Stern Pro Circuit Final 2020

How great was Jason Werdrick’s run?

Published

September 12, 2026

The 2020 Stern Pro Circuit final was 20 player ladder tournament, which started with the 4 lowest-seeded players and eliminated the lowest scorer every round to bring in the next lowest remaining seed. Jason Werdrick started in the first round and advanced in an impressive 16 consecutive games before being eliminated in 5th place.

I’m going to say ‘win’ a lot when ‘advance’ would maybe apply better. But just know I mean not-loss in a given round, not winner of the entire tournament.

(Stern Pinball 2023)

That seemed like quite a run, but it got me thinking about post-hoc analysis and how unlikely this actually is. Since you only have to be not-last to move on, and maybe my intuition is wrong and someone was likely to have a winning streak that long.

Here’s how the tournament turned out

rank	player	seed	rounds_won	ifpa_rating
1	Karl DeAngelo	6	8	1931
2	Aleksander Kaczmarczyk	5	6	1932
3	Escher Lefkoff	2	2	1943
4	Steven Bowden	1	0	1651
5	Jason Werdrick	17	15	1680
6	Raymond Davidson	3	0	1831
7	Keith Elwin	4	0	2062
8	Lydia Lewis	8	3	1855
9	Andrew Rosa II	13	7	1880
10	Bowen Kerins	7	0	2016
11	Jim Belsito	10	2	1876
12	Andy Rosa	9	0	1724
13	Colin MacAlpine	11	1	1779
14	Brian O'Neill	12	1	1727
15	Eric Stone	16	4	2024
16	Zach Sharpe	18	4	1704
17	Joe Lemire	14	0	1863
18	Trent Augenstien	15	0	1646
19	Luke Nahorniak	19	1	1734
20	Derek Price	20	0	1689

Negative binomial

Here’s something that doesn’t work.

Assume each player is equally skilled and has the same 1 in 4 chance of not losing in round. The distribution of games won is negative binomial. Then if each player is independent, we can use one of my favorite results about the distribution of order statistics to compute the maximum number of games a player would win in sample of 20 players

Order statistics are ranked observations from a sample. The first order statistic \(X_{(1)}\) is the minimum and the last \(X_{(n)}\) for a sample of size \(n\) is the maximum.

\[ \begin{align} P(X_{(j)} = x) &= P(X_{(j)} \leq x) - P(X_{(j)} \leq x - 1) \\ P(X_{(j)} \leq x) &= \sum_{k=j}^{n} \binom{n}{k} F_X(x)^k (1-F_X(x))^{n-k} \\ \end{align} \]

So \(P(X_{(20)} = x - 1) = F_X(x - 1)^{20} - F_X(x - 2)^{20}\), where \(F_X\) is the cumulative negative binomial distribution and we shift everything down one cause that counts games played and we’re interested in wins. The distribution of the longest win streak looks like

This color is Stern red:#CF2E2E

That model is cute, but there are a bunch of problems with it. Win streaks aren’t distributed as negative binomial, cause the support isn’t right, it takes at least 3 games to win the tournament and it eventually ends, so nobody can win more than 19 games. Players don’t have the same, independent probability of losing the underlying games; it’s skill dependent and most players in a round are also in the next round.

Worse, even if we knew the distribution of the number of wins, we can’t just do the cool order statistics thing. Since players compete against each other, their longest win streaks aren’t independent–every match I lose makes 3 other player’s streaks longer.

That’s intimidating, so I pre-emptively gave up on the math to do a simulation.

Simulated win streaks

Uniform win probability

To start, assume players have the same win probability (which is not unreasonable–these are 20 of the best tournament players in pinball).

# given a set of players and their relative win probs, return the longest streak
sim_ladder <- function(skill_data) {
  # initialize results and first active players
  seed <- 1:20
  round_out <- rep(NA, length(seed))
  active <- 20:17
  
  # check for glicko-like names
  skill_type <- 
    if (all(c("r", "rd") %in% names(skill_data))) {
      "glicko"
    } else {
      "raw"
    }
  
  # sim tournament
  for (round in 1:19) {
    # get skills for active players
    skill <- 
      if (skill_type == "glicko") {
        skill <- compute_p_lose_all(player_data = skill_data,
                                    player_seeds = active)
      } else {
        skill <- skill_data[active]
      }
    
    # sample loser weighted by skill
    loser <- sample(active, 1, prob = skill)
    
    # remove loser
    active <- active[active != loser]
    # record info 
    round_out[loser] <- round
    
    # add next active player
    if (round < 17) {
      active <- c(active, 17 - round)
    }
  }
  
  # assign winner to phantom last round
  round_out[active] <- round + 1
  
  return(round_out)
}

It surprises me that the median win streak is so high. My initial intuition was more like 5, but since each game has 3 ‘winners’ by our definition, I was underestimating the number of ways streaks can exist.

