Honestly, I really like the markov chain idea - given the last shot what is the next shot type deal. Lets us sim out each frame/match and generate lines that way.

For sure, if you and or Diced want to code the Markov model out go for it. Afterwards, I can post what I projected for the moneylines, spreads, totals etc. from the recent quarter, semi, and finals if you want to see how close the different granular approaches are to each other and the market.

Re Markov chain, pretty sure a few top players have an empirical notion of it, i.e. when to risk a low % pot chance with a reward of 16 subsequent 95% pots and a winning frame. Selby as much as anybody. Bingham seemed to change his strategy early in the match toward Selby's style and at one point was up 12-9.

Slow pony here, thanks.

Do we even have the data needed to do a markov chain? Seems like we'd need more shot by shot type stuff than we have.

2021-22 snooker schedule out: http://www.snooker.org/res/index.asp...=2&season=2021

Think that is rather implied odds?

Overall shouldn't a model of the game be based on defence and attack?

Defence broadly being assessed on the % that when scoring zero, the opponent does not score at their visit.

Attack based on scoring average when in a break.

A final stat could look at whether the opponent scores when the break ends (ie identifying how a player manages risk).

What’s a snooker

The following stats are compiled by the TV production team:

-Safety %: a non-potting shot which results in no pot success for the opponent;
-Short pot success %: A shot less than 6 feet resulting in a pot;
-Long pot success %: A shot more than 6 feet resulting in a pot.

I don't think these stats are archived anywhere, unfortunately.

I don't believe there is a stat collected for pot attempted and failed yielding opponent's pot success.

Markov chain model can be represented by a state matrix and a transition matrix. The model would then use different transition matrices (based on player skills and available options) to yield the next state. The state matrix should describe the opportunities for potting a red/color, and safeties.

Typically players look at least a few shots ahead, so the state matrix should account for that to some degree.

Meme version of pool basically

off betting topic but on topic recommended watch - Gods of Snooker ...

Are there any tennis databases that track whether a player serves or receives after winning the coin toss?

Edit: Although I suppose just taking a look at the first set game 1 serve/receive ratio might give me a pretty good idea of their preference

I haven't seen that. The player that serves first wins the matches more than they should -- maybe 52%. I always assumed that all players would choose to serve first.

I agree that it makes sense to serve first. But I saw a women's match the other day where the coin toss winner chose to receive. The announcers were offering praise, saying things such as it will allow her to get settled in a bit before serving on the second game. So I don't know if that is the conventional wisdom, or if there's a lot of variation amongst players, or if the player was an outlier, or if it is just more of a women's thing to receive first.

I am brainstorming some ideas for a model focusing on tennis total games, and realized it would be valuable to know each player's preference. This seems really obscure though to record on any stat sheet or point-by-point log. Although if it's true that only a small percentage of players prefer to receive, they will be easy to spot when combing through the data.

Not a big tennis guy, but wouldn’t serving first mean you have an extra serve if it goes an odd number of games? Seems like enough of an edge that everyone should do it, but maybe the math isn’t strong enough for some women where the break % is a lot higher.

It shouldn't matter since you have to win by two, thereby giving your opponent an opportunity to break back. And you only win when your opponent fails that opportunity.

If the poster above who said that serving first shows a long term advantage of 52% is correct, I have a few guesses why that would be:
1) Some psychological boost of winning the first game
2) Motivational boost of knowing you need to break back to survive after you've been broken (as opposed to getting broken at 5–6 and immediately losing)
3) The balls are slightly fresher. Balls are changed every nine games (after the first seven games since they also use them to warm up), and the older and fluffier they are, the slower they are, and the better it is for the returner. So if there are three ball changes during a match, and you get fresher balls twice, that's a tangible advantage.

The biggest factor would be the pressure of serving second while 'behind' a game constantly. Same reason teams taking the first penalty in soccer win penalty shoot outs more often.

Would be interesting to see whether shooting first is an edge in the NHL or not over a big enough sample

New exercise for the group. Many books offer a series wager for MLB teams. When teams play a four-game series, some books offer a two-way line with a 2-2 series tie being a push. Others offer a three-way line with a tied series being a betable option. Here is an actual scenario for today.

Two-Way
Tigers +271
White Sox -335

Three-Way Line
Tigers +750
White Sox -180
Tie +215

Where would you rather bet each side and why?

As a simplifying assumption, let's assume for now that every game has equal probability. If you bet $1 on Tigers, here's a plot of your EV versus the probability that tigers win a single game. I'll plot it from 0 to 0.5 since tigers are the clear underdogs.



The 3way EV is always greater than the 2way, so you would always prefer 3way Tigers over 2way Tigers at those odds.

Betting on White Sox is a bit more interesting since the EV lines cross each other.



There's no way White Sox are 80% though, they're like 65% based on vig-free odds. So realistically 2way White Sox is always better than 3way White Sox.

Code

Now here's something interesting. If you bet $1 on white sox 2way and $1 on tie, what does your EV graph look like? (Orange line is just y=0, above it is +EV)



As long as W.Sox are between .57 and .69 to win a single game you're making a +EV bet between 0 and 4.5% ROI (under our extreme assumption that every game is equally likely). CWS were .68 today and .63 tomorrow based on vig-free odds.

Whoops had a bug in my code. Here's the fixed graphs. Same conclusions, 3way tigers > 2way tigers, 2way w.sox > 3way w.sox. For the $1 w.sox 2way and $1 on tie strategy, the corrected version actually makes the +EV window .52 to .67

Corrected Graphs
Corrected Code

$1 on 2way w.sox and $0.60 on tie looking pretty respectable though.
https://i.imgur.com/XXx0Juh.png

Nice job, you get a gold star. I like your approach since it looks at the EV for a range of possibilities.

Alternate solution

Intuitively, this made sense to me, but the math was telling me otherwise. But I guess the math is only suggesting that serving first makes you (slightly) more likely to win more games, but would be neutral for winning sets/Matches.

Looking at a simple example. If you win in straight sets with an early break in each set...

Serving first you would win 6-3, 6-4, 6-4

Serving second you would win 6-4, 6-4, 6-4.


I do find the 52% number interesting then, but I guess the psychology aspect makes sense.

Oh that’s a nice one