How to evaluate tournament team

[allenciox]

So.... I wanted to examine a question: how do I determine how good your tournament team is compared to other teams?

I was looking at this question, and it turns out, you can figure out quite a lot from looking at your tournament history. Just hit the button "Show traditional tournaments" after logging in, select the tournament type info from the dropdown lists that you are interested in, choose "Only Finished" for Status, and then click the tab "Your tournaments". The image is from where I have done this for my bronze b07-t32 tournaments (pretty much the only tournament type I currently play). What you want to record is the total number of tournaments you have played, and the number of times each "status" was achieved (winner, 2nd place, and 3rd/4th place in the case of b07-t32 tournaments). You don't have to examine the tournaments or anything. An easy way to total up the tournaments is to count the number on one screen, then scroll one page at a time until you get to the end, and just count your number of scrolls, multiply by the # per scroll, and count up the extra lines on the last screen.

So with that information you can address the following questions:
1. How many "packs" am I earning relative to the "expected" number of packs?
2. Am I one of the top tournament players, am I better than average, or worse than average?

With that info, you can decide whether you need to adjust your team.

So I actually tally this information every couple of days, and then see how I am doing relative to expectation. But I realized that I can actually determine "a lot" more information than I thought, by using some math and a simple spreadsheet.

So, here is my data across two teams for bronze b07-t32s since after the first "weekend" of OOTP 22:

1069 tournaments, 74 wins, 70 2nds, 119 3/4 finishes. In all, assuming 10 packs for first, 5 for second, and 3 for 3/4 finishes, I have received 1447 packs, or 1.35 per tournament. The "expected" number would be 10 + 5 + 3*2=21 per 32 tournaments, or .656 per tournament. So I have received a bit more than twice as many as the "expected" number, so I can judge that my team is better than average. But, how much better, and how many better players are out there than me?

So what I realized is that I get a lot of information regarding the percentage of time I am winning the last two rounds. Based on my 1sts and 2nds, I have been winning 74/144 =51.4% of the time I am in the final round, and 144/(144+119)=54.75% of the time I am in the semifinal round. The probability that I will "place" in a tournament is (74+70+119)/1069 = 24.6%

Here is where the "math" comes in. Suppose in a pairing of two teams, one of the teams is favored to win p% of the time. What are the odds that that team is going to win that series?

Well, of course, the result depends on the series length, and it can be determined based on the binomial distribution. Thankfully, Excel, OpenOffice (and I assume Google spreadsheets) has a function, called binomdist, that can figure it out. For a best-of-seven series, you can use binomdist(3;7;p;True) to indicate that you want to determine the percentage of time that a team that has p% chance of winning will win three or fewer times in seven games. For a best-of-five, it would be binomdist(2;5;p;True). That would indicate the probability of "losing" that series, you can use 1-binomdist() to determine the probability of winning.

So I constructed a spreadsheet to determine what my results indicate about my chances of winning.

Here is the result:

Rnd	p(win)	P(Rnd)	P(remain)
1	58.00%	67.06%	67.06%
2	56.00%	62.94%	42.21%
3	54.00%	58.69%	24.77%
4	52.00%	54.37%	13.47%
5	50.50%	51.09%	6.88%

Here, that P(Rnd) column indicates the probability that I am going to win the round, based on that binomdist() function assuming that my average probability of winning any game is in the first column.

So, one problem with this is that the figures that we can estimate are the P(Rnd) figures for the fourth and fifth round. But that is where the spreadsheet can be helpful. I played with entering different values in the prob(win) for the fourth and fifth rows that would correspond, once the binomial is computed, for the observed values in the second column for those rows. Once I have that, I can estimate the p(win) rates for the first, second, and third round until I get the observed p(remain) results for the third round (indicating my probability of placing). As you will note, the results in the spreadsheet come extremely close to the results I am getting in actuality.

This suggests that my team has a 58% chance of winning a game against an "average" tournament team (i.e. one that I would face in the first round), but pretty close to even money that I would win against a team in the final round. Since some of that time the final round is against a team that just "got lucky", this suggests that there are probably at least a couple of teams in a tournament that are better than mine, so I can still improve my team a bit --- though I am probably in the top three or four teams in the average tournament.