Player skill

What if we don’t assume all players are equal? I would expect the distribution of the longest streak to shift left, because players with longer possible streaks are lower seeds and are more likely to lose.

We can pull Matchplay skill estimates from the day of that tournament (October 19, 2022) for that. My understanding is that these use Glicko, which gives pairwise comparisons, so how do we translate that into win or elimination probability?

One (possibly bad) way is to think of a 4 player match as \(\binom{4}{2} = 6\) head-to-head matches and model those win probabilities, then find the probability of each player losing to every other player. That won’t make a probability distribution over the 4 players because they don’t add to 1, but we can treat them as ‘relative risks’ of losing to everyone and scale them up.

I know there are papers out there about rankings for multiplayer games, but that’s a topic for another day. Perhaps never.

Glicko, quicko

\[ E = \frac{1}{1 + 10^\frac{-g \big( \sqrt{RD_i^2 + RD_j^2} \big) (r_i - r_j)}{400}} \]

where \(g(x) = \frac{1}{\sqrt(1 + (3q^2x^2)/\pi}\) and \(q = \frac{\ln(10)}{400}\)

For Matchplay.events: provisional rating 1500, max rd 125, min rd 15, system constant 3.7775 (Matchplay.events 2026)

For example, consider the first 2020 Stern Pro Circuit Final matchup.

seed	player	ifpa_rating	matchplay_rating	matchplay_rd
17	Jason Werdrick	1680	1762	25
18	Zach Sharpe	1704	1790	29
19	Luke Nahorniak	1734	1795	23
20	Derek Price	1689	1769	24

The resulting pair-wise matchups, in this example Luke Nahorniak is slightly favored over all other players (since this is based on ELO and nothing else, the highest ranked player will always be ranked over all others, no rock-paper-scissors effects).

Then we can compute the probability (assuming independence) of each player losing to every other player (which is a proxy for coming in last), then normalize that to get a probability distribution of coming in last.

Independence is the part that I think hurts this the most, since a bad game in a head-to-head matchup would only cause one loss, but in a 4 player game would be 3 head-to-head losses.

p1	p_lose_all	normalized
Derek Price	14%	28%
Jason Werdrick	15%	30%
Luke Nahorniak	10%	21%
Zach Sharpe	11%	22%

Apply to Monte Carlo

It’s…similar enough to uniform. Longer streaks are slightly more likely, the opposite of what I expected. Maybe lower seeds were under-seeded relative to their Matchplay rankings.

Jason’s 15 win streak is still somewhat surprising, but not eye-popping. Under this model, about 15% of the time someone was going to have a streak at least that long in this ladder format.

Simulated tournament

We’re basically simulating the whole tournament, so let’s look at individual player results to see if it’s doing something reasonable. Bars here are 5% quantiles of rank from the simulation and dots are the observed ranks.

I don’t have much to say about this besides that looking at the marginals for each seed could be misleading cause long streaks necessarily mean other players have shorter ones. We could look at ‘rounds played’ instead and at least they’d all start at the same point but I think that would mostly just left-align this graph.

Perhaps more interestingly, here’s the simulated probability of winning the entire tournament for each player. The red line is the ‘uniform skill’ win probability (which comes from the tournament structure, since the player with seed \(i\) has to play \(i\) 4-player games, one 3-player game, and one 2-player game to win it all).

The differences from that line are differences from equal Elo, magnified by the rank. Steve Bowden is a great player, but he’s far below the line here because his win probability is far from zero and most of the time he’d have to beat Escher (who has 4 career major championships), Ray (3 majors), or Keith (11 majors) to win the tournament.

Note that Elo isn’t skill, kind of like how IQ isn’t intelligence. It’s a model parameter constructed to hopefully be high when our operational definition of skill (beating players especially those who tend to beat other players) is also high.

This does make me want to learn more about IFPA’s ranking system, how it handles multiplayer matches, and what fundamentally multiplayer ELO models are like.

The other thing I’d like to think about more is the effect of being ‘cold’, since some players were sitting around for a while before getting in. They may have been warming up on other games, and there are probably better sources of data for this (like tournaments with lots of byes).

References

Matchplay.events. 2026. “Match Play Ratings.” 2026. https://docs.matchplay.events/data-crunching/match-play-ratings.

Stern Pinball. 2023. “2020 Stern Pro Circuit Championship Game 1.” https://www.youtube.com/watch?v=pIqx6ZF6K9Q&list=PL6U8vZQpW5rxAQdLoSmNI5JOMOTbFj0kA&index=10.