to come up with the rating for home and away games. It was done for both leagues so if you wanted to play a whole season you could concentrate on the single team and “Fastplay” the rest of the schedule. These “Fastplay Charts” started out as a free download then when they became more popular you had to pay for them. I downloaded a few seasons before they went on sale. I wish I had done more but didn’t have the time to make it happen. Two names that pop up as possible developers of this were Dave Sayers or Dave Morris but I am not going to swear to it. I hope this gets you in the right direction for what you are looking for.
Walt Taylor
thanks Walt. I’ll have to see if I can find it.
Anyone come up with anything on this? I’m working through a Pirates replay and would love to get the rest of the standings without having to play all those games.
*** WARNING: POSSIBLY BAD MATH BELOW. PROCEED AT OWN RISK ***
Another option I use is to use calculate the probability of Team A beating Team B and then random-number generator at random.org to get a 000-999 number that does or doesn’t fall within Team A’s expected winning percentage. Team A has a .692 chance of beating Team B & the random.org result is 691 or lower (gotta remember 000 counts as a Team A win here), then A wins. 692-999 and B gets the win.
Calculating A/B expected winning percentages, well, to be frank, I’m not entirely sure the math is right, but it’s similar to what I think Log5 does. At any rate to me it makes sense and gives intuitive results. As an example:
1) Both teams are .500 teams, Team A’s expected win% = .500
2) A is a .600 team, B is a .500 team. A’s ExW% = .600
3) A is a .600 team, B is a .400 team. A’s ExW% = .692.
4) A is a .400 team, B is a .450 team. A’s ExW% is .449
Calculation: Ratio of Team A’s winning percentage * Team B’s “losing percentage” to the reverse. In the third example (A=.600/B=.400), multiply A’s .600 W% by B’s .600 L% and we get .36. B’s .400 W% * A’s .400 L$ = .16. Ratio of .36 to .16 gets A a 69.2% chance of winning. Then off to random.org
Again, there might be disasterously bad logic in that, but it works for me (and quick once you write the spreadsheet).
Just a thought.