So, what about a situation that the "average" tournament team faces? Well, we can extrapolate from my results something like the following:

Rnd	p(win)	P(Rnd)	P(remain)
1	50.00%	50.00%	50.00%
2	48.00%	45.63%	22.82%
3	46.00%	41.31%	9.42%
4	44.00%	37.06%	3.49%
5	42.00%	32.94%	1.15%

in other words, that team places only 9.4% of the time, gets second 3.49%, and wins only 1.15% of the tournaments they enter. They would expect to win 0.41 packs in an entered tournament, or only .41/.656= 62.5% of the "expected" packs. This was a surprise to me, that an average team would fare so poorly. It is due to the 7-game series structure. In a do-or-die, 3-game series, or 5-game series, their odds would be much better. The seven game series structure favors the best teams at the expense of the average or below average teams. So if you have a par or sub-par team, you should probably play the shorter formats.

So, one thing about bronze tournaments is that, by this time, the best teams are not that much better than the average team. When I look at teams in bronze tournaments, just about every team has Paige, Bonham, and Gross as three of its five starters. The "meta" is pretty well-known by now. So the "variance" between teams is less.

So, what about a different tourney structure, one whose "meta" isn't as well known by now (for example, gold tourneys?).

Well, let's take a hypothetical where someone has built a pretty good, but not great, team in such a structure: one whose team will win 60% of the time against an average team, but is actually slightly worse than the average team in the finals. The result might look like this:

Rnd	p(win)	P(Rnd)	P(remain)
1	60.00%	71.02%	71.02%
2	56.50%	63.98%	45.44%
3	53.50%	57.62%	26.18%
4	50.50%	51.09%	13.38%
5	48.00%	45.63%	6.10%

So, here, they end up with almost exactly the same "expected" number of packs (1.358) as in my actual bronze example (1.357) earlier: they will win more games, but will not get better results overall. And because they go deeper in tourneys before losing, they will actually be able to enter fewer tournaments total, so the result in time lost is greater. Of course, a team that is one of the best in that format will do much better than a "best" team in the bronze format.

Just some interesting notes.

[vyshka]

Been a long time since I last studied math and statistics. Is there a function that can go from the result of the cumulative distribution function and give you the probability for the event? So you could go from your success rate for a round and determine your likely game win rate?

[RunninYakAngler]

My Bronze tourney team with Rose, Baines, Raines, Moose, Guidry, Satchell, Nathan, etc. is getting way up there in price and while usually going to the quarterfinals, they're just as likely to get beaten by a team full of Lives. I think it mostly depends on how fresh the bullpen stays. If the other team sweeps and your team survives a long 7 games series, you're probably getting beat in the next round no matter how much better your team is.

Really amazing information/stats/math. I've often wondered how well my team is doing compared to others. I've felt that since I win/get packs more than once every 32 entries I should be doing at least average.

[bailey]

Understanding that your team is above or below average by looking at results doesn't help you improve said team. I haven't won a pack since the update, so I don't have to do any fancy pants computation to realize that my team is no good.

[jeffstified]

Interesting...I just posted my results in another thread and commented how I have no idea if their good, bad or somewhere in between.

Going back to 4/16, I've entered 287 Bo7 Bronze tournaments. I've won 261 packs or 0.909 per tournament. About 1.4 times expected. Not nearly as well as you. Although, if I look at just last week, that number goes to about 1.8 times expected.

I'm pulling all the stats, so using Pitcher Wins I can calculate my record in each round.

Rnd  W-L
1   176-111
2    91- 85
3    50- 41
4    28- 22
5    11- 17

If I use my actual winning pct for each round as p(win), my chart looks like this:

Rnd	p(win)	p(Rnd)	p(Rem) Actual
1	61.32%	73.5%	73.5%  61.3%
2	51.71%	53.7%	39.5%  31.7%
3	54.95%	60.7%	24.0%  17.4%
4	56.00%	62.9%	15.1%   9.6%
5	39.29%	27.6%	4.2%    3.8%

The last column is the number of series wins divided by number of entries (287). Looks like I'm underperforming expectations. Is that how you would read that?

I know when I make it to the finals, my team is usually pretty exhausted. I've been working on improving that